Relaxation times were measured for the surface tension
relaxation of spread and soluble surface films at the water/air
interface. Measurements were done in a modified Langmuir trough
with a Wilhelmy Pt sensor attached to an electrobalance using
surface sweeping rates between 6.4 and 57.6 Hz-1•
The relaxation times were determined in the stationary state
from the phase angle between the perturbation function (surface
sweeping) and the response function (dynamic surface tension). The
calculated values for the relaxation times of oleic acid films were
between 0.25 and 1.25 s, and were inversely proportional to both
the rate of sweeping and to the concentration of molecules in the
surface film. For the soluble surfactant, sodium dodecylsulfate, the
relaxation times were reaching a minimum value of 0.2 s, at a bulk
concentration between 9.1 and 18.3 ~t mol dm-3

Dj. Dragčević

V. Pravdić

English

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CROATICA CHEMICA ACTA CCA-1183 CCACAA 53 (1) 1-7 (1980) YU ISSN 0011-1643 UDC 541.18 Original Scientific Paper Steady-State Relaxation Times for Surfactant Films at the Water/ Air Interface Dj. Dragcevic and V. Pravdic Laboratory of Electrochemistry and Surface Phenomena, Center for Marine Research, »Ruder Boskovic« Institute, Zagreb, Croatia, Yugoslavia Received November 5, 1979 Relaxation times were measured for the surface tension relaxation of spread and soluble surface films at the water /air interface. Measurements were done in a modified Langmuir trough with a Wilhelmy Pt sensor attached to an electrobalance using surface sweeping rates between 6.4 and 57.6 Hz-1• The relaxation times were determined in the stationary state from the phase angle between the perturbation function (surface sweeping) and the response function (dynamic surface tension). The calculated values for the relaxation times of oleic acid films were between 0.25 and 1.25 s, and were inversely proportional to both the rate of sweeping and to the concentration of molecules in the surface film. For the soluble surfactant, sodium dodecylsulfate, the relaxation times were reaching a minimum value of 0.2 s, at a bulk concentration between 9.1 and 18.3 ~tmol dm-3• INTRODUCTION There are two major fields for which the rate of formation of surface films of soluble and insoluble surfactants at the water/air interface is of interest. One, the technology and science of mineral, ionic and bacterial flotation1. Two, the science of sea/atmosphere exchange processes2• It is the rising bubble which scavenges the aqueous bulk from both film formtng surfactant material and of the dissolved/dispersed ionic or particulate material. The efficiency of collection is dependent on the rate of formation of the surface film sur-rounding the gas(air) bubble3• The properties of the film at the bubble surface would determine its penetrability for gases and/or ionic and particulate material. Compressed films have been shown to retard significantly gas exchange and lower the rate of evaporation of water4• Thus, bulk surface active material of appropriate composition might produce solid films and influence the overall exchange rate of carbon dioxide and oxygen between the natural water and the atniosphere5•6. At least part of the problem whether or not the sea acts as an effective sink for man-made C02 would be answered by knowing precisely whether the rate of exchange is influenced by the presence of surface active materiaF. The present paper describes laboratory experiments designed to measure the relaxation times of surface films in the steady-state, non-equilibrium perturbation mode. 2 DJ. DRAGCEVIC AND V. PRAVDIC EXPERIMENTAL Techniques The surface tension relaxation was measured by a conventional, commercially available technique8•9•10 comprising a Wilhelmy plate surface tension sensor attached to an electrobalance (Dynamic Surface Tension Accessory, Cahn Instruments, Ventron, Palo 4~to, California) shown schematically in Figure 1. The surface tension is 0 0 w u "' 0 LL Figure 1. The schematic of the surface tension apparatus with x-y and x1, x,-time recorders. For explanation see text. measured by the pl;;itinum plate. sensor (1) in a PTFE lined Langmuir trough (5) . The surface is swept periodically by two reciprocating PTFE surface sweepers (2) actuated by a motor pulley (4) at controllable rates. The surface tension is measured as the force ex erted on the Pt sensor by an electric microbalance (3). The output from the microbalance and of the sweep mechanisms is fed to either an x -y recorder (6) or an x1, xz-time recorder (7) the approximate recordings being shown. One analyses either the hysteresis curve in the force - area coordinates, or measures the phase angle between the· 'sam e, time dependent fu11ctions. The rate of sweeping in the present configuration has been varied in · 5 steps from 6.4 to 57.6 s per · cycle, from an area between the sweepers of 25.4 and 37.0 cm~ (1 : 1 :5 surface area ratio), in a trough of 68 cm~ of total exposed surface area and of a surface to volume ratio of 0.7 cm-'. Chemicals and the Techniques of Film Formation · Pure oleic (cis-octadecen (9, 10) oic) acid was dissolved in ethanol to a 3 X 10-4 mol drri-3 solution. Appropriate aliquots have been taken by micropipettes and spread onto the surface of water in the trough. Sodium, dodecylsulfate (SDS) (Merck, Darmstadt, purum) was dissolved in water to prepare a stock solution of 9.14 X 10-4 mol dm-3• Final concentrations were prepared by dissolution in water in a volumetric flask and this solution was poured into the trough of the surface tension apparatus. The low concentration of SDS in the final experimental solution and the sole aii;n of this work to measure the overall relaxation times proved satis-factory; without requiring additional purification of the t:hemicals used. All experiments were done at 20.0 ± 0.1 °c. RELAXATION T IMES OF SURF ACT ANT FILMS 3 RESULTS The results of measurement of the relaxation of surface tension for an oleic acid film are shown in Figure 2. In the left part of the figure there are two phase shifted sinusoidal curves. The first one, indicated by the »area« sign is the excitation function : the movement of surface wipers. The second SURFACE TENSION,cf/mNm 1 55 60 65 'E z E -... ~ - 60 z Q !/) z w I-~ 55 w Lt :E a: I- ::i !/) 50 1.5 1.5 RELATIVE AREA RELATIVE AREA Figure 2. DynaJ\liC surface tension on two recorders for oleic acid. The left hand side shows 2 sinusoidal functions, surface area (2 »area«) and surface tension (y), with the resulting phase shift ll.q> recorded on a x., x 2-time recorder. The right hand side shows the surface tension -area hysteresis curve for the same experiment, recordecl on a x-y recorder. one, marked by y, is the response of the surface tens.ion sensor. The phase angle between the two, indicated by analogy with electrical phase angle phe-nomena11•12, relates to the relaxation time by: , = _1_ ( tan t:i cp ) e 2 n: f where T is the relaxation time, Cfl the phase angle, and w = 2 n f is the angular excitation frequency (sweep rate). The right hand side of the same figure shows the surface tension-area curve. One film was chosen out of many studied, which shows a positive hysteresis at compression (high surface pressure) and negative hysteresis at expansion (low surface pressure). Calculated phase angles at the point of maximum compression of the surface are plotted against the reciprocal frequency of the sweep rate in Figure 3. Similar phenomena are observed also for soluble surfactants. Figure 4 shows the results of measurements of the phase angle for 5 concentrations of 4 I/) c: 0 0 DJ. DRAGCEVIC AND V . PRAVDIC Oieic acid on distilled water O 0.41 nm 2/molecule 0.26 {expanded 0.21 state) 0.14 ";j ~·0 . 4f--~~-lll!t"<-t~~~~---'"t" ..... ..,=-~~-t-~~~~~t-~~~~~t-~~~~-t~~--! CL> Ol c: 0 ~ of--~~~-i'----~~~~~;;:--=::::"'="9'~~~-e--4--;;;;;;;::::::-~-t-~~~~-l-~--1 0 .J::. a_ 10 20 30 40 so 60 1/f, Hz-1 Figure 3. Phase angle in radians vs. the reciprocal frequency, Hz-1, for 4 concentrations of oleic acid films spread on water. Concentrations are calculated from the quantity of. added oleic acid to surface of water, in the point of maximum expansion. VI c: 0 :0 0 ~ CL> I/) 0 .J::. a_ +1.2 +Q.81--~~~~-+~""""~~-"~~~~~~~+-~~~~~+-~ 10 20 30 1/f, Hz-1 40 SOS in distilled water 0 0.17 0 2.4 6. 9.1 • 18.3 • 32.3 so )J mol · dm-3 60 Figure 4. Phase angle in radians vs. the reciprocal frequency, Hz-1, ior 5 concentrations of sodium dodecylsulfate. Average bulk concentrations are indicated. RELAXATION TIMES O F SURFACTANT FILMS 5 SDS in water. The general phenomenology is the same as for insoluble films. The phase angle is reverted from positive to negative with increasing con-centration and with decreasing rate of perturbation. However, the calculation of the relaxation times, obtained from the phase angle at maximum expansion, show different patterns. Table I sum-marizes the calculations done for the insoluble surface films of oleic acid spread on distilled water. The relaxation times, in seconds, are seen to decrease with the increase in the perturbation rate (Hz-1 = seconds per sweep cycle). Also, the increase in the surface coverage (decrease in the area per molecule) tends to produce shorter relaxation times. Table II summarizes the corresponding data for the soluble SDS. Here the tendency is shown towards constant values of the relaxation times; if there is a change observed, then the values tend to increase with the increasing sweep rate. The concentration dependence shows little general influence, indi-cating possibly a minimum value of 0.20 s for concentrations of 9.1 and 18.3 µmol dm-3. TABLE I Relaxation Times, s, for Oleic Acid Spread on Distilled Water Sweep Area per molecule*/nm" rate Hz-1 0.41 0.26 0.21 0.14 0.10 57.6 1.00 0.90 0.90 0.81 0.67 37.8 0.68 0.68 0.68 0.68 0.45 19.2 0.65 0.65 0.47 0.39 0.38 9.5 0.65 0.56 0.33 0.28 0.28 6.4 1.24 0.31 0.25 0.25 0.25 • calculated from spreading data at max. ex pansion TABLE II Relaxation Times, s, for Surface Films Formed by Dissolving Sodium Dodecylsulphate (SDS) in Distilled Water Sweep Bulk concentrationhtmol dm-3 rate Hz-1 0.17 2.4 9.1 18.3 32.3 57.6 0.67 0.22 0.22 0.22 0.22 37.8 1.04 0.45 0.22 0.22 0.22 19.2 LOO 0.55 0.22 0.22 0.30 9.5 1.16 0.56 0.23 0.20 0.33 6.4 2.09 1.31 0.20 0.20 0.34 6 DJ. DRAGCEVIC AND V. PRAVDIC DISCUSSION This paper introduces the measurements and calculations of the relaxation times for relaxation phenomena in surface f.ilms, both soluble and insoluble. The simplicity of the technique of the dynamic surface tension measurements in a Langmuir trough with two reciprocating surface sweepers is subject also to some scrutiny. The Wilhelmy plate surface tension measuremen,ts are precise only if the wetting angle of the sensor (platinum in the present case) in the film covered surface is constant. This has been difficult to prove, however, two experiments were done in this sense. The film was repeatedly swept until steady state conditions were achieved. In the first experiment the position of the surface tension sensor was changed by rotating it in the plane for 90°. Thus only the molecular phenomena related to wetting are brought to bear: the dir2ct compression of the surface film by wipers was eliminated, considering the thickness of the sensor (0.01 cm) vs. its perimeter (2 X 1 cm). No differences were observed. In the second experiment one of the wiper blades was removed: thus the compression ratJi.o was halved and the surface film was compressed assymetrically with respect to the sensor. Once again, the effects were the same within the experimental accuracy. · It is thus quite probable that the data relate to true molecular level phenomena in the surface films. From the dependence of the relaxation times on the perturbation rate it is clear that what one observes is the compound process of surface spreading and of diffusion from the bulk to the surface. Essentially the same oonclusi:on has been reached by Veer and Van den Tempel1°, who have also pr-oposed an equation to resolve for the two contributions, surface spreading and bulk diffusion. However, this proved virtually imposible unless one enters with additional assumptions into the calculations. Lucassen and Van den Tempel13 have worked out a technique of excitation of the film covered surface by longitudinal waves of a frequency in the range of 1 Hz. Their results indicate the possibility of resolving the dilatational modulus (a component of the surface spreading process) from true relaxation. The latter has been shown to be absent if films were produced of decanoic acid at concentrations of 4.5 X 10-s mol dm-3 or 1-ower. Thus, relaxation phenomena were found in the time scale of about 1 s. At that point the cited papers1o,i3 ceased to supply further information on the experimentally observed dynamic behavior of surface films at aqu.eous interfaces. It would be impossible by the present techniques to resolve accurately the contributions of each of these processes to the final relaxation times, since the observed phenomena are related to a particular steady state, and not equi-librium oonditions. For oleic acid films the surface spreading must be the faster process, since the relaxation times decrease with increasing perturbation rate. The molecules in the collapsed monolayer are progressively prevented to appear and rearrange at the surface by the fast rate of sweeping. For soluble films, it seems, that both of the mentioned transport processes are of the same order of magnitude, and consequently, no much influence is seen whether the control is by surface spreading at fast perturbation, or by diffusion from the bulk, a process of importance at low perturbation rates. Acknowledgment. - This work has benefitted from a grant by the US Environ-mental Protection Agency (PL 480) through which instrument purchases were made possible. The support of the Authority for scientific research of the SR of Croatia in the continuation of this work is duly acknowledged. RELAXATION TIMES OF SURFACTANT FILMS 7 REFERENCES 1. R. Lem 1 i ch, Adsorptive bubble separation techniques, Academic Press, New York, 1972, 331 p. 2. E. B. Kraus, Atmosphere-ocean interaction, Clarendon, 1972, 275 p. 3. D. C B 1 an ch a rd, Advances in Chem. Series 145 (1975) 360. 4. J . T. D a v i e s and E. K . R i d e a 1, Interfacial phenomena, 2nd ed. Academic, 1963, 480 p. 5. P . S. Liss and F. N. Martine 11 i, Thalassia Jugoslav . 14 (1978) 215. 6. P. S. Liss, Deep-Sea Research 20 (1973) 221. 7. M. B 1 an k and F . J. W. Roughton, Trans. Faraday Soc. 56 (1960) 1832. 8. R. M. Menden ha 11 and A . L. Menden ha 11, Jr., Rev. Sci . Instrum. 34 (1963) 1350. 9. R. Bienkowski and M. S k o 1 nick, J . Colloid Interface Sci. 39 (1972) 323. 10. F. A. Ve er and M. Van den Temp e 1, J . Colloid Interface Sci. 42 (1973) 418. 11. D. N. Hague, Fast Reactions, Wiley-Interscience, New York, 1971, pp. 29-47. 12. V. De 1 Toro, Principles of Electrical Engineering, Prentice-Hall, Englewood Cliffs, N. J. 1965, Ch. 6, pp. 184 ff. 13. J. Luc assen and M. Van den Tempel, J . Colloi d Interface Sci. 41 (1972) 491. SAZETAK Relaksacijska vremena za stacionarne povrsinske filmove na granici faza voda/zrak Dj. Dragcevic i V. Pravdic Vremena relaksacije topljivih i netopljivih povrsinskih filmova na granici faza voda/zrak odredivana su tehnikom dinamicke povrsinske napetosti. Mjerenja su izvrsena u modificiranoj Langmuirovoj kadi s Wilhelmyjevom ploCicom kao sen-zorom povrsinske napetosti prikljucenom na elektricku vagu. Stacionarn0 stanje po-stignuto je kontinuiranom kompresijom i ekspanzijom povrsinskog filma s pomocu dva reciprocirajuca teflonska brisaca brzinom od 6,4 do 57,6 Hz-1 (sekundi po ciklusu), u kadi povrsine 68 cm2 i odnosa povrsine prema volumenu od 0,7 cm-1. Izracunavanje relaksacijskih vremena izvrseno je ocitavanjem faznog kuta izmedu funkcije pobude povrsine kompresijom i ekspanzijom, i odgovora sistema dinamickom napetosti povrsine. Istrazivani su netopljivi filmovi oleinske kiseline u koncentracijama od 0,41 do 0,10 nm2/molekuli, kao i topljivi filmovi natrijeva dodecilsulfata u granicama volurr.-nih koncentracija od 0,17 do 32,3 µmol dm-3• Izracunane vrijednosti vremena relaksacije za oleinsku su kiselinu izmedu 0,25 s i 1,25 s; relaksacijska vremena opadaju kako s koncentracijom molekula u filmu, tako i s brzinom perturbacije. Za natrijev dodecilsulfat karakteristicna vremena relak-sacije teze prema minimalnoj vrijednosti od 0,2 s koja se postifo za volumne kon·· centracije izmedu 9,1 i 18,3 ~tmol dm-3• LABORATORIJ ZA ELEKTROKEMIJU I POVRSINSKU KEMIJU CENTAR ZA ISTRAZIVANJE MORA Prispjelo 5. studenog 1979. INSTITUT »RUDER BOSKOVIC«, ZAGREB 

Steady-State Relaxation Times for Surfactant Films at the Water/ Air Interface

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