350
Langmuir 1988, 4, 350-354
indicative of a decrease in the oxidation state of the Ti. The Ti02(001) surface is known to be unstable and reconstructs. Using LEED, Firmentg has determined that the first ordered structure obtained by annealing a sputtered surface at 900 K for long periods (hours) is composed of (011) facets with the facet planes in a 2 x 1 reconstruction. Further annealing at 1300 K results in a surface composed of (114)facets. These results suggest that the annealing conditions used here most likely did not result in long-range restructuring of the outermost surface layer, which is sensitive to LEED. However, significant compositional changes do occur in the outermost atomic layer as detected by ISS. The fact that ISS shows different amounts of oxygen at the surface depending upon whether the surface is annealed under vacuum or in oxygen suggests that different types of defects or vacancies may be present on the sputtered surface. One type fills by annealing the surface under vacuum, and another fills only by annealing in 02. This suggestion is consistent with the study of Henrich et aI.,l4which found evidence for the presence of three distinct phases dependent upon the extrinsic surface defect concentration. The first contains isolated surface states, the second is associated with the creation of Ti3+ pairs, and the third consists of an ordered Ti203surface layer. The ESCA spectra shown in Figure 6 indicate that Ti203is formed by annealing a fully oxidized surface in hydrogen. The ESCA spectra in Figure 3 show that any Ti0 species present are oxidized by migration of 0 from the bulk and that Ti203species are oxidized by annealing in 02.
Conclusion ISS, AES, ESCA, and HRAES have been used to characterize a Ti02(001)surface after sputtering, annealing under vacuum, annealing in H2, and annealing in 02. ISS and AES show that the sputtered surface contains the least amount of 0, that annealing under vacuum or in H2 increases the amount of surface 0 to about the same level, and that annealing in O2 further increases the amount of surface 0. ESCA shows that Ti2+,Ti3+,and Ti4+are all present on a sputtered surface and that annealing under vacuum results in oxygen migration to the surface forming a mixture of Ti203and Ti02. Annealing in oxygen converts the Ti in the surface region of a sputtered sample to predominantly Ti02. Corresponding chemical-state changes are observed in the HRAES spectra, but they are more apparent in the dN/dEspectra than in the N ( E ) spectra. After a well-oxidized sample is annealed in lo+ Torr of H2 at 400 OC for 1 h, a relatively small amount of Ti02 is reduced to Ti203.It appears that at least two types of vacancies or defect structures are present on a sputtered surface and that these defects behave differently. One type of defect is filled by oxygen which migrates from the bulk to the surface region during annealing under vacuum. Another type fills by annealing the surface in 02. Acknowledgment. Financial support for this research was received from the NSF through Grant No. CPE8416380 and Travel Grant No. INT 83-19755. Registry No. TiO,, 13463-61-7;H2, 1333-74-0;02,7182-44-1; Ti203,1344-54-3; Ti3+,22541-75-9.
Flow-Induced Creation and Destruction of Supermicelles in Surfactant Solutions E. Ruckenstein,*+P. 0. Brunn,i and J. Holweg* University of Bayreuth, Department of Physical Chemistry, Bayreuth, West Germany, and University of Erlangen, Department of Fluid Mechanics, Erlangen, West Germany Received December 23, 1986. I n Final Form: August 26, 1987 The flow behavior of surfactant solutions through a porous medium is studied experimentally. The results indicate a sudden abnormal increase in resistance (compared to that of the pure solvent) at a certain velocity, which depends upon the nature of the surfactant and its concentration and temperature. The subsequent increase of the velocity leads to a gradual decrease of the resistance down to that of the pure solvent. These experimental results are explained in terms of the flow-induced creation and destruction of supermicelles.
Introduction Dilute solutions of high molecular weight polymers exhibit in laminar flow through porous media a sudden abnormal increase in resistance, compared to that of the pure solvent.'-' Figure 1shows a typical example of an aqueous 50 ppm polyacrylamide solution (Pusher 700 from Dow Chemical, Rheinmunster). As can clearly be seen, a t a certain onset Reynolds number, Re, denoted Re,, the resistance coefficient A, A = fRe, where f is the friction factor, rises sharply. After onset, A remains almost constant, 'University of Bayreuth. On leave of absence from State University of New York at Buffalo, Department of Chemical Engineering, Buffalo, New York, as a Humboldt Prize Winner. Address correspondence to E. Ruckenstein, State University of New York a t Buffalo, Department of Chemical Engineering, Buffalo, New York 14260. University of Erlangen. f
0743-7463/SS/2404-035o$o1.5o/0
decreasing only slightly with increasing Reynolds number. Most likely, this slight decrease is due to polymer degradation. Here the Reynolds number Re and the friction factor f are defined via the expressions
(1)Marshall, R.J.; Metzner, A. B. Ind. Eng. Chem. Fundam. 1967,6, 393. (2) Savins, J. G. Ind. Eng. Chem. 1969, 61, 18. (3)Wissler, E. H.Ind. Eng. Chem. Fundam. 1971, 10, 411. (4) Vossoughi, S.;Seyer, F. A. Can. J. Chem. Eng. 1974, 52, 666. (5) James, D. F.; McLaren, D.R. J. Fluid Mech. 1975, 70,733. (6)Michele, H.Rheol. Acta 1977, 16, 413. (7)Durst, F.;Haas, R.; Interthal, W.; Keck, T. Chem.-Ing.-Tech. 1982, 54, 213.
0 1988 American Chemical Society
Flow Behavior of Surfactant Solutions 10
Langmuir, Vol. 4, No. 2, 1988 351
LL Dow Pusher 700
c = 50 ppm
T = 25 C
0 0 O-
1021-2 10
I
I
1
1
I
10-1
100
10 1
10 2
Re
Figure 1. Porous medium flow behavior of a dilute aqueous polyacrylamide solution.
\p Figure 2. Porous medium flow system (schematically).
where MIL denotes the pressure drop per unit length, u the superficial velocity, d the diameter of the particles, q8 the solvent viscosity, ps the solvent density, and e the porosity. The solid line, given by the empirical relation
nomena in viscometric f l o w ~ , l ~the ~ O drag reduction in turbulent tube ~ ~ o wand, s as , will ~ ~be shown ~ ~ in ~ this ~ ~ ~ article, the sudden increase in resistance in porous media flows. The behavior in viscometric flows has been attributed A = 185 + 1.75Re to the creation of supermicellar aggregative structures (frequently termed shear-induced states, SIS). Evidence has been found to describe the behavior of a Newtonian for this effect was provided by the shear stress growth fluid up to a Reynolds number of about 200. function,18the primary normal stress growth function,l9 In turbulent tube flow, dilute aqueous solutions of high the shear viscosity,2othe primary normal stress difference,lg molecular weight polymers are known to lead to drag rethe flow birefringence,20and the extinction angle.lg It has duction.8 The viscoelastic behavior of the dilute polymer been that the shear-induced state (SIS) is also solutions is responsible for both the pressure drop increase responsible for the drag reduction in turbulent pipe flow. in the flow through the porous medium a t low Reynolds Small-angle neutron scattering experiments seem to pronumbers as well as for the drag reduction in turbulent pipe for this conjecture.21 flow. The large ratio between the extensional s t r e s s e ~ ~ ~ ~vide ~ ~ Jsupport ~ I t is the purpose of the present paper to report experof a viscoelastic and Newtonian fluid explains the pressure imental resulta for the flow of a cationic surfactant solution drop increase in the porous media. It also explains the through a porous medium and to show that these results delay in the renewal of the elements of liquid which the are also in accord with the concept of a flow-induced suturbulent fluctuations bring in contact with the wall. This permicellar structure. delay increases the path length which these fluid elements cover along the wall and hence decreases the average shear Experimental Section stress along the wa1l.l' Thus, the drag reduction in turSample Material. The measurements were carried out on bulent pipe flow and the increased resistance in low dilute aqueous solutions of the cationic surfactant C16TMA-Sal Reynolds numbers porous medium flows have a unitary (hexadecyltrimethylammonium salicylate). Equimolar mixtures explanation. of C16TMA-Br with the electrolyte sodium salicylate (Nasal) were Since high molecular weight polymers are subjected to used. According to the manufacturer (Hoechst AG, Frankfurt), mechanical and thermal degradation, surfactant solutions the molecular weights are 364.46 g/mol (C16TMA-Br)and 160.11 g/mol (Nasal). The concentrations listed (ppm by weight) refer have become interesting.12-16 It is well known that surto equimolar mixtures. Master solutions of 5000 ppm were factant molecules in aqueous solutions self-assemble into prepared at 90 "C. After these solutions were cooled down to room micelles a t concentrations greater than the critical micelle temperature, they were kept for at least 2 days before any dilution concentration (cmc).16J7 The micelles are spherical or took place. The diluted solutions were also kept for extended spheroidal when the surfactant concentration is not too periods of time (up to a couple of days) to ensure that they were large but become rodlike if the concentration is greater in thermodynamic equilibrium, therefore ensuring the reprothan a transition concentration ct.18 For concentrations ducibility of the results. c larger than ct the solutions display interesting viscoelastic Apparatus. Viscosity measurements were carried out in a effects. Examples are the sudden shear-thickening pheTeflon capillary of 0.9-mm inner diameter. The spirally wound capillary of length 18.75 m was immersed in a water bath, the temperature of which could be adjusted between 20 and 50 "C with an accuracy better than AO.1 "C. After leaving the capillary, (8) Viscous Drag Reduction; Wells, C . S., Ed.; Plenum: New York, 1969. the solution entered a 200-mL storage tank (also in the water bath) (9) Denn, M. M.; Marrucci, G. AIChE J. 1971,17,101. from which it was sucked again into the capillary. The pump used (10) Gupta, R. K.; Sridhar, T. Rheol. Acta 1985,24, 148. was a precision dosing pump (RCT-M16O)with two pistons, one (11) Ruckenstein, E. Chem. Eng. Sci. 1971,26,1075; J. Appl. Polym. for sucking the solution into and the other one for pumping the Sci. 1973, 17, 3239. solution through the capillary. The volume flow rate could be (12) White, A. Nature (London) 1967, 214, 585. held constant with an accuracy better than 0.1% . After a stepwise (13) Savins, J. G. Rheol. Acto 1967, 6 , 323. (14) Barnes, H. A.; Eastwood, A. R.; Yates, B. Rheol. Acta 1975, 14,
53. (15) Ohlendorf, D.; Interthal, W.; Hoffmann, H. Proceedings of IX International Congress on Rheology; Mexico, 1984; p 41. (16) Tanford, C. The Hydrophobic Effect;Wiley: New York, 1980. (17) Mukerjee, P. Adu. Colloid Interface Sci. 1967, 1, 241. (18) Hoffmann, H.; Platz, G.; Rehage, H.; Shorr, W.; Ulbricht, W. Ber. Bunsen-Ges. Phys. Chem. 1981,85, 255.
(19) Rehage, H.; Wunderlich, I.; Hoffmann, H. Progr. Colloid Polym. Sci. 1986, 72, 51. (20) Ohlendorf, D.; Interthal, W.; Hoffmann, H. Rheol. Acta 1986,25, 468. (21) Bewersdorff, H. W.; Frings, B.; Lindner, P.; OberthOr, R. C. Rheol. Acta 1986, 25, 642.
Ruckenstein et al.
352 Langmuir, Vol. 4 , No. 2, 1988
A
I m pas1
1OOOppm
2000ppm
IO0
. .. .. ., .. ..-..-._-
r
diam 09"
' A-
A
10'
IO0
101
0
CD I
lo2
@ O
1
lo3 1 [ s-']
Figure 3. Apparent shear viscosity of C16TMA-Sal solutions
against rate of shear at 20 O C . lo'
i l jI[
lo:,
C16TMA-Sal.NaBr
c
= 750ppm
T = 50°C
m 2
10 1
100 Re
101
102
Figure 4. Typical porous medium flow curve of a 750 ppm equimolar mixture of C16TMA-Sal and NaBr in aqueous solution. Re
change of the pumping speed the volume flow rate was held constant. The corresponding presaure difference AP was recorded after reaching a constant value. The differential pressure transducer connected to the ends of the capillary had a range of 103-105Pa. The volume flow rate could be varied between 3 and 170 mL/h in steps of 0.1 mL/h. The porous medium flow measurements were performed in an apparatus schematically shown in Figure 2. The solution is sucked from a 7-L temperature-controlledstorage tank (A) into a cylinder (B) and then pushed with a piston through the porous medium. Two pressure transducers (C), with a range of 5-2000 Pa and 37.5-150000 Pa, respectively, measured the pressure difference over a 1-cm distance in the packed beds. These were 2.5-cmdiameter stainless steel (V4A)pipes (D), 2 cm long. The particles used were glass beads with a narrow size distribution around an average diameter d = 0.392 mm. The volume flow rate was determined by measuring the distance the piston traveled during a given time. The temperature was held constant with a maximum deviation of 10.5 "C. The porosity of the bed was 0.38.
Results A representative apparent flow curve is shown in Figure 3. It is quite apparent from the graph that the solution shows rather sudden shear-thickening behavior, which decreases with decreasing concentration. Figure 4 shows a typical porous medium flow curve. One should notice the sudden increase in A at some onset Reynolds number Re, and the gradual decrease of A down to the resistance of the pure solvent with increasing Reynolds number. It is instructive to replot these data in terms of the directly measured quantities, namely, the volume flow rate V and the pressure drop AP. Figure 5 shows that the sudden .increase in resistance corresponds to a slight increase in V for a rather large increase of AP, while the subsequent decrease corresponds to a large increase in V for only a slight increase of hp. Especially in
Figure 6. Effect of temperature on the porous medium flow curve
of an aqueous 750 ppm CIGTMA-Sal + NaBr solution.
the later s 9 e s of the decrease in A, AP is almost constant, although V changes rapidly. It should be noted that no pertinent data regarding the micellar solutions used here are available, although for free salt aqueous solutions of the surfactant C16TMA-Sal data do exist.20 In static equilibrium conditions, an increase in temperature T a t constant surfactant concentration c leads to a decrease in the average micellar size, while the average sue increases if c is increased at constant T. The addition of salt has qualitatively the same effect as the lowering of T: the average size gets larger and the transition concentration ct for the transition from spheroidal to rodlike micelles gets smaller. Figure 6 shows the effect of T on the porous medium flow curve. With increasing T the onset Reynolds number Re, increases (shifts to the right) and the maximum resistance Amax decreases. Above a certain temperature T, (T,= 55 O C for the solutions considered in Figure 6), no increase in resistance is observed. As explained later, it is likely that the viscoelastic behavior involves rodlike micelles and therefore it sets in for surfactant concentrations greater than ct. For this reason, at temperatures above T,, ct is likely to be greater than the surfactant concentration used. Indeed, at 55 "C, cmc = 100 ppm and ct = 1250 ppm for the aqueous C16TMA-Sal solution without additional electrolyte.20 In the present experiments, the concentration of C16TMASal in the solution with salt was 600 ppm. It is clear that this concentration might still be below the ct of our solution even though it contains electrolyte. Figure 7 shows the effect of surfactant concentration on the porous medium flow curve. Quite generally one can say that below a
Langmuir, Vol. 4, No. 2, 1988 353
Flow Behavior of Surfactant Solutions 10
10 a
a: L
lo3
J 103
21 lo 10 -2
10-1
100
101
io2
Re
Figure 7. Effect of surfactant concentration on the porous medium flow curve of aqueous ClGTMA-Sal+ NaBr solutions at T = 40 O C . A
2 10 x)1-2
C16TMA-Sal+ NaBr C16TMA-Sal
I ,0-1
loo
101
lo2
3Ql
Re
Figure 8. Effect of salt on the porous medium flow curve. The concentration of C16TMA-Sal in either solution was 402 ppm.
certain concentration-which can be equated to c,-no increased resistance is observed. When the concentration is increased above this value, a sudden increase in AP a t a certain onset Reynolds number Re, occurs. For c > et, an increase in c involves a decrease in Re, and an increase in Am,. In addition, the range of Reynolds numbers in which increased resistance is observed gets larger with increasing values of c. The effect of salt is shown in Figure 8. Starting from a salt-free solution (ct zz 250 ppm a t 40 "C),the addition of salt has three effects: (a) Re, decreases, (b) A,, increases, and ( c ) the range of Reynolds numbers in which increased resistance occurs gets larger.
Discussion Concerning the effect of temperature, one may note that the anomalous behavior is greater a t lower temperatures. The curves for the lower temperatures envelop the curves for the higher temperatures. In the region where A decreases, the curves approach each other with increasing Re, although they remain separated from each other until their complete breakdown. As far as the effect of concentration is concerned, one can see that no drag increase is observed below a critical concentration, which is probably in the vicinity of et. Above this concentration an increase in c produces an increase in resistance (A, increases) over an increasing range of Reynolds numbers (Figure 7). Qualitatively the same behavior is observed if, a t constant T and c, salt is added to a salt-free solution (Figure 8). As stated in the Introduction, the shear-thickening behavior in viscometric flows has been associated with the creation of supermicelles. While much experimental evidence has been brought in this respect,1920there is one
additional line of thought which is instructive. It is known that a solution has viscoelastic behavior if the molecules of the solute or the extended aggregates it contains are sufficiently large in length. The spherical micelles are very small and it is therefore unlikely that they could generate such large aggregates. The rodlike micelles can be large, of the order of 40 nm or so. For this reason, the likelihood for the generation, via aggregation, of large units, composed of rodlike micelles, is much higher. In order to use the SIS concept for the present experimental results in porous medium flows, it is helpful to recall the shape of the porous medium flow curve of a dilute polymer solution (Figure 1). There, it was noted that the slight decrease after onset is due to polymer degradation. The drastic decrease encountered with surfactant solutions would thus require complete "degradation". Kinetically such a point of view is not far fetched. In an equilibrium, static situation, the association-dissociation equilibrium determines the average size of the micelles. For a 2000 ppm solution of C16TMA-Sal in H20 a t 30 "C the micelles are rodlike with a length and radius of 33 and 2.2 nm, respectively.22 In a velocity gradient field, the association-dissociation process can be modified in comparison to its static equilibrium limit. In addition, the rate of shear increases the collision frequency between micelles, leading to their aggregation, and also affects the dissociation of these aggregates. If the velocity gradients are small, the equilibrium is displaced toward aggregation. The flow-induced increased collision frequency leads to increasingly larger structures as the rate of shear increases. In this picture, increasingly greater "supermicelles" composed of micelles are formed, for relatively small velocity gradient fields, when the rate of shear increases. However, the aggregated "supermicelles" increasingly dissociate, with increasing rate of shear, if the latter become large enough. At onset, the size of the supermicelles must be sufficiently large for the fluid to have viscoelastic behavior. An increase in the stress after onset is almost entirely used up in pushing these superstructures through the pores to create still larger structures. The volume flow rate in this region (rapid increase in A) will almost remain constant. When the stress is increased still further, the dissociation process will play an increasingly greater role. Gradually the superstructures will be decomposed into micellar units, thus allowing the solution to become increasingly less viscoelastic and to flow with less and less resistance through the pores. The end result is an "inactive" surfactant solution. Complete reproducibility of the results with a solution which had been already used before shows that the surfactant molecules are not destroyed. A few consequences of this model can be immediately verified: If the temperature is raised, the size of the micelles is expected to decrease and this implies (a) larger stresses to generate supermicelles and (b) smaller supermicelles. In the A-Re diagram this means that (a) the onset should occur a t a higher Reynolds number and (b) the increase in A after onset should be less pronounced. Figure 6 shows that this is indeed the case. If the surfactant concentration is lowered, larger stresses are required to form supermicelles of the same size as those a t the higher concentration. This implies that the onset occurs a t a higher Reynolds number, again in agreement with experiment (Figure 7). Adding salt to a salt-free solution increases the size of the rodlike micelles. Su~~
(22) Ohlendorf, D.; Interthal, W.; Hoffmann, H. Proceedings of I X International Congress o n Rheology; Mexico, 1984; p 31.
354
Langmuir 1988,4, 354-359
fluid is therefore losing its viscoelastic and drag reduction permicelles can therefore be formed much easier. The capabilities. Again, the described behavior is observed results shown in Figure 8 are in agreement with this exexperimentally. pectation. Although the SIS model has already been shown to be responsible for drag reduction in turbulent tube f l 0 ~ , ~ ~ 9 ~ 1 ~ ~ Conclusions it is instructive to examine why this drag reduction is It is generally agreed that the SIS model is responsible different a t low and a t high temperatures. At relatively for the behavior of aqueous C16TMA-Sal solutions in both low temperatures (2" = 45 "C), large supermicelles with a viscometric flows and in turbulent tube flow. That the relatively rigid structure are generated, near the wall, at same model can also explain the results in the flow through relatively low velocity gradients, as a result of aggregation. a porous medium has been shown in this study. It is The latticelike organization of the micelles leads in this suggested that the competition between aggregation and case to a pressure drop which is even higher than that dissociation of micelles determines the extent of superencountered in the turbulent flow of the pure solvent. micellization. Both these processes depend on the velocity When the velocity gradient is increased, the supermicelles gradient, temperature, and flow characteristics. At reladecrease in size and become more flexible, and the vistively low temperatures, for the turbulent flow in a pipe, coelasticity which they impart to the fluid leads to drag the aggregation process, which leads to a latticelike orreduction. A further increase of the velocity gradient ganization of the micelles, is dominant, a t relatively low decreases the size of the supermicelles to such an extent velocity gradients. Increasing the rate of shear leads to that the fluid completely loses its viscoelasticity and hence supermicelles with viscoelastic capabilities and further to its drag reduction capabilities. The experiments at low their destruction because the dissociation process becomes temperatures do show the above suggested b e h a v i ~ r . ' ~ ~ ~important. ~ In different conditions, such as flow through At higher temperatures (T = 65 " C ) , supermicelles start a porous medium or higher temperature turbulent pipe to form after the transition to turbulence and only when flow, the aggregation process among micelles is more the velocity gradient becomes sufficiently large. They grow moderate and increases with the rate of shear at low rates in size with increasing velocity gradient, thus imparting of shear. The dissociation process plays, however, an imincreasing viscoelasticity and drag reduction to the fluid. portant part a t high rates of shear. Under the latter When the velocity gradient becomes too large, the dissoconditions the supermicelles disappear. ciation process begins to play an important role and the Registry No. C16TMA-Sal, 61482-44-8. size of the supermicelles becomes increasingly smaller. The
Micelle Formation of Detergent Molecules in Aqueous Media. 2. Role of Free Salicylate Ions on Viscoelastic Properties of Aqueous Cetyltrimethylammonium Bromide-Sodium Salicylate Solutions Toshiyuki Shikata* and Hirotaka Hirata Department of Physical Chemistry, Niigata College of Pharmacy, Kamishin-ei-cho, Niigata 950-21, Japan
Tadao Kotaka Department of Macromolecular Science, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan Received August 10, 1987 The factor governing the stability of micelles and hence controlling the rheological behavior of aqueous solutions of cetyltrimethylammoniumbromide (CTAB) containing sodium salicylate (Nasal) was investigated. The solutions containing fully entangling threadlike micelles of CTAB-Nasal complexes may be modeled by a Maxwell model with a single relaxation time. Concentrations CS*of free salicylate ions in the systems were estimated by carrying out 'H NMR measurement on deuterium oxide solutions with varying CTAB (C,) and NaSal (Cs)concentrations. The results of NMR measurement suggested that the threadlike micelles existed in the form of a 1:l complex between CTAB and NaSal. Thus, the relation Cs* = Cs - CD was obtained in the range Ds> CD. On the other hand, we confirmed that the relaxation time 7, is influenced only by Cs* independently of CD,and thus the factor controlling 7, is Cs*. Furthermore, consideration on the basis of a quasi-network model led to an idea that the free salicylate ions are behaving as a catalyst for a disentangling reaction.
Introduction Certain cationic detergents with ammonium or pyridinium head groups often form rodlike or threadlike micelles in aqueous solution and exhibit remarkable viscoelasticity when a salt or an acid with aromatic rings is added.'-4 (1) Gravsholt, S. J. Colloid Interface Sci. 1976, 57, 575. (2) Rehage, H.; Hoffmann, H. Rheol. Acta 1982, 21, 561.
In our previous paper," we reported unique viscoelastic properties of aqueous cetyltrimethylammonium bromide (CTAB) solutions with sodium salicylate (Nasal) as an added salt. The features of their unique viscoelasticity (3) Bunton, C. A. Reaction Kinetics in Micelles; Plenum: New York, 1973. (4) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987,3,1081-1086.
0 1988 American Chemical Society 0143-1463/SS/2404-035~~01.50/0
