Langmuir 1995,11, 3395-3400
3395
Equilibrium and Kinetic Studies Associated with the Binding of Sodium Dodecyl Sulfate to the Polymers Poly(propylene oxide) and Ethyl(hydroxyethy1)cellulose D. M. Bloor,* W. M. 2.Wan-Yunus, W. A. Wan-Badhi, Y.Li, J. F. Holzwarth,? and E. Wyn-Jones Division of Chemical Sciences, University of Salford, Salford M5 4WT, U.K. Received February 23, 1 9 9 5 . In Final Form: June 12, 1995@ Equilibrium measurements associated with the binding of sodium dodecyl sulfate (SDS)with the polymers poly(propy1eneoxide)(PPO)and ethyl(hydroxyethy1)cellulose (EHEC)have been carried out using emf and isothermal titration calorimetry. Gel filtration was also used to study the SDSPPO system. In the SDS/ PPO system, "free" micelles occur in solution well before the polymer becomes fully saturated with bound surfactant aggregates. A quick calculation shows that the SDSPPO complex consists of one micellar-type aggregate bound to two to three polymer molecules. In the SDS/EHEC system, a gel-like polymer network is formed, which with further addition of SDS breaks down to a "string of beads" like the complex involving one polymer molecule and several micellar-type aggregates. In this system, free micelles occur in solution only after the polymer becomes fully saturated with bound aggregates. We have also carried out ultrasonic relaxation measurements on both systems in an attempt to study the kinetics of the monomer surfactant bound aggregated surfactant exchange process.
-
Introduction As a result of their uses in manipulating the properties of various colloidal systems, mixtures of surfactants and polymers in aqueous solution have received much attention.'+ They have been the subject of several fundamental investigations covering many W e r e n t equilibrium, structural, and dynamic aspects of their behavior. Although the majority of the work has been the subject of recent review articles, there is currently considerable interest in understanding the behavior of hydrophobic or hydrophobically modified polymers with surfactant^.^-^ In this paper, we report our investigations on the interaction between sodium dodecyl sulfate (SDS)with the polymers poly(propy1ene oxide) (PPO) and ethyl(hydroxyethy1)cellulose (EHEC),both of which can be regarded as hydrophobic polymers in the context of surfactant binding. We report a systematic study involving electrochemical, gel filtration, viscosity, isothermal titration calorimetry, and ultrasonic relaxation measurements. As far as we are aware, there are three other studies involving these systems that have been rep~rted.~-ll
Experimental Section (i) Materials. The SDS used in this work was synthesized and purified using the method described by Davidson.12 PPO was a commercial product (Aldrich) of molecular weight 1000 and used without further purification. EHEC was obtained from ~~
~~
Present address: Fritz-Haber Institut der Max Plank Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany. Abstract published in Advance ACS Abstracts, September 1, 1995. (1)Goddard,E.D. Colloid Surf. 1986,19,255andreferencesquoted therein. (2)Goddard, E. D. J . Soc. Cosmetic Chem. 1990,41,23. (3)Robb, I. P. Anionic Surfact.,Surfact.Sci. Ser. 1981,ll(Chapter +
Berol Nobel (Sweden)under the trade descriptionCST-103. The molecularweight ofthis polymerwas 120 000, and it was purified as described in the literature.1°-13 The Sephadex gels were purchased from Pharmacia LKB and used without further purification. All other reagents were of Analar grade. (ii) Electrochemical Measurements. The constructionof the SDS-membrane-selective electrode has been described elsewhere, and the electrode has been used successfullyin other related studies.l4-ls The poly(viny1 chloride) used to prepare the membranewas synthesized as described by Davidson.12The emf of the SDS electrode was measured relative to a commerical bromide(Corningsolid-stateISE 30-35-00)and also a commerical sodium electrode (Corning 476211). All solutions contained sodium bromide [lO-4 mol dm-3] and were measured at 25 "C. The binding measurements and the method to determine the degree of micellar dissociation were carried out as described previously.1s (iii) Gel Filtration. The purpose of the gel filtration experiment is to identify the SDS concentrationcorresponding to the occurrence of different ionic species in solution. On the basis of previous reports,l6Vz1it is possible to identify the SDS concentration corresponding to the onset of binding and also that corresponding to the formation of %ee" micelles. The experimental setup used was based on the method described by Sasaki et ~ 2 . 2 1 and was used successfully to investigate the interaction between SDS and poly(N-vinylpyrrolidone).ls The apparatus employed a 500-cm3solvent reservoir and two glass columns, 20 cm x 1.7 cm and 20 cm x 1 cm. A conductivity cell was used as the detector which was coupled to a digital conductivitymeter (JENWAY4020) and a chart recorder. The gels used were various classes of Sephadex (G75 and G25) recommended for gel filtration. (iv) Isothermal Titration Calorimetry (ITC). The calorimeter used in this work was the Microcal ITC instrument. In
@
4), 109. (4) Dualeh, A. J.; Steiner, C.
A.Macromolecules 1990,23,251. (5)Swadasan, K.;Somasundaran,P. Colloids Surf. 1880,49,229. (6)Dualeh, A. J.; Steiner, C. D. Macromolecules 1991,24,112. (7)Biggs, S.;Selb, J.; Candan, F. Langmuir 1992,8,838. (8)Brackman, J. C.; Engberts,J. B. F. N. Chem. SOC.Rev. 1998,22, 85. (9) Carlsson,A.; Karlstrom, G.; Lundman,. B.; Stenberg, 0. Colloid Polymer Sci. 1988,266,1031. (10)Holmberg, C.; Nilsson, S.; Singh, S.K.; Sundelof, L.-0. J . Phys. Chem. 1992,96,871. (11)Witte, F.M.;Engberts, J. B. F. N.Colloids Su$. 1989,36,417.
(12)Davidson, C. J. Ph.D. Thesis, University of Aberdeen, 1983. (13) Mantley, R.St. J. Ark. Chem. 1966,9,519. (14)Painter, D. M.; Bloor, D. M.; Takisawa, N.; Hall, D. G.; WynJones, E. J . Chem. Soc., Faraday Trans. 1 l988,84,2087. (15)Takisawa,N.;Brown, P.; Bloor, D. M.; Hall, D. G.; Wyn-Jones, E.J . Chem. Soc., Famday Trans. 1989,85,2099. (16)Wan-Badhi,W. A,; Wan Yunis,W. M. Z.;Bloor, D. M.; Hall, D. G.; Wyn-Jones, E. J. Chem. Soc., Faraday Trans. 1998,89,2737. (17)Eggers, F.Acoustica 1968,19,3223. (18)Eggers,F.;Funk,J. L.; Richmann,K. H.Rev.Sci. Instrum. 1976, 42. --, 361.
(19)Palepu, R.; Hall, D. G.; Wyn-Jones,E. J. Chem. S O ~ Fama'uy ., Trans. 1990,86,1536. (20)Bloor, D.M.;Holzwarth, J. F.; Wyn-Jones,E. Langmuir 1996, 11, 2312. (21)Sasaki, T.; Kushima, K.; Matsuda, K.; Susuki, H. Bull. Chem. Soc. Jpn. 1980,63,1864.
0743-746319512411-3395$09.00/0 0 1995 American Chemical Society
Bloor et al.
3396 Langmuir, Vol. 11, No. 9, 1995 0 -20
a
1
I
4
'"I 1.0
0.5
-I4&
""'O:I ' I ' IO ' IO0 Total SDS Concentration x 103 [mol dm-31
'
""""
""""
' " ' Y
""""
Figure 1. Plot of the emf of the SDS electrode (referenceBr-) as a function of total SDS concentration for the SDSPPO system: (A) 0% PPO; (0)0.5%PPO. I20 100
->
0
60
d
B
40
+
20
B
0
80
0 -20 -40
-68.k1
'
' '""" 0.1
'
' '
"'"'1
'
' '
IO
"""
'
' '
100
"""
Total SDS concentration x 103 [mol dm-31
Figure 2. Plot of the emf of the SDS electrode (referenceBr-) as a function of total SDS concentration for the SDSEHEC system: (A) 0% EHEC; (0)0.5%EHEC.
the ITC experiment, one measures directly the energetics (enthalpy changes) associated with the processes occurring at constant temperature. Experimentswere carried out by titrating a micellar SDS solutioninto a sample solutioncontainingaknown amount of polymer. An injection schedule (number of injections, volume of injection, and time between injections)is set up using interactive software, and this schedule is automatically carried out with all data stored to disk. After each injection, the heat released or absorbed as a result of various processes occurring in the solution is monitored by the calorimeter, with the time between injectionsbeing adjusted such that the system is allowed to return to equilibrium. In the present work, we present the results of two ITC experiments that we have carried in relation to the present work. These involve the titration of concentrated micellar SDS containing 0.5%w/v of the two polymers into an aqueous solution containing 0.5% polymer at 25 "C. (v)Viscosity and Density. The viscositymeasurements were performed using a conventional Ubbelohde capillaryviscometer, and solution densitieswere measured using a commercialdensity meter (DMA55, A. Paar, Austria). All measurementswere made at 25 "C. (vi) Ultrasonic Relaxation. Ultrasonic absorption and velocity measurements were made using the Eggers resonance method17J8at 25 "C which spans the frequency range 0.4-17 MHz. All solutions were made up in sodium bromide mol dm-31.
Results (i)Emf Data of the Surfactant Electrode Relative to a Bromide Ion Electrode. The emf measurements as a function of surfactant concentration are shown in Figures 1 and 2 both in the absence and presence of 0.5% w/v PPO and 0.5%w/v EHEC, respectively. (Although we recognize that the characteristics of the interaction between surfactant and polymer depend on the polymer concentration, the polymer concentrations used in this work (0.5% w/v) are optimum values which enable the majority of the different experiments to be conducted with confidence, resulting in real measurable effects.) The
0 . 0 ~ " ' ~ " " ~ " ~ ' ~ ' ~ ' ' ~ ' ~ ' ' ' ~ 0 50 100 150 200 250
Total SDS Concentration x 103 [mol dm-31
Figure 3. Plot of the SDS monomer concentration (ml) as a function of total SDS concentration for the SDSPPO [0.5%w/vl system.
measurements for the pure surfactant show a break a t the cmc (8.3 x mol dm-3) after which the monomer surfactant in the micellar range decreases as the total surfactant concentration is increased. In the presence of both polymers, the emf data for surfactant and polymer/surfactant coincide at very low SDS concentrations. At a critical concentration, the emf data for the polymer/surfactant solution deviate from that of the pure surfactant. This corresponds to the onset of SDS binding to the polymers, and as binding proceeds, the two emf curves diverge until another critical concentration is reached when the emf s of the surfactant solution with and without polymer are the same. Historically, these limiting concentrations are referred to as TIand Tz, respectively; TIcorresponds to the onset of binding, and T2 is assumed to correspond to the surfactant concentration at which the polymer becomes fully saturated with bound surfactant (for PPO, TI= low3mol dm-3 and TZ= lo-' mol dm-3). It is now generally accepted that the bound surfactant exists in the form of micellar-type aggregates. In some cases, e.g., SDS/poly(N-vinylpyrrolidone) (PVP),TZalso corresponds to the SDS concentration at which free micelles occur. The exact sigruficance of Tz,however, can be resolved by the ITC and gel filtration experiments. When conducting the SDSAZHEC emf experiments, it was found that the system took a t least 15 min to reach equilibrium following each addition of SDS to the titration. Because of this, the output from both emf cells was connected to a chart recorder, and only when the emf's were constant to within f 0 . 5 mV for 5-10 min were readings taken. (ii) Degree of Micellar Counterion Dissociation, a. The emf of the surfactant electrode was measured relative to a commercial bromide and also a sodium electrode. From the experimental data with the bromide electrode, it is possible to evaluate the monomer surfactant concentration (ml) in the binding region, and plots of m1 against the total surfactant concentration are shown in Figures 3 and 4. From the data using a sodium electrode, e.g., Figure 5, it is possible to evaluate the monomer sodium counterion concentration (mz) and also the mean activity coefficient (y+). The detailed procedures used to carry out this exercise have been described elsewhere.l6,I9 At any surfactant concentration where aggregation occurs, the following mass balance equation holds:
m2 = m,
+ C,+ a(C, - m,)
(1)
Cs is the concentration of added salt mol dm-3 NaBr), and a is the degree of micellar counterion dissociation a t a total surfactant concentration, CI.The a values evaluated are plotted as a function of total SDS concentration and are shown in Figure 6.
Binding of SDS to PPO and EHEC
Langmuir, Vol. 11, No. 9, 1995 3397 Sephadex G75 Column SDS
monomer
PPO-SDS complex
I I
I
Sephadex G75 + G25 Columns SDS
free micelles
PPO-SDS
SDS
complex
monomer
0 0
0 0 0 0
2.0
1
0
10
20
30
50
40
....
60
I d . . I ...I
70
80
90
I
Total SDS Concentration x 103 [mol dm-31
Figure 4. Plot of the SDS monomer concentration (ml)as a function of total SDS concentration for the SDSEHEC [0.5% w/v] system.
->
250
L
:
s 200: L
E
0 4 4
*
t I50 -
. 58.h
100
%
:
. . -*-...- 0.1 1 10 **...' Total SDS Concentration x 103 [mol dm-31 a
**.*..*
a
**...**
*
IO0
Figure 5. Plot of the emf of the SDS electrode (referenceNa+) as a function of total SDS concentration for the SDSEHEC system: (A) 0%EHEC; (0)0.5%EHEC.
c
Total SDS Concentration x IO3 [mol dm-3)
Figure6. Plot of the degree of micellar counteriondissociation (a) as a functionoftotal SDS concentration: (+)SDSPPO [0.5% w/vl system; (0)SDSEHEC [0.5% w/v] system.
Characteristics of the Binding in the SDWPO System (i) Emf Data. As we have mentioned previously, the emf data show the onset of binding to occur at 2'1 mol d~n-~). It is also clear from the emfdata using a sodium electrode that counterionbinding also starts at 2'1, showing that the bound surfactant exists in the form of micellartype aggregates. A close inspection of Figure 1also reveals a change of slope in the emf data occumng around 11 x mol dm-3, indicating a change in the solution properties of the system. The binding proceeds until a SDS concentration denoted by 2' (=lod1 mol dm-3) is reached. "his type of behavior is typical of anionic surfactantheutral polymer systems.la-l6 At this concentration, the polymer becomes fully saturated with bound surfactant aggregates, and at SDS concentrations exceeding 2'2, the polymer is no longer involved in any process involving concentration changes in the surfactant monomer. In some systems, 2'2 also signals the existence of "free" micelles in solution.
SDS Concentration [mMl lime
+
Figure 7. Conductance m e s for the gel filtration experiment using the SDS/PPO [0.5% w/v] system. Each curve is shown as a function of time at the total SDS concentration [mMl indicated under the curve.
(ii) Gel Filtration. In the determination of 2'1, a 20cm x 1.7-cm column packedwith Sephadex G75 was used. The sample volume was 10 cm3 at a flow rate of 1.25 mL min-l. Chromatograms were recorded at SDS concentrations of 1,2,3,4,5, and 10 x mol dm-3, respectively, and from these data, 2'1 is estimated from the concentration at which two peaks start occurring in the chromatogram. These two peaks belong to ionic species which are respectively the monomer surfactant and polymedsurfactant complex. From the data shown in Figure 7,Tl is estimated to occur in the SDS concentration range (2-3) x lom3mol dm-3. When using the same setup at higher concentrations ( > EmM) of SDS, only two peaks could be resolved. However, ifan additional column(20 cm x 1cm)containing fully swollen Sephadex G25 is used in the series with the first column, then it is possible at higher SDS concentrations (-60 x low3mol dmV3)to partially resolve three peaks. From these chromatograms (Figure71, we estimate that the three peaks start occurring in the chromatogram mol dm-3, in the SDS concentration range (20-30) x these peaks belonging, respectively, to the occurrence of free SDS micelles, the SDSFPO complex, and free monomer SDS in solution. At best, these limiting concentrations can only be estimated with the gel filtration experiment in its present form. We carried out several experiments using the apparatus but were unable to obtain the almost perfect stepwise results reported by Sasaki et aL21for the SDS/ poly(ethy1ene oxide) system-the present results representing the best possible data that we were able to obtain which showed reasonable resolution of the peaks by varying the length of the column, Sephadex type, and the rate of flow. (iii)Isothermal Titration Calorimetry. An inspection of the enthalpy profile (mi), Figure 8, as a h c t i o n of total SDSconcentration taken from the ITC experiment shows behavior similar to what we have reported previously20 for SDSPVP and other systems, i.e., a very pronounced maximum (in the vicinity of 21' 0.4 x mol dm-3) followed by a minimum, with Mi eventually approaching a value correspondingto that found for pure SDS micelles (-350 cal mol-'). The minimum in the ITC enthalpy profile signals the existence of free micelles, which in the present work were found to occur at 25 x lop3mol dm-3 SDS. At first inspection, the above data for 2'1 found for the SDSPPO system using different methods of measurement appear to be very inconsistent. For example, 2'1 from the emf and gel filtration data is estimated to be at 1 and (2-3) x mol dm-3
-
Bloor et al.
3398 Langmuir, Vol. 11, No. 9, 1995
:
O.b.1
1
10
IO0
I o1
0
Total SDS Concentration x 103 [mol dm-31
Figure 8. Plot of the enthalpy change per injection (Mi)as a function of total SDS concentration for the SDSPPO system in the ITC experiment.
respectively, whereas from the ITC experiment a value of -0.4 x mol dm-3 is estimated. (A close inspection of Figure 1shows the slope of the emf data begins to change a t -0.4 mM, in agreement with the ITC data. However, when one considers the experimental error in the data, we do not regard this change to be significant until 1 mM.1 In comparison with other published data on TI, we do not, however, consider this to be a major discrepancy, although in the present case we regard the emf data to be the more precise. T1 for this system cannot be defined in a precise manner, with only a gradual change in the properties of the system occurring over a range of concentrations. In considering the data reported in this work, it must be remembered that the different techniques measure the different properties of the system. For example, the surfactant electrode measures the monomer surfactant concentration, and it cannot distinguish whether the quantity C1- ml, which denotes the concentration of the aggregated surfactant, exists as bound surfactant aggregates, free micelles, or both. On the other hand, the gel filtration is essentially a chromatography experiment, and the existence of three peaks in the region 25 x mol dmF3clearly signals the onset of the formation of free micelles in solution. The ITC experiment measures the enthalpy changes per injection when concentrated SDS 0.5%w/v PPO is added to 0.5%PPO, and the existence of a minimum in the enthalpy profile a t 25 x mol dm-3 confirms the gel filtration experiment, which signals the formation of free micelles a t this concentration. On this basis, from the above experiments we conclude that mol dm-3 between the concentrations of 25 and 100 x two competitive aggregation processes occur in solution, namely, the formation of surfactant aggregates on the polymer and free micelles in solution. In our previous work,20we have shown that the former process is accompanied by a n increase in ml with total SDS concentration, whereas micellization is accompanied by a decrease in m1 with total SDS (see Figure 1for pure SDS). In the present work, the maximum in ml as a function of total SDS concentration (Figure 3) occurs a t a n intermediate concentration of 45 x mol dm-3. In theory, ml is a consequenceofthe two stepwise aggregation schemes which describe the formation of both bound aggregates and free micelles from monomer SDS. The free energy of the bound aggregates is a factor of approximately [(2 - a’)/(2 - a)lRTln(Tl/cmc)= 5 k J mol-I times more stable than micellar SDS, where a and a’ are the values of the degree of micellar and bound aggregate counterion dissociation (estimated from Figure 6). Here ml depends on the equilibrium constants in the two energetically different multistep schemes, leading to the formation of these aggregates.l It is therefore not surprising that the maximum in the ml plot is somewhat
+
5
10
15
20
25
30
35
40
45
50
Total SDS Concentration x 103 [moldm-31
Figure 9, Plot of the reduced viscosity (rsdC)as a function of total SDS concentration for the SDSPPO [0.5%w/vl system.
intermediate between the formation of free micelles a t 25 x mol dm-3 and TZ (=lo0 x mol dm-3)-the exact position depending on which of the aggregation processes is dominating. In the context of surfactantipolymerbinding, in general, the SDSPPO system is not well defined. For example, it has been reported that difficulties were encountered when attempts where made to interpret the surface tension data for this system.l As a result of the very low molecular weight of the polymer (-1OOO), the structure ofthe polymer surfactant complex involves one micellar-type aggregate bound to more than one polymer molecule. In other words, the system resembles what one would refer to as a solubilization experiment rather than polymer binding. However, we have conducted our experimental approach from the point of view of a binding experiment, and in such circumstances, the results have been interpreted in this context.
Characteristicsof the Binding in the SDWEHEC System (i)EmfData. We now consider the data for the system SDSEHEC. The emf plots shown in Figure 2 indicate that the onset of surfactant binding takes place a t a Tl mol dm-3 SDS. With the addition of value of 2 x more surfactant, binding proceeds until the polymer becomes fully saturated with surfactant aggregates at a T2 of 30 x mol dm-3 SDS. However, in between these two critical concentrations, the solution becomes very viscous (Figure 9) in the range (4-12) x mol dm-3, with a maximum in viscosity occurring at 6 x mol dm-3SDS. This is an observation which has been reported previouslyl0 for this system and also other surfactant solutions containing hydrophobically modified polymers.’ A n explanation for this viscosity increase is shown schematically in Figure 10, where three distinct regions are apparent. Region I, a t SDS concentrations of less than TI, shows no interaction between the polymer and surfactant (Figure loa). Once SDS binding starts a t T1, a “normal” type of binding process initially takes place with small surfactant aggregates bound to the hydrophobic side chains of a single polymer chain. However, as a SDS concentration of approximately 4 x mol dm-3 is reached, the bound surfactant aggregates act as bridging cross-links between a t least two different polymer chains (region 11, Figure lob). Thus, an interchain polymer network is created, giving rise to the increase in viscosity of the solution. In region 111, further addition of SDS results in the breaking of the cross-links in the sense that the surfactant aggregates are now only associated with one polymer chain. This reduces the viscosity, and eventually, the network is destroyed, after which the second phase of normal-type binding occurs. At T2, the polymer becomes fully saturated a t a n SDS concentration
Binding of SDS to PPO and EHEC
Langmuir, Vol. 11, No. 9, 1995 3399
(a) Region 1
0
5
10
15
20
30
25
(Cl-ml) x 103 [mol dm-31
Figure 12. Plot of the ultrasonic relaxation data @,,,Js) vs the concentration of "bound" SDS (C1- nl): (+) SDSPPO [0.5% w/vl system; (0)SDS/EHEC [0.5% w/vl system.
(c) Region 111
in combination, it leads to the positive conclusion that in this system free micelles only occur in solution following the saturation of the polymer with bound aggregated surfactant. Figure 10. Schematic representation of the SDSIEHEC system.
Ultrasonic Relaxation The ultrasonic relaxations associated with the SDSI
PPO and SDSIEHEC solutions have been measured in the concentration ranges of (4-32)and (4-22)x mol
~II-~,respectively. The observed relaxation is attributed to the perturbation of the monomer surfactant bound aggregated surfactant exchange process. In all cases, the absorption data in the frequency range 0.4 17 MHz were consistent with a single relaxation process. The relaxation time (t)and maximum absorption per wavelength bmax) were evaluated a t each surfactant concentration, and a n attempt to analyze the data in terms of the phenomenological approach described in detail in earlier publication^'^-'^ was carried out. Ifit is assumed that the dissociation of a monomer from the bound aggregate is a first-order rate process proportional to the concentration of the bound aggregate (C1 ml), then the following equation applies:
-
-0.5
I
IO
100
Total SDS Concentration x 103 [mol dm-31
Figure 11. Plot of the enthalpy change per injection (AHl)as function of total SDS concentration for the SDSIEHEC [0.5% w/vl system in the ITC experiment.
of -35 x mol dm-3 and, after which, behaves very much like a polyelectrolyte.' Although the data reported by Holmberg and co-workers1° are a t a different temperature to the present data, the initial behavior of the binding data follows a similar pattern. However, unlike these authors, we do not see any evidence of desorption ofbound surfactant aggregates from the polymer a t T2. (ii) Gel Filtration. Due to the large changes in viscosity discussed above, it was not possible to carry out gel filtration experiments on the SDSIEHEC system. (iii)Isothermal Titration Calorimetry. In the ITC experiment, the enthalpy profile that occurs followingthe injection of concentrated SDS 0.5% wlv EHEC into a solution containing 0.5% EHEC is shown in Figure 11. This profile shows a pronounced maximum at TI (3x mol dm-3) followed by another pronounced maximum at 8 x mol dmm3,which signals the second phase of normal binding following the breakdown of the interchain network. This second maximum is followed by a minimum at T2 (30x mol dm-3),with the enthalpy per injection finally leveling off a t a value close to that found for pure SDS micelles. From the plot of mi against SDS concentration shown in Figure 4,a maximum also occurs a t Tz (32 x mol dm-3). Thus, in this system, T2, free micelles, and the maximum in ml occur at approximately the same SDS concentration. In addition, there is some evidence from the viscosity measurements that a measurable maximum in vsp occurs over the SDS concentration range (30-40) x mol dm-3. When all these observations are taken
+
where AV is the volume change for the process, e is the density, v is the sound velocity at a total surfactant concentration C1, R and T have their usual meanings, and k b is the dissociation rate constant. In eq 2,pmaxand t are known from the relaxation data and ml is known from the electrode measurements. In the rhs of eq 2,the bracketed term and k b are assumed to be constant, andin these circumstances,pm&is directly proportional to the dissociation rate. Accordingly, a plot ofpm& against C1- ml should be a straight line passing through the origin. Indeed in the case of SDSPVF', this type of behavior is observed.16 The plots in the present work are shown in Figure 12, and in the case of these hydrophobic polymers, there is evidence of first-order kinetic behavior at the initial stages ofbinding. However, as binding proceeds, the dissociation rate appears to reach a constant value for the SDSEHEC system and actually decreases for SDSPPO. The narrow concentration range over which first-order kinetic behavior is obeyed gives a value ofkb (using reasonable estimates for A m of the order of mol dm-3 s-l, which is very close to the value for pure SDS22and also bound SDS aggregates on PVP.l6The SDS concentration a t which the kinetic data shows (22) Wan-Badhi, W.A.; Lukas, T.;Bloor, D.M.; Wyn-Jones, E.J. Colloid Int. Sci. 19B6,169, 462.
3400 Langmuir, Vol. 11, No. 9, 1995
Bloor et al.
deviation from first-order behavior does not appear to correspond to any of the critical concentrations observed in the equilibrium measurements. In a n attempt to understand this kinetic behavior in the present work, we intend to investigate the binding of SDS to further hydrophobic polymers.
monwealth Fellowship. W.A.W-B. thanks the Malaysian Government and the Agricultural University of Malaysia for a postgraduate studentship. Y.L. thanks the University of Salford and the ORS for support. We also thank the British Council for a research grant awarded under the British-German Research Collaboration Programme.
Acknowledgment. W.M.Z.W-Y. thanks the U.K. Commonwealth Scholarship Commission for a Com-
LA9501389
