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Langmuir 1997, 13, 1392-1399
Articles Thermodynamic Properties of Surfactant/Polymer/Water Systems with Respect to Clustering Adsorption and Intermolecular Interaction as a Function of Temperature and Polymer Concentration Christina Holmberg, Stefan Nilsson, and Lars-Olof Sundelo¨f* Physical Pharmaceutical Chemistry, Uppsala University, Uppsala Biomedical Centre, P.O. Box 574, S-75123 Uppsala, Sweden Received November 28, 1994. In Final Form: October 23, 1996X This investigation forms part of a more extensive physicochemical study of the interaction of amphiphiles with different polymers, partially as a background for a better understanding of the function of pharmaceutical excipients. For the ethyl hydroxyethyl cellulose (EHEC)/sodium dodecyl sulfate (SDS)/ water system, the dialysis equilibrium between a solution containing polymer and a solution not containing polymer has been investigated over a composition interval of the amphiphile ranging from zero up to well above cmc and for the polymer from zero up to slightly above the concentration of critical overlap. It is found that the amphiphile begins to redistribute preferentially to the polymer at a “foot point” (critical aggregation concentration) concentration of 2 mM SDS, rises to a maximum value at an SDS concentration most likely corresponding to the onset of formation of normal micelles in bulk, and then decreases. The maximum adsorption corresponds to approximately two DS- ions per structural unit of the polymer. It is proposed that the results observed could be interpreted in terms of a redistribution of surfactant to the polymer coil regions leading to locally enhanced surfactant concentration, cluster formation, and adsorption. In combination with polymer reconformation this model suggests an explanation of some specific effects observed on this system: the increase in average cluster size with increasing polymer concentration, the marked decrease in intrinsic viscosity at the onset of surfactant adsorption combined with a strong hydrodynamic interaction (high value of the Huggins’ constant), and the considerable increase in macroscopic viscosity during the first phase of adsorption. The decrease in specific adsorption after the maximum probably derives from changes in DS- ion activity and saturation of the polymer, as well as the formation of normal micelles. Temperature is found to have only a small influence on the redistribution in an interval from room temperature up to the cloud point. The correction for the Donnan effect is discussed and results from conductometric measurements are used to calculate the degree of dissociation of surfactant in the micellar clusters.
Introduction During the last 10-15 years, there has been a considerable interest in investigations on amphiphilic systems and micelle formation mechanisms and the specific problem of surfactant, polymer interaction has attracted much interest. A number of reivews exist.1-3 In general, a surfactant interacts in a cooperative manner with an uncharged polymer starting at a surfactant concentration often denoted critical aggregation concentration (cac) which is lower than the normal cmc. The cac value is independent of polymer concentration. The cooperativity is normally interpreted in terms of a model where the surfactant and the polymer both contribute to form mixed micelles.1 One may describe the interaction either as the formation of surfactant clusters on the polymer chain or as polymer adhering to clusters. Various details in this model have been suggested.1-3 For the PEO-SDS system, for instance, the interaction has been described as the X Abstract published in Advance ACS Abstracts, February 1, 1997.
(1) Dubin, P., Ed. Microdomains in Polymer Solutions; Plenum Press: New York, 1985. (2) Goddard, E. D., Ananthapadmanabhan, K. P., Eds. Interaction of Surfactants with Polymers and Proteins; CRC Press: Boca Raton, FL, 1993; Chapter 5. (3) Robb, I. D. In Anionic Surfactants-Physical Chemistry of Surfactant Action; Lucassen-Reyders, E. H., Ed.; Surfactant Science Series 11; Marcel Dekker: New York, 1981; pp 109.
S0743-7463(94)00934-0 CCC: $14.00
polymer chain wrapping itself around a micelle.4,5 At higher cluster concentrations one could also visualize the interaction as leading to a necklace of cluters along the chain. The “adsorption” of surfactant continues until the chain becomes “saturated”, whereafter normal micelles begin to form when the overall surfactant concentration is increased. The point of saturation depends, of course, on the polymer concentration. The adsorption gives to the macromolecule specific properties, which for instance, are reflected in the rheological behavior. The EHEC/SDS/ water system is somewhat special and behaves in a way diffrent from the ways of many other similar systems.6-13 Several cellulose derivatives, especially derivatives containing ether linkages like ethyl(hydroxyethyl)cellulose (4) Cabane, B. J. Phys. Chem. 1977, 81, 1639. (5) Nagarajan, R.; Kalpacki, B. In Microdomains in Polymer Solutions; Dubin, P., Ed.; Plenum Press: New York, 1985; p 369. (6) Holmberg, C.; Nilsson, S.; Singh, S. K.; Sundelo¨f, L.-O. J. Phys. Chem. 1992, 96, 871. (7) Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1994, 272, 338. (8) Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1995, 273, 83. (9) Holmberg, C.; Sundelo¨f, L.-O. Langmuir 1996, 12, 883. (10) Bloor, D. M.; Wan-Yunus, W. M. Z.; Wan-Badhi, W. A.; Li, Y.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 1995, 11, 3395. (11) Calsson, A.; Karlstro¨m, G.; Lindman, B.; Stenberg, O. Colloid Polym. Sci. 1988, 266, 1031. (12) Thuresson, K.; So¨derman, O.; Hansson, Per.; Wang, G. J. Phys. Chem. 1996, 100, 4909. (13) Wang, G.; Olofsson, G. J. Phys. Chem. 1995, 99, 5588.
© 1997 American Chemical Society
Properties of Surfactant/Polymer/Water Systems
(EHEC), are characterized by mixed hydrophobic and hydrophilic structural units. Furthermore, these structural elements are normally unevenly distributed along the polymer backbone and the substituents may consist of shorter or longer chains, hence with a varying degree of hydrophobicity. This complex structure can give the macromolecule extraordinary properties often of great interest in applications. They result also in an extensive interaction with surfactants. A specific property closely related to the degree of hydrophobicity is the solubility as a function of temperature and the existence of a phase separation limit (cloud point, CP) when the temperature is raised above room temperature.7,9 The present work has been undertaken with the aim to further clarify the interaction in a salt free EHEC/SDS/ water system and discuss how it deviates from more wellknown systems. In previous papers the hydrodynamic properties and cluster sizes have been discussed at constant temperature.6-8 It has been found that the intrinsic viscosity of the polymer, which is a measure of the hydrodynamic volume [η] and thus indirectly reflects the conformation, decreases dramatically during the first phase of clustering adsorption. The cluster size Np has been found to increase with increasing polymer concentration up to a value approximately equal to the size of normal micelles. A rheological property of potential interest in applications is the marked increase in (reduced) viscosity found in a region beginning at the onset of adsorption provided that the polymer concentration is high enough. From a macroscopic point of view the interaction affects the viscosity and other rheological properties of the polymer/amphiphile system in a sometimes conspicuous way. This indicates that the polymer probably undergoes conformational changes and that in certain composition intervals the polymer/polymer interaction increases until under specific circumstances a gel state is approached.14 The main aim of this paper is to determine as precisely as possible the adsorption isotherms. Apart from defining the degree of adsorption, they are also basic in the analysis of a number of other system properties as discussed above. The adsorption isotherm for a polymer/surfactant/water system can be determined by several methods such as equilibrium dialysis,15-22 NMR,12 conductivity,23-25 isotherm titration microcalorimetry,10,13,26,27 and potentiometry using ion specific electrodes.28-30 Some of those are, unfortunately, unable to give data at higher surfactant concentrations, especially after saturation of the polymer (14) Carlsson, A.; Bogentoft, C.; Lindman, B.; Andersson, L. Proceedings of the 18th International Symposium on the Controlled Release of Bioactive Materials; 1991; p 455. (15) Sakamoto, N. Polymer 1987, 28, 288. (16) Fishman, M. L.; Eirich, F. R. J. Phys. Chem. 1971, 75, 3135. (17) Arai, H.; Murata, M.; Shinoda, K. J. Colloid Interface Sci. 1971, 37, 223. (18) Nakagaki, M.; Shimabayashi, S. Nippon Kagaku Zasshi 1974, 93, 1496. (19) Arai, H.; Horin, S. J. Colloid Interface Sci. 1969, 30, 372. (20) Lewis, K. E.; Robinsson, C. P. J. Colloid Interface Sci. 1970, 32, 539. (21) Smith, M. L.; Muller, N. J. J. Colloid Interface Sci. 1975, 52, 507. (22) Shirahama, K.; Ide, N. J. Colloid Interface Sci. 1976, 54, 450. (23) Lo¨froth, J.-E.; Johansson, L.; Norman A.-C.; Wettstro¨m. K. Prog. Colloid Polym. Sci. 1991, 84, 73. (24) Zana, R.; Biana-Limbele, W.; Kamenka, M.; Lindman, B. J. Phys. Chem. 1992, 96, 5461. (25) Kamenka, N.; Burgaud, I.; Treiner, C.; Zana, R. Langmuir 1994, 10, 3455. (26) Bloor, D. M.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 1995, 11, 2312. (27) Thuresson, K.; Nystro¨m, B.; Wang, G.; Lindman, B. Langmuir 1995, 11, 3730. (28) Shirahama, K.; Himuro, A.; Takisawa, N. Colloid Polym. Sci. 1987, 265, 96.
Langmuir, Vol. 13, No. 6, 1997 1393
chain.28,29 In this paper, the thermodynamics of the interaction equilibrium is explored using dialysis experiments in a temperature region from room temperature up to the cloud point. The method has the advantage that the equilibrium can be studied up to compositions far above the point of saturation and that the redistribution of surfactant (expressed in moles per mass unit of polymer) is obtained directly. Since the system properties change with polymer concentration and with temperature, data are presented for a concentration interval from zero up to above the concentration of critical overlap and for temperatures from room temperature up to the vicinity of phase separation. Interactions in similar systems have been studied by others15-22,28-30 through equilibrium dialysis15-22 or by using surfactant-selective electrodes.28-30 In some of these studies, however, an excess of salt (approximately 0.1 m) was present, thus more or less eliminating the Donnan effect,17,19,22 while others found the Donnan effect insignificant for their systems.18 In our investigation, added salt was excluded and corrections for the Donnan effect had to be made. To provide further insight into the adsorption process, conductivity determinations have been performed,31,32 the results of which allow a more precise calculation of the Donnan correction while also taking into account the degree of dissociation of the amphiphile.21 When compensating for the Donnan effect, one also has to consider the complication that, when the polymer chain is saturated, free micelles with a lower degree of ionization than the degrees polymer-bound clusters will be present in the solution. In this work, we show that not compensating for the Donnan effect in our salt-free system gives a rather large deviation from true equilibrium values. However, the difference between data corrected for the Donnan effect and data corrected for both the Donnan effect and the degree of ionization is small. The results will be discussed in terms of a molecular picture partly based on cluster size data obtained elsewhere.8 When studying thermodynamic properties of the interaction between a polymer and a surfactant by equilibrium dialysis, it is essential to make sure that a true equilibrium is attained. In a previous paper the time dependence of macroscopic properties during approach to equilibrium are discussed in detail.7 It is shown, however, that if sufficient time is allowed to elapse after solution preparation, equilibrium properties will be reached. However, amphiphiles at concentrations above cmc require considerable time to reach dialysis equilibrium.33,34 This was confirmed for the present system. However, when polymer was present, the time to reach equilibrium was considerably reduced. The experiments described here were all performed in such a manner that the data given apply to the equilibrium condition. Experimental Section Materials. The following chemicals were used: sodium dodecyl sulfate (SDS), 99.9% pure, used as supplied, Lot 733L488460, Batch 1.58553-100, MERCK, Spa˚nga, Sweden; radioactive SDS, 35S, Lot JC 1981, Batch 8803, Amersham, England; ethyl(hydroxylethyl)cellulose (EHEC) fraction CST(29) Carlsson, A. Nonionic Cellulose Ethers-Interactions with Surfactants, Solubility and Other Aspects. Ph.D. Thesis, University of Lund, Lund, Sweden, 1989. (30) Shirahama, K.; Oh-ishi, M.; Takisawa, N. Colloid Surf., A 1989, 40, 261. (31) Jones, M. N. J. Colloid Interface Sci. 1967, 23, 36. (32) Carlsson, A.; Lindman, B.; Wantanabe, T.; Shirahama, K. Langmuir 1989, 5, 1250. (33) Hugerth, A.; Caram-Lelham, N. Private communication. (34) Abu-Hamdiyyah, M.; Mysels, K. J. J. Phys. Chem. 1967, 71, 418.
1394 Langmuir, Vol. 13, No. 6, 1997 103 Mw ) 510 000, as determined by classical light scattering, MSeo ) 0.7, DSethyl ) 1.5, L920 32, Berol Kemi, Stenungsund, Sweden. The EHEC stock solution was freed from remaining salt by dialysis in tube membranes (MW cutoff was approximately 10 000) from Union Carbide, Chicago, IL. The stock solution of EHEC was filtered through 0.8 µm Millex-AA filters, Millipore SA, Molsheim, France. All solutions were prepared with MilliQ water (Millipore) as solvent. In the dialysis experiments SPECTRA/POR membranes (MW cutoff 12000-14000) were used. Preparation of Solutions. Dialysis. The stock solution of SDS was prepared by dissolving SDS in water to a concentration of 0.1m. SDS concentrations are calculated as moles per 1000 g of solvent (molal), but, since all solutions are dilute, they will be given on the molar scale. Radioactive SDS was dissolved in water and diluted to provide the required activity for the experiments. A stock solution of EHEC was prepared according to a standard procedure described elsewhere.6 After cleaning, dialysis of the EHEC stock solution conductometric measurements were made to ensure that only minute traces of salt remained. The stock solution was filtered to remove insoluble material like microgels and dust particles before the concentration was determined by drying samples to constant weight at 105 °C. For the actual dialysis experiments, two ways of mixing the solutions were applied to see if and to see how the order of mixing the components affects the adsorption behavior of SDS with respect to EHEC. Similar precautions were taken in a study of hydrodynamic properties, since it was evident that pronounced time dependent effects with a slow decay towards equilibrium were present. In the first case (a), one polymer solution of a certain concentration and a set of surfactant solutions were made for a series of experiments. A polymer solution was made by weighing an amount of EHEC stock solution into water to a certain concentration, and the set of SDS solutions had different concentrations varying from 1 to 40 mM. To the SDS solutions was added radioactive SDS so the activity equaled 50 000 dpm/ mL. One such series was made from each polymer concentration. In the second case, (b), individual polymer solutions containing SDS, as well as individual SDS solution, were prepared. These polymer solutions were prepared by weighing a certain amount of EHEC stock solution into an appropriately diluted SDS stock solution. Corresponding SDS solutions with exactly the same SDS concentration as the that of the one one containing polymer were also prepared. Small and equal amounts of 35SDS were added to both solutions so that they contained the same amount of radioactivity, approximately 25 000 dpm/mL. For one complete dialysis equilibrium determination (adsorption isotherm), 20 such “sets” of solutions were made with constant polymer concentration, and the SDS concentration varied from 1 to 20 mM both in the polymer and surfactant solution. Several series of this kind were made with different polymer concentrations. Conductometry. To determine the cmc of SDS in water, surfactant solutions were prepared by weighing from a SDS stock solution. For a determination of the degree of ionization, solutions were prepared by weighing the required amounts of the EHEC stock solution into appropriately diluted SDS stock solutions. All solutions were placed on a rotating table immediately after preparation since continuous stirring proved essential for stable conductometric results. To make sure that experimental data would apply to an equilibrium situation where all time dependence effects had settled, all samples were prepared 24 h before starting the actual experiments. The necessity of such precautions was evidenced by the previously mentioned systematic study of time dependent effects in certain polymeric systems.7 Cloud Point. Solutions for cloud point determinations were prepared by weighing the required amounts of the EHEC stock solution into appropriately diluted SDS stock solutions. All samples were prepared 24 h in advance to let the time dependent effects settle.7 Methods. Dialysis. The equilibrium dialysis experiments were carried out in specially designed cells, with retentate and dialysate compartments separated by a membrane. The cell design was similar to the one used by Fishman and Eirich.16 Before filling, the cells were thoroughly rinsed with deionized water. The water was then removed and the compartments were filled with the actual measuring solutions mixed according to
Holmberg et al. method a above. A series of experiments consisted of a polymer solution of a certain concentration, which was filled into the retentate compartment in each dialysis cell, then a set of surfactant solutions with concentrations ranging from 1 to 40 mM SDS was put into the respective dialysate compartments. Three cells were used with identical filling to ensure the reliability of the results. The cells were left to equilibrate in an air thermostat for a week. In order to find out if the dialysis equilibrium was dependent on the initial conditions, i.e., the composition of the solutions initially filled into the retentate and dialysate compartments, respectively, the experiments were carried out in yet another way. In this second procedure, a series of polymer, surfactant solutions, with constant polymer concentration and SDS concentrations ranging from 1 to 20 mM mixed according to method b above was poured into the retentate compartments until full and the corresponding surfactant solutions of exactly the same SDS concentrations were put into the respective dialysate compartments. Each set of EHEC/SDS and pure SDS solutions were poured into three different cells until full to improve the reliability of the results. Both methods a and b gave the same results within experimental error. It is well-known that the transport of amphiphiles across a membrane is proportional to the free amphiphile concentration difference, and hence the attainment of dialysis equilibrium may require considerable time. Results from experiments to determine the time required for the system to equilibrate showed that four days were sufficient, although seven days were allowed as a precaution.33 The concentrations of DS- ions in the EHEC/SDS and SDS solutions, respectively, were determined by scintillation counting. Experiments indicated that the presence of EHEC did not cause an extinction of the scintillation, and the volumes of scintillation cocktail were chosen as to avoid phase separation of the polymer. Conductometry. Solutions were placed in a thermostated, water-jacketed compartment for measurement of the conductivity with a Metrohm conductometer and an immersion-type measuring cell. Repeated measurements on each sample made sure that the recorded value was reliable. It was found important, in order to obtain stable readings on the conductometer, to take the solutions to be measured directly from the rotating table where they were kept after preparation. To ensure that a stabilized dissolved state had been reached, one series of solutions was remeasured after two more days on the rotating table. No change outside the experimental accuracy was observed. The calculation of degree of dissociation requires very precise data, and hence the reproducibility was checked by preparing and measuring a completely new series of solutions of a constant polymer concentration and varying SDS concentrations. Sufficient accuracy was assured. The conductivity (4-6 µS/cm) of the pure polymer solutions was subtracted from the measured values to obtain the conductivity of the amphiphile. Cloud Point. The cloud point of the EHEC/SDS solutions were determined by visual observation in glass tubes and taken as the temperature when the last visible sign of clouding in the solution disappeared upon cooling.
Data Treatment In this section, a procedure is presented for the handling of dialysis data. The experimentally observed effect in such experiments is the difference in amphiphile (surfactant) concentration on the two sides of the dialysis membrane. This difference, expressed on the molar scale, is denoted ∆[A]. After appropriate corrections for Donnan effects, this means essentially that only the concentration of adsorption complexes is measured. It has been previously shown8 that this adsorption occurs in the form of clusters PAn, where P denotes an adsorption site on the polymer, A the amphiphile monomer, and n the average number. This cluster formation begins at a well-defined amphiphile concentration, the “foot point”, denoted cac, well below the normal cmc point. The total amphiphile concentration is denoted [A]. The experiments have shown that for [A] > cac the adsorption parameter ∆[A] shows a rapid increase up to a maximum at [A] ) Cm. (Cm is the amphiphile concentration when the polymer is saturated
Properties of Surfactant/Polymer/Water Systems
Langmuir, Vol. 13, No. 6, 1997 1395
with surfactant and when normal micelles start to form in the bulk solution.) After this maximum, ∆[A] decreases almost linearly with increasing [A]. It will be shown in the discussion of experimental results that Cm corresponds to the cmc point in the presence of polymer. For finite polymer concentration Cm < cmc, but Cm approaches cmc as the polymer concentration is decreased. The general experimental features of the cluster adsorption isotherms just described come out clearly in our experimental results and will be discussed below. All concentrations are expressed on the molar scale. For simplicity most experimental results will be plotted vs [A]eq instead of [A] where [A]eq is the total amphiphile concentration not bound to polymer on the polymer side of the dialysis membrane (retentate side). [A]eq is calculated from the amphiphile concentration on the nonpolymer side of the membrane (dialysate side) applying appropriate corrections for the Donnan effect, etc. For [A] > Cm this means that [A]eq is the sum of monomolecularly dissolved amphiphile plus the amphiphile aggregated in normal micelles Am, i.e.,
[A]eq ) [A]free + m[Am]
(1)
where all concentrations refer to that one-half of the dialysis cell that contains polymer and m denotes the aggregation number in normal micelles. It is convenient to express the redistribution (adsorption) of surfactant ∆[A] per unit mass concentration of polymer. This normalized adsorption parameter is denoted y and is defined by
y ) ∆[A]/cp
(2)
where cp is the mass concentration of polymer, or more precisely, grams of polymer per 1000 g of solution. From the scintillation determination of 35SDS, the difference of DS- ion concentrations between the retentate and the dialysate compartments could be extracted. Thus, the amount of SDS redistributed to EHEC could be calculated assuming that the bound ions make no contribution to the ionic activities while correcting for the Donnan effect. With the assumption that activities may be replaced by concentrations, and since electroneutrality prevails within the equilibrated solutions on respective sides of the membrane, the solution denoted r (retentate, the solution containing only polymer initially) and the solution denoted d (dialysate, the solution containing only surfactant) yields
cry + [DS ]r ) [Na ]
(3)
[DS-]d ) [Na+]d
(4)
-
+
where cr ) concentration of EHEC in the retentate solution expressed as grams of substance per liter of solution, [DS-]i ) concentration of free DS- ions in solutions (i ) d or r) expressed as moles per liter of solution, and [Na+]i ) concentration of Na+ ions in solutions (i ) d or r) also expressed as moles per liter of solution. According to (3), y is defined as an experimental binding ratio in the sense that cry gives the excess amount of DS- ions with respect to the equilibrium free ion concentration in the retentate solution. A chemical potential balance at equilibrium (approximating activities with concentrations) leads to the condition
[Na+]r[DS-]r ) [Na+]d[DS-]d Combining (3-5) gives
(5)
[DS-]r ) [DS-]d2/Cr
(6)
Cr ) cry + [DS-]r
(7)
where
is the total concentration of DS- ions in solution r. Both Cr and [DS-]d are measured directly in the experiment. According to the definitions above, y is calculated from
y ) {Cr2 - [DS-]d2}/(crCr)
(8)
However, to arrive at (8) it is assumed that the degree of amphiphile dissociation is 1, i.e., none of the sodium ions is condensed on the polymer-bound SDS cluster. Conductometric measurements of EHEC/SDS solutions allow, however, the average ionization degree of the surfactant/ polymer complex to be determined by a standard technique35-37 used for normal micelles. The degree of ionization R of micelles can be obtained in the following way. If conductivity is plotted vs total surfactant concentration, a curve with one breakpoint is obtained which corresponds to the cmc of the surfactant. The ratio between the slopes before and after the breakpoint equals the ionization degree of the micelles. The degree of ionization of a polymer/surfactant complex23,24,38 can be calculated in a similar way. The conductivity of a surfactant/polymer solution plotted vs the total surfactant concentration forms a curve with two breakpoints. The ratio between the slopes before and after the first breakpoint equals the ionization degree of the polymer/ surfactant complex. The degree of dissociation obtained represents an average value, since the size of the cluster grows continually with the added amount of SDS in the concentration interval corresponding to the slope between the two breakpoints. This allows the adsorption isotherm to be corrected for both the Donnan effect and degree of dissociation R according to the following procedure:21
[Na+]f,r [DS-]f,r ) [Na+]d [DS-]d
(9)
([DS-]f,r + [DS-]b)Vr + [DS-]dVd ) SDStm (10) ([Na+]f,r + [Na+]b)Vr + [Na+]dVd ) SDStm (11) [Na+]d ) [DS-]d
(12)
[Na+]b ) (1 - R)[DS-]b
(13)
where the indices f and b refer to the free and bound states, respectively, the indices r and d correspond to the retentate and dialysate as before, and R is the degree of ionization of the SDS/EHEC complex. Vr and Vd are the retentate and dialysate volumes. SDStm is the total amount of moles of SDS present in the two compartments during the experiment. Combining (9-13) gives
[DS-]b ) {B - (B2 - 4AC)1/2}/(2A)
(14)
with A ) (1 - R)Vr2, B ) (2 - R)(SDStm - [DS-]dVd)Vr, C ) (SDStm - [DS-]dVd)2 - ([DS-]dVr)2. Since Vr, Vd, SDStm, and [DS-]d can be measured, it is possible to calculate (35) Botre, C.; Crescenzi, U. C.; Mele, A. J. Phys. Chem. 1959, 63, 650. (36) Abu-Hamdiyyah, M.; Al-Mansour, L. J. Phys. Chem. 1979, 83, 2236. (37) Gilanyi, T. Acta Chem. Scand. 1973, 27, 729. (38) Zana, R.; Lang, J.; Lianos, P. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1982, 23, 39.
1396 Langmuir, Vol. 13, No. 6, 1997
Figure 1. Plot of the SDS concentration difference ∆[A]u ) [SDS]r - [SDS]d across the dialysis membrane at equilibrium as a function of the initial concentration of SDS, [A]0 ) [SDS]d,0, placed in the dialysate compartment at the beginning of an experiment: 2, 0.05% EHEC; O, 0.10% EHEC; and b 0.20% EHEC.
Holmberg et al.
Figure 2. y (millimoles of SDS redistributed per gram of polymer) corrected for the Donnan effect as a function of [SDS]eq for different polymer concentrations at 20 °C: 2, 0.05% EHEC; O, 0.10% EHEC; and b, 0.20% EHEC.
[DS-]b if R is known, and then [DS-]f,r ) [DS-]eq can be calculated from (9). [DS-]b divided by the polymer concentration gives the number of moles of DS- bound per gram of polymer, i.e., y. [SDS]tot equals the total concentration of SDS in the retentate solution, i.e., the sum of [DS-]b and [DS-]f,r. Calculations have only been made up to the maximum point since complications as to the proper interpretation of experimental data arise when normal micelles form in the solution. Results and Discussion The polymer/amphiphile interaction often leads to a change in the physical properties of the system which is quite dramatic. In order to be able to perform a deeper analysis of such effects, a fundamental knowledge of the stoichiometry of the adsorption is mandatory, i.e., of the true adsorption isotherm. Results will be given here concerning adsorption isotherms for the EHEC/SDS/water system as obtained from dialysis experiments. When a solution of an amphiphile (here assumed to be negatively charged) is brought into contact with a solution of a suitable polymer, e.g., EHEC, across a dialysis membrane, there will be a redistribution of the amphiphile such that after equilibrium has been established the concentration of amphiphile is in excess in the dialysis compartment containing polymer. This excess of amphiphile, due to the presence of polymer, will become noticeable only if the amphiphile concentration is higher than the critical value cac, the foot point. In Figure 1, the directly determined (i.e., in all senses uncorrected) excess of amphiphile concentration in the polymer dialysis compartment at equilibrium, denoted ∆[A]u, is plotted vs the initial amphiphile concentration in the nonpolymer dialysis compartment, denoted [A]0. The quantity ∆[A]u is uncorrected with respect to the Donnan effect and to incomplete amphiphile dissociation. The excess of amphiphile is found to increase until the total amphiphile concentration reaches a certain value, Cm, which corresponds to saturation of the polymer and most probably the onset of formation of normal micelles in the bulk, as will be discussed below. The excess increases with increasing polymer concentration, and the maximum is roughly proportional to the polymer concentration. Even if the main features of the redistribution effects can be extracted from the raw data given in Figure 1, they
Figure 3. Equilibrium dialysis data corrected for the Donnan effect at 20 °C plotted as [SDS]eq vs [SDS]tot: 2, 0.05% EHEC; O, 0.10% EHEC; b, 0.20% EHEC; and 0, 0.50% EHEC.
are not directly suitable for a more quantitative analysis. Corrections must be applied for the Donnan effect and for the degree of dissociation of the amphiphile. The calculation procedure adopted to introduce these corrections has been described in a previous section. Figure 2 gives results corrected for the Donnan effect only and for three polymer concentrations: 0.05, 0.10, and 0.20%. The different polymer concentrations display the same general features, starting abruptly with a foot point at [SDS]eq ≈ 2 mM, followed by a steep increase in adsorption up to the point of saturation, where desorption is thought to occur. It seems likely that the maximum in adsorption coincides with the incipient formation of normal micelles. This view is supported by the following observation. When [SDS]eq, which corresponds to the concentration of free SDS in the polymer solution, is plotted vs polymer concentration, the points will converge to the normal cmc for SDS when cp f 0.9 The steepness of the curve indicates a cooperative mechanism of adsorption, and it increases with polymer concentration. The increase in cooperativity with increasing EHEC concentration can be seen more clearly in Figure 3, where [SDS]eq vs [SDS]tot for 0.05-0.5% is plotted. There seems to be a break point in the adsorption curve, which is brought out more clearly when the data are plotted as KD30 (KD ) y/[SDS]eq) vs log[SDS]eq. KD is an apparent distribution coefficient of surfactant between
Properties of Surfactant/Polymer/Water Systems
Figure 4. Redistribution coefficient KD plotted vs log[SDS]eq at 20 °C: 4, 0.05% EHEC and 2, 0.20% EHEC.
Figure 5. Conductivity κ of SDS/EHEC/water solutions as a function of the total SDS concentration at 20 °C: +, 0.00% EHEC; O, 0.10% EHEC; and b, 0.20% EHEC.
the aqueous bulk solution and ‘polymer coil phase’. The break point in the curve as seen in Figure 4 could indicate that there are two patterns of adsorption.39 The dialysis data presented represent an average of a large number of individual experiments. Up to and slightly above the maximum the reproducibility is very good and of the order of a few percent. For still higher values of [SDS]eq, i.e., at the downward slope in Figures 1 and 2, the scatter between individual experiments becomes larger. The degree of dissociation R has been calculated from conductivity measurements, Figure 5, from which corrected dialysis data are obtained up to the composition where free micelles are being formed, Figure 6. The values of R are listed in Table 1. After the maximum redistribution, no correction for degree of dissociation was tried due to the difficulty to unambiguously differentiate between clusters on the polymer and normal micelles. The results for 30 °C are quite similar to those at 20 °C. The dissociation correction shifts the isotherm to slightly higher values of [SDS]eq in such a way that the difference between results from different polymer concentrations decreases. The explanation seems to be that the degree of dissociation of the amphiphile is somewhat different if it has been adsorbed to a polymer site compared to the (39) Evertsson, H.; Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Langmuir Accepted for publication.
Langmuir, Vol. 13, No. 6, 1997 1397
Figure 6. Equilibrium dialysis data corrected for the degree of ionization and the Donnan effect plotted as y (millimoles of SDS redistributed per gram of polymer) vs [SDS]eq at 20 °C: 2, 0.05% EHEC; O, 0.10% EHEC; and b, 0.20% EHEC.
Figure 7. Dialysis data of SDS for 0.05% EHEC presented as a plot of y (millimoles of SDS redistributed per gram of polymer) as a function of [SDS]eq: 2, data without any correction; O, data compensated for the Donnan effect and the ionization degree; and b, data compensated for the Donnan effect only.
free state. For higher polymer concentrations, a larger portion of the total amount of amphiphile present is adsorbed to the polymer. Hence the correction effect becomes the more important the higher is the polymer concentration, and since it affects the value of [SDS]eq calculated, all curves are shifted along the [SDS]eq axis towards higher values when the correction is performed. Obviously the corrections introduce a considerable increase in the numerical value of y compared to the noncorrected results. The difference between values corrected for both the Donnan effect and imcomplete amphiphile dissociation and those only corrected for the Donnan effect is not so large, however, but the difference (decrease in y) is still of the order of some 10%, as can be seen in Figure 7. Since the correction for the degree of dissociation is not reliable above the maximum redistribution, the discussion of this region will be based on data in a form only corrected for the Donnan effect. It must be understood, however, that precise numerical values require some correction also for incomplete dissociation. To illustrate the effect of concentrations, the average aggregation number of polymer bound clusters Np was determined by the steady state fluorescence-quenching method proposed by N. J. Turro and A. Yekta as described
1398 Langmuir, Vol. 13, No. 6, 1997
Holmberg et al.
Table 1. Calculated Values of the Degree of Ionization r at Different Polymer Concentrations for the SDS/EHEC/ Water System at 20 and 30 °C, respectively temp °C
EHEC %
R
20
0 0.05 0.10 0.15 0.20
0.39 0.75 0.74 0.70 0.69
temp °C
EHEC %
R
30
0 0.05 0.10 0.15 0.20
0.39 0.79 0.77 0.74 0.71
Figure 9. y(millimoles of SDS redistributed per gram of polymer) corrected for the Donnan effect as a function of [SDS]eq for different polymer concentrations at 30 °C: 2, 0.05% EHEC; O, 0.10% EHEC; and b, 0.20% EHEC.
Figure 8. Average aggregation number Np of polymer bound SDS clusters as a function of [SDS]eq at 20 °C: b, Np at 0.20% EHEC calculated from dialysis data corrected for the Donnan effect; O, Np at 0.20% EHEC calculated from dialysis data corrected for the Donnan effect and the degree of ionization; 2, Np at 0.05% EHEC calculated from dialysis data corrected for the Donnan effect; and 4, Np at 0.05% EHEC calculated from dialysis data corrected for the Donnan effect and the degree of ionization.
in ref 40 using the surfactant concentrations, based on one hand on the adsorption isotherm corrected only for the Donnan effect and on the other hand on the isotherm corrected both for the Donnan effect and the degree of dissociation, respectively, in the calculations. In fluorescence-quenching studies, the total cluster concentration is obtained, and from simultaneous quantitative knowledge of the amount surfactant adsorbed, the cluster size is calculated in terms of average aggregation numbers.8,23-25,38-45 For some systems it is assumed that the knowledge of a cac value is sufficient23-25,39-44 to calculate Np properly, but it has recently been shown8,45 that both the EHEC/SDS/water and the HPMC/SDS/water systems require complete adsorption isotherms. As seen from Figure 8, the value of Np is affected by the correction for the degree of dissociation shifting the curve to higher values of [SDS]eq. The following general features can be discerned from the experimental data. At 20 °C, as seen in Figure 2, y as a function of [SDS]eq varies only slightly with polymer concentration in the interval investigated but there are some clear tendencies. The maximum in y decreases with increasing cp perhaps due to that two or more polymer adsorption sites share one cluster. Furthermore, the concentration [SDS]eq for which the maximum in y occurs (40) Winnik, F. M. In Interaction of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993; Chapter 9. (41) Zana, R.; Lianos, P.; Lang, J. J. Phys. Chem. 1985, 89, 41. (42) Winnik, F. M.; Winnik, M. A. Polym. J. (Tokyo) 1990, 22, 482. (43) Lissi, E. A.; Abuin, E. J. Colloid Interface Sci. 1985, 105, 1. (44) Zana, R.; Lang, J.; Lianos, P. In Microdomains in Polymer Solutions; Dubin, P., Ed.; Plenum Press: New York, 1985; p 357. (45) Nilsson, S. Macromolecules 1995, 28, 7837.
decreases with increasing cp. This could be explained by a higher redistribution to the coil region. The function y vs [SDS]eq becomes the steeper the higher is cp, which reflects the higher values of the aggregation number observed in a previous study.8 The steep increase in adsorption also implies a high degree of cooperativity. The decreasing part of the y vs [SDS]eq curve after the maximum is the result of a complex situation in which the polymer is distributed in a medium also containing normal micelles. This will certainly affect the adsorption equilibrium, and furthermore, it is known that the activity of the free surfactant anion decreases in this region.46,47 NMR and other self-diffusion measurements have also indicated a slow decrease in the amount of free ions.25,47,48 From the applied point of view, where the polymer is considered as a potential reservoir of adsorbed matter, this region needs further attention. At 30 °C, as Figure 9, indicates the redistribution seems to be generally somewhat smaller than at 20 °C and the maximum is almost independent of cp. This could be explained by the very strong increase in the polymer/ polymer interaction as the cloud point is approached, as seen in Figure 10. This view is also supported by the fact that for the lowest polymer concentration the curve y vs [SDS]eq is less steep and with a more pronounced curvature than at 20 °C. The maximum slope, however, attains the same value at 30 °C as at 20 °C, indicating that the degree of cooperativity is not much different at 30 °C from that at 20 °C when a sufficient amount of SDS has been added. The number of surfactant molecules adsorbed per macromolecule unit may be approximated as follows. Assuming an average monomer molecular weight (M1) of 300, one find that at maximum adsorption approximately two amphiphile molecules are “adsorbed” per polymer monomer. From the experimental values of y and N at the adsorption maximum the “site molecular weight”, Ms is estimated to be approximately 30 M1. If a Gaussian chain segment distribution is assumed, the average distance ds between cluster centers within the polymer coil would be given by (46) Gunnarsson, G.; Jo¨nsson, B.; Wennerstro¨m, H. J. Phys. Chem. 1980, 84, 3114. (47) Lindman, B.; Puyal, M.-C.; Kamenka, N.; Rymde´n, R.; Stilbs, P. J. Phys. Chem. 1984, 88, 5048. (48) Hammarstro¨m, A.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1993, 271, 1129.
Properties of Surfactant/Polymer/Water Systems
Langmuir, Vol. 13, No. 6, 1997 1399
Figure 10. The cloud point temperature as a function of the total SDS concentration for 0.20% EHEC solutions.
ds2 ) Cvl2
(15)
where l is the length of the monomer unit, v is the average number of segments between cluster sites, and C is a structural constant.49 Since v ≈ 30 and if we assume l ) 5 Å and C ) 3, we have ds ≈ 50 Å, which indicates a fairly dense population of clusters bound to the polymer coil. If it is further assumed that those clusters are statistically linked with the same structural constant one finds an end-to-end distance of about 1500 Å as compared to about 275 Å for the pure polymer. However, along with the adsorption of clusters the solvation of the polymer chain is changed and the effect of this is difficult to judge. Furthermore, the almost free draining49 polymer chain could change into a nondraining state as voluminous clusters are adsorbed which certainly would affect at least the hydrodynamic properties. Such effects are very difficult to investigate experimentally, however. The physical picture of the situation at the maximum of amphiphile redistribution, that is at Cm, as just described, supports the view that at Cm the chain is really saturated with adsorbed amphiphile. Certainly this will also affect the solvent/solute interaction in the sense that the chain “surface” will become much more hydrophilic due to the negatively charged cluster surfaces. This is in accord with the rapid increase in cloud point above [SDS]tot ≈ 5-8 mM, as seen in Figure 10. On the basis of the experimental results, the following model is suggested. In the binary surfactant/water system, micelles begin to form at cmc by a cooperative process and the cooperativity (in the case of SDS) becomes very pronounced over a small interval of concentration increase of surfactant. Let us now assume a water solution of the EHEC polymer to which we gradually add SDS. Assume now the polymer concentration to be very dilute so that the polymer molecules have a negligible coil/coil interaction. When surfactant is added it begins to (49) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: New York, 1953.
redistribute to the coil region, i.e., locally a higher surfactant concentration is achieved, and at a certain critical overall concentration (cac) this local concentration reaches a value where clusters begin to form on the chain. It could be anticipated that for dilute polymer solutions the conditions would only allow a certain degree of cooperativity, i.e., the redistribution leads to a local surfactant concentration that only suffices to create clusters with an average aggregation number smaller than that for the fully developed normal micelles. EHEC has furthermore a very expanded structure, almost free draining,49 and the initially extended coil structure can be expected to interact, due to its hydrophobic side chains, with the redistributed surfactant in a way that will “compact” the polymer conformation. This means that the hydrodynamic volume will decrease and hence also the intrinsic viscosity. As the polymer concentration is increased, one gradually increases the polymer/polymer interaction leading to an increased redistribution of surfactant per polymer molecule and the cooperativity would increase and hence the average aggregation number. The hydrodynamic interaction should then be expected to increase. This means that Huggins’ constant should increase, which has been observed.6,9 The coil would still continue to reduce its size. Finally, a polymer concentration is reached such that the segments are more or less evenly distributed over the solution volume and the polymer does not have to respond to the cooperativity by reducing its sizesthere is a balance between surfactant redistribution and reconformation and the intrinsic viscosity will no longer decrease. At this point the probability that several polymer chains being to interact by “sharing” micelles will increase, thus creating tie points in a three-dimensional pattern. This would be responsible for the strong increase in (reduced) viscosity observed experimentally above a certain (critical) polymer concentration close to the coil overlap composition. Further increase of surfactant will “saturate” the polymer chains, and the tendency to form tie points will gradually disappear. The solution then becomes more and more homogeneous with respect to both polymer segments and clusters, and eventually a situation is reached, which, as far as the surfactant is concerned, closely resembles the binary system and one could expect the micelles to attain normal size. The model just described is based on the redistribution concept which is familiar from multicomponent polymer solutions, for instance, those containing one polymer in two different solvents. Generally, one of the components is favorably redistributed to the coil region, and such a redistribution can locally reach considerable deviations from the bulk concentration.50 Acknowledgment. Financial support from the Swedish Natural Science Research Council and from the Swedish Research Council for Engineering Science is gratefully acknowledged. LA940934Z (50) Kratochvil, P.; Sundelo¨f, L.-O. Acta Pharm. Suec. 1986, 23, 31.
