Transport Properties for Aqueous Sodium Sulfonate Surfactants

Transcription

1 Journal of Colloid and Interface Science 216, (1999) Article ID jcis , available online at on Transport Properties for Aqueous Sodiu Sulfonate Surfactants 2. Intradiffusion Measureents: Influence of the Obstruction Effect on the Monoer and Micelle Mobilities Onofrio Annunziata, Lucia Costantino, Gerardino D Errico, Luigi Paduano, and Vincenzo Vitagliano Dipartiento di Chiica, Università di Napoli, Federico II, via Mezzocannone 4, Napoli, Italy E-ail: VITA@chena.dichi.unina.it Received July 24, 1998; accepted April 14, 1999 Intradiffusion coefficients of sodiu alkylsulfonates [CH 3 (CH 2 ) n 1 SO 3 Na,C n SNa] (n 5 9, 11) in ixtures with heavy water were easured by the PGSE-NMR technique at 25 C. A slope change in the experiental trends perits the deterination of the critical icelle concentration (CMC). In the icellar coposition range, solubilized TMS olecules were used to deterine the icelle intradiffusion coefficient, fro which the icelle radii were obtained. Both the onoer surfactant and the icelle intradiffusion coefficients show a sharp decrease above the CMC. These results can be interpreted in ters of the obstruction effect due to the icelles. The electrostatic repulsion aong charged particles strongly enhances this effect. A siple approach that perits the coputation of the Gouy Chapan layer thickness fro the experiental coefficients has been proposed and the results are briefly discussed Acadeic Press Key Words: intradiffusion; icelles; sodiu alkylsulfonates. INTRODUCTION The association of aphiphilic olecules into icellar aggregates in aqueous solutions leads to a reduction of the energetically unfavorable contact between water and the apolar parts of the aphiphilic olecules while the polar groups are still solvated by water. Although the hydrophobic interactions aong the apolar oieties in the icellar core have been extensively analyzed (1, 2), the understanding of the interactions involving the polar groups is less well developed. The strength of the interactions between the surfactant olecules largely depends on their hydrophilic oieties. In recent years, we have extensively studied icellar systes fored by nonionic ethoxylated tensides (3 6). For dilute solutions of these surfactants, the interactions between the polar heads are weak. On the contrary, for ionic surfactants the electrostatic onoer onoer, onoer icelle, and icelle icelle interactions are iportant and deterine the behavior of the systes (7). In this paper we present the results of intradiffusion easureents for aqueous solutions of soe anionic surfactants of the sodiu alkyl sulfonates class [CH 3 (CH 2 ) n 1 SO 3 Na, C n SNa]. These tensides, particularly the shorter ones, have high critical icelle concentration (CMC) values, so that the onoers cannot be neglected and all the above-entioned interactions ust be considered. In these conditions, obtaining unique and reliable values of the icellization paraeters is difficult. For this purpose, techniques are required that can distinguish the properties of the icelles fro those of onoeric units. Fro this point of view, transport property easureents see to be an appropriate experiental approach. The paper presented here is a part of a ore extensive work on the transport properties of alkyl sulfonates sodiu salts in aqueous solution. In a copanion paper utual diffusion coefficients in the sae syste are presented and discussed (8). In this work we report and coent on surfactant intradiffusion coefficients. The PGSE-NMR technique provides accurate intradiffusion coefficients for the rando theral otion of surfactants in systes of unifor cheical coposition. In the following sections we deterine separately the intradiffusion coefficient of both the icellar aggregates and the onoeric units. The diffusion coefficient of icelles extrapolated to infinite dilution is related to their hydrodynaic diension. Furtherore, we analyze the experiental data and propose a very siple approach to obtaining inforation on the electrostatic interactions in solution. We think that our data eventually will be useful for testing theoretical treatents for these kinds of systes. EXPERIMENTAL Materials. Siga analytical reagent grade sodiu 1-pentanesulfonate [C 5 H 11 SO 3 Na, C 5 SNa], sodiu 1-hexanesulfonate [C 6 H 13 SO 3 Na, C 6 SNa], sodiu 1-heptanesulfonate [C 7 H 15 SO 3 Na, C 7 SNa], sodiu 1-octanesulfonate [C 8 H 17 SO 3 Na, C 8 SNa], sodiu 1-nonanesulfonate [C 9 H 19 SO 3 Na, C 9 SNa], and sodiu 1-undecanesulfonate [C 11 H 23 SO 3 Na, C 11 SNa] (declared purity 98%) were dried under vacuu before use and used without /99 $30.00 Copyright 1999 by Acadeic Press All rights of reproduction in any for reserved. 16

2 AQUEOUS SODIUM SULFONATE SURFACTANTS 17 further purification. The solvent used was D 2 O obtained fro Siga ( 99.96% isotopic purity). All solutions were prepared by weight. As will be discussed later, solubilized tetraethylsilane (TMS, Siga, purity 99.9%) was used in the icellar coposition range to easure the icelle intradiffusion coefficient. Intradiffusion easureents. The intradiffusion coefficients were obtained by using the FT-PGSE NMR technique (9, 10). A spectroeter operating in the 1 H ode at 80 MHz and equipped with a pulsed agnetic field gradient unit ade by Stelar (Mede, Italy) was used. The Varian spectroeter was odified for better teperature control by using an external refrigeration and water recycling built by RefCon (Naples) according to our design. This equipent provides efficient teperature control of the water cooling the agnet and of the air cooling the saple. A Stelar variable teperature controller (Model VTC87) was used to keep the saple teperature constant within 0.1 C. The individual spin-echo peak aplitude, A, for a given line is given by A A 0 exp 2 g 2 a 2 3, [1] where A 0 is a constant for a given set of experiental conditions, is the gyroagnetic ratio of the proton, a is the intradiffusion coefficient of the species responsible for the NMR signal, g is the strength of the applied gradient, and and are tie paraeters in the pulse sequence. The tie between the 180 and 90 pulses,, was kept constant. The duration of the two gradient pulses,, was varied over a suitable range to observe the decay of the spin-echo signal A. The paraeters in the above equation were obtained by applying a nonlinear least-squares routine to the decay of A as a function of. In order to evaluate the values of the intradiffusion coefficients, g ust be known. Measureents to establish its value were perfored on a reference saple with known intradiffusion coefficient; we used heavy water with trace aounts of light water ( HDO s 1, 11). The sulfonates intradiffusion coefficients were easured following the signal intensities of the CH 2 groups protons not adjacent to the sulfur ato ( 1.3). The experiental errors on the intradiffusion coefficients were generally less than 2%. In order to correct the intradiffusion coefficients obtained in deuterated solutions back to those in noral water, it is necessary to ultiply a by the factor 1.23 (12), which is the ratio of intradiffusion coefficients of noral and deuterated water. Siilarly, the olalities in heavy water were ultiplied by the * D2 O / * H2 O ratio in order to obtain the olalities in light water. The concentrations were coputed using the literature density data (8, 13). (No literature data are available for C 8 SNa. In this case densities were estiated by interpolating the C 7 SNa and C 9 SNa data.) The isotopic substitution of the solvent ight result in an alteration of the structural properties of the icellar aggregates. In fact D 2 O is thought to be slightly ore structured than H 2 O (14). Berr (15) showed that these differences are very sall and becoe appreciable only for surfactants with long hydrophobic chains. For this reason we neglected this effect. RESULTS AND DISCUSSION The developent of explicit theories describing icellar aggregation beyond therodynaic treatents is a difficult proble because the olecular interactions involved are too coplex to be described in ters of statistical echanics. Thus odels are used generally for linking icelle foration to olecular solution structure. These odels perit analysis of the experiental data in order to obtain inforation about the icellization process. The icellization process of a surfactant can be described as a phase separation (16), so that the concentration of the onoer species becoes constant and equal to the critical icelle concentration (CMC) at higher concentration. For intradiffusion easureents, the CMC deterination was discussed in a previous paper (5). Above the CMC, according to this odel, the onoer concentration is constant, while the icelle concentration is approxiately given by (17) C M C CMC, [2] n where C is the stoichietric concentration of surfactant, C M the icelle concentration, and n is the aggregation nuber. Alternatively, the icellization process can be described as a cheical equilibriu (18). For anionic surfactants (S ), ns qm S n M q n q [3] K S n M q S n M q, [4] where M is the counterion and q is the nuber of counterions bound to each icelle. If n is sufficiently large, the equilibriu odel also predicts the onset of icellization in a very narrow range of concentration. However, the onoer concentration does not becoe constant at higher concentrations. Both odels are siplified odels that do not account, for instance, for the polydispersity or for the activity coefficients of the solute species. However, they are good enough to give reasonable insight into the behavior of surfactants solutions through the icellization process (19), although ore sophisticated odels are described in the literature (20, 21). The choice of the odel is ainly related to the discussion of experiental results. We have used both odels in the past. For surfactants with short hydrophobic tails, which usually present high and poorly arked CMC values, the properties of

3 18 ANNUNZIATA ET AL. the systes are well described by the equilibriu odel. In this work the experiental intradiffusion coefficients are first treated according to the phase separation odel. The results perit coputation of the equilibriu paraeters fro the utual diffusion coefficients (8). These paraeters have been used to reanalyze our intradiffusion data to obtain new inforation about the intericellar interactions. This is an interesting exaple in which the cobined analysis of intradiffusion and utual diffusion data largely iprove the inforation that can be obtained fro a single technique. The experiental intradiffusion coefficients are collected in Table 1 and shown in Figs In all cases shows a change of slope at the CMC. The easured CMC values are collected in Table 2, where they are copared with soe literature values. In the cases of C 9 SNa and C 11 SNa, whose CMCs are very low, we were not able to easure the intradiffusion coefficient in the preicellar coposition range. The intradiffusion coefficients obtained for the C 8 SNa aqueous solutions are in very good agreeent with those easured by Lindan et al. (22). In the preicellar coposition range the intradiffusion coefficients ay be fitted as a function of the square root of the ionic strength (23), I, as is usual for electrolyte solutions: 1 I 1/ 2 [5] The fitting paraeters are reported in Table 2. The intradiffusion coefficients extrapolated to infinite dilution,, can be copared with those coputed by the Nernst relationship, RT 2, [6] where is the Faraday constant and is the liiting conductivity of the surfactant anion. Clunie et al. (24) obtained for the sodiu n-alkyl sulfonates fro experiental equivalent conductances assuing the liiting conductivity of Na, oh 1 c 2, fro the literature (25). As one can see in Table 2, the agreeent between the experiental and the coputed is very good. Actually, these values are different fro the liiting coefficients of utual diffusion. In fact, fro the Nernst Hartley expression, the liiting utual diffusion coefficient is given by D utual 2 RT 2. [7] Given the rapid exchange aong free and icellized surfactant olecules, in the icellar coposition range the experiental intradiffusion coefficient is a ean value between that of the free onoers, F, and that of the icellized olecules, M. Thus, p F F 1 p F M C F C F nc M C M, [8] where p F is the fraction of aphiphile in the onoeric state and C F is the free onoer concentration. For the systes under consideration the value decreases sharply above the CMC. The strong dependence on concentration is usually attributed to the obstruction effect. In fact the ean square root displaceent of a particle decreases if it eets soe hindrance in its otion; big particles, like icelles, slow the otion of other icelles and of the free onoer. F and M both depend on the volue fraction of icelles. The presence of charged particles increases this effect because of electrostatic repulsion. As a consequence for ionic tensides: the free onoer intradiffusion coefficient, in the icellar coposition range, is different fro that easured at the CMC, CMC F, where icelles are absent, and shows a dependence on the surfactant concentration; the icelle intradiffusion coefficient is not constant. Micelle intradiffusion coefficients. M can be estiated experientally by the addition of TMS to the syste. In fact, for a copound in a icellar solution which is entirely confined to the icelles and has a negligible solubility in the intericellar solution, the observed intradiffusion coefficient will be the sae as the intradiffusion coefficient of the icelles (26). With this purpose, we added TMS in trace aounts to our solutions. TMS is a strongly hydrophobic olecule and is solubilized in the icellar core. Below the CMC no NMR signal fro TMS was observed. This was ascribed to the diffusion of the probe to the air water interface in the absence of solubilization sites in solution (27). In icellar solutions, electrostatic repulsion should prevent intiate icelle icelle contacts, barring collisional transfer of solubilized olecules. For these reasons we followed the TMS NMR signal, in order to easure directly the icelle intradiffusion coefficient. The TMS intradiffusion coefficients are collected in Table 1. Inspection of Figs. 1 6 shows that M 3 as the surfactant concentration increases and the onoeric contribution becoes negligible. As a consequence, it sees realistic to assue that the added solubilizate does not perturb the icelles, i.e., by reducing the CMC or affecting appreciably icelle shape and size. In a first approxiation, the siple pseudo-phase-transition odel can be assued; in this case the icelles start to for at the CMC. This concentration can be considered as the infinite dilution for icelles. Furtherore, the icelle concentration is proportional to the total surfactant concentration inus the CMC (see Eq. [2]). For this reason, the concentration dependence of M can be expanded as a polynoial of (C CMC), M CMC M 1 A M C CMC B M C CMC 2..., [9]

4 AQUEOUS SODIUM SULFONATE SURFACTANTS 19 TABLE 1 Intradiffusion Coefficients for the Systes D 2 O(1) Surfactant(2) at K C5SNa C6SNa C7SNa C8SNa C9SNa C11SNa

5 20 ANNUNZIATA ET AL. FIG. 1. C 5 SNa aqueous solutions: (F) tenside intradiffusion coefficients, ( ) TMS intradiffusion coefficients, (E) liiting intradiffusion coefficients coputed fro conductivity data, ( ) free onoer intradiffusion coefficients; the dashed line shows the utual diffusion coefficient trend. FIG. 3. C 7 SNa aqueous solutions: (F) tenside intradiffusion coefficients, ( ) TMS intradiffusion coefficients, (E) liiting intradiffusion coefficients coputed fro conductivity data, ( ) free onoer intradiffusion coefficients; the dashed line shows the utual diffusion coefficient trend. although the graphs of Figs. 1 6 show that M is alost a linear function of C. Since we are going to discuss the ter A M later, we collect the fitting paraeters of Eq. [8] in Table 3. It is possible to relate the icelle intradiffusion coefficients, extrapolated at the CMC ( CMC M ), to the hydrodynaic size of the aggregates using the Stokes Einstein equation to calculate the apparent radius, r (28), r k B T 6 CMC M CMC, [10] where CMC is the viscosity of alkyl sulfonate solutions at the CMC. In the preicellar solutions of alkyl sulfonate the viscosity follows the relation (29) 0 1 BC, [11] where 0 is the water viscosity and B is an interpolating coefficient. For a low nuber of carbon atos in the hydrocarbon chain, n C 1 6, the following was found (in ol 1 d 3 ) (29): B n C. [12] For n C 6, we extrapolated B fro Eq. [12]. CMC was obtained fro Eq. [11], with C CMC; CMC values are reported in Table 3. FIG. 2. C 6 SNa aqueous solutions: (F) tenside intradiffusion coefficients, ( ) TMS intradiffusion coefficients, (E) liiting intradiffusion coefficients coputed fro conductivity data, ( ) free onoer intradiffusion coefficients; the dashed line shows the utual diffusion coefficient trend. FIG. 4. C 8 SNa aqueous solutions: (F) tenside intradiffusion coefficients, ( ) TMS intradiffusion coefficients, (E) liiting intradiffusion coefficients coputed fro conductivity data, ( ) free onoer intradiffusion coefficients.

6 AQUEOUS SODIUM SULFONATE SURFACTANTS 21 FIG. 5. C 9 SNa aqueous solutions: (F) tenside intradiffusion coefficients, ( ) TMS intradiffusion coefficients, (E) liiting intradiffusion coefficients coputed fro conductivity data, ( ) free onoer intradiffusion coefficients; the dashed line shows the utual diffusion coefficient trend. FIG. 6. C 11 SNa aqueous solutions: (F) tenside intradiffusion coefficients, ( ) TMS intradiffusion coefficients, (E) liiting intradiffusion coefficients coputed fro conductivity data, ( ) free onoer intradiffusion coefficients; the dashed line shows the utual diffusion coefficient trend. The easured r values are shown in Table 3. They can be copared with those of the alkyl chain length coputed according to the Tanford relation, n C [13] where is approxiately the hydrophobic core radius (in n). As can be seen, r, with a ean difference of n, due to the sulfonic heads, the bound counterions, and the hydration water. M CMC ust coincide with the liiting icelle utual diffusion coefficient (30, 31). The knowledge of M CMC perits the coputation of the n, q, and K values for the icellization equilibriu fro the utual diffusion easureents. These paraeters perit calculation of the concentration of all species present in solution (8). The results indicate that the free onoer concentration decreases above the CMC. The icelle concentration, C M, starts to be significant slightly below the CMC and increases linearly with total surfactant concentration. We can reconsider Eq. [9] according to the cheical equilibriu odel using the true value of C M : M M CMC 1 A M C M B M C M [14] The calculated paraeters are reported in Table 4. Clearly, A M na M and B M n 2 B M ; however, the results obtained fro Eq. [14] ust be preferred, considering that the aqueous solutions of our tensides are better described by the equilibriu odel. The concentration dependence of M is generally due to the cobination of two effects: intericellar interactions and change of icelle size. At oderate ionic strength the first effect is prevailing (32, 33). In order to interpret our experiental results, we neglected the second effect. TABLE 2 Critical Micellar Concentration and Fitting Paraeters for the Equations in the Text CMC (ol d 3 ) CMC (ol d 3 ) a 10 9 (ol d 3 ) 1/2 n b q/n b ln K b C 5 S c C 6 S c C 7 S C 8 S c (17) d (0.8) d (50.1) d e C 9 S e C 11 S 0.02 e a Data fro Ref. (24). b Data fro Ref. (8). c Data fro Ref. (44). d Interpolated data. e Data fro Ref. (45).

7 22 ANNUNZIATA ET AL. TABLE 3 Fitting Paraeters for the Equations in the Text M CMC 10 9 CMC (cp) A M (ol 1 d 3 ) B M (ol 1 d 3 ) r C 5 S C 6 S C 7 S C 8 S C 9 S C 11 S Although a large body of literature has been developed about the proble of interactions aong polyelectrolytes in aqueous solution in the presence and absence of added salts (34 36), only incoplete odels have been used so far to describe intericellar interactions (37, 38). On the other hand, several odels have been developed for describing the interaction aong uncharged spherical particles. Batchelor (39) has shown that in a dilute suspension of spherical particles it is appropriate to express the intradiffusion coefficient as a power series of the particles volue fraction,. Considering two- and threebody hydrodynaic interactions the following relation holds (40): [15] In the following discussion we assue the shape of the icelles to be not very far fro the spherical one. Furtherore, we preserve the sae dependence on of Eq. [15] for charged spherical particles. In this case, of course, the particle s volue will appear larger than the real one because of the effect of the electrostatic interactions. Coparing Eq. [15] and Eq. [14] one can show that A M 1.73 C M 1.73V M 2.31 N A r 3, 16 where V M is the excluded volue due to the presence of icelles, r is the corresponding radius (in n), and N A is the Avogadro nuber. The coputed r values are reported in Table 4. As can be seen r r is always positive (Table 4). This point will be discussed later. Monoer intradiffusion coefficients. The free onoer intradiffusion coefficient, F, can be coputed fro Eq. [8]; its trend is shown in Figs F is affected by the ionic strength of the aqueous ediu and by the obstruction effect due to the icelles. The forer effect can be assued to be the sae as in the preicellar region: F (I) 1 I 1/ 2. [17] The ionic strength of the aqueous ediu was coputed considering the free onoers and counterions concentrations obtained fro the equilibriu paraeters: I 1 2 2C F n q C M. [18] Due to the presence of the charged icelle surface, the ion distribution is not unifor; consequently, the ionic strength coputed through Eq. [18] is an approxiate value. Bell (41) proposed a odel for taking in account the obstruction effect exerted by spherical icelles on a sall particle such as the free onoer, F F , [19] TABLE 4 Fitting Paraeters for the Equations in the Text A M (ol 1 d 3 ) B M (ol 1 d 3 ) r A F (ol 1 d 3 ) r 1 C 5 S C 6 S C 7 S C 8 S C 9 S C 11 S

8 AQUEOUS SODIUM SULFONATE SURFACTANTS 23 where F 0 is the onoer intradiffusion coefficient in absence of obstructing particles. This relation holds for uncharged spheres; however, we can preserve this expression for our systes. As a consequence, F in the icellar region can be interpolated by the following relation: F F I 1 A F C M. [20] A F is related to the obstruction effect aplified by the electrostatic interactions. The calculated A F values are reported in Table 4. Coparing Eq. [20] with Eq. [19], it can be seen that A F 0.5 C M 0.5V M 0.67 N A r 3, [21] where V M is the apparent olar volue of the icelle, considered as the obstructing object, r is the corresponding radius (in n). In Table 4 the r values are reported. Coparing r r with, it can be seen that the obstruction exerted by the icelles on the onoers is stronger than that exerted on the other icelles. r and r, coputed in the coposition region near the CMC where the icelle concentration is low, ust be considered as indications of the friction encountered, respectively, by the icelle and the onoer to change their position during the diffusion process; i.e., they are hydrodynaic properties. The hydrodynaic volues can be uch larger than the partial olar ones because of the interactions in solution (42). They cannot be assued as true volues of actual species in solutions. In fact, using these volues for coputing the space occupied by particles in oderately or highly concentrated solutions, volues larger than those of the whole solution would be found. In order to understand the eaning of and, the structure of a icellar syste fored by an anionic surfactant ust be taken in account. An ionic icelle can be represented as a sperical aggregate whose inner core region consists of ethylene tails. The negatively charged headgroups are located on the aggregate surface, in contact with water olecules. The icelle behavior can be described in ters of the polyions theory. The electrostatic potential due to the charges on the icelle surface causes a gradient of the counterion concentration in going fro the surface to the bulk solution (34). Oosawa (35) and Manning (36) stated that a fraction of counterions will condense on the polyion to lower the charge density of its surface. The adsorbed counterions, along with the surfactant headgroups, for the Stern layer. The residual charge density on the icelle surface produces, on the ediu surrounding the icelle, the electric potential o exp x, [22] FIG. 7. Gouy Chapan layer thickness: (F) ; ( ) ; ({) 1. where x is the distance fro the icellar surface, o is related to the surface charge density, and depends on the nature of the intericellar ediu, e 2 N A 0 r k B T I, [23] where 0 is the vacuu dielectric constant and r is the intericellar dielectric constant (which we assue to be that of pure water). is a linear function of the square root of the ionic strength. Because of the potential given by Eq. [22], near the icelle surface there are excess unbound counterions, while the onoer surfactant anions are rejected. The counterion concentration decreases continuously in going fro the icelle surface to the bulk solution. A siple approxiated odel is often assued, in which the excess counterions are confined in a well-defined region surrounding the aggregates, called the Gouy Chapan layer (43). Its thickness ay be identified with 1, which has the diension of length. In Table 2 the coputed 1 values are reported. To estiate 1, the ionic strength in Eq. [23] was assued to be equal to the CMC. The difference can be seen as the thickness of the layer surrounding the icelle, where free surfactant anions are hindered fro entering because of the electrostatic repulsion due to the icelle charge. In the sae anner is the thickness of the layer surrounding the icelle in which another icelle cannot enter because of the repulsion between the two charged surfaces. and ust be proportional to the diension of the Gouy Chapan layer. Inspection of Fig. 7, where 1,, and are reported as a function of I 1/2 for the surfactants under consideration, shows that and have the sae trend of 1. They increase as the ionic strength decreases and are good indices of ionic repulsion. Hence, and perit a realistic view of the interactions in the icellar systes fored by ionic surfactants.

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