J. Phys. Chem. 1994,98, 63596367
6359
lH NMR Self-Diffusion and Multifield *H Spin Relaxation Study of Model Associative Polymer and Sodium Dodecyl Sulfate Aggregation in Aqueous Solution Susanna Abrahdn-Alami and Peter Stilbs' Physical Chemistry, Royal Institute of Technology, S-I O 0 44 Stockholm, Sweden Received: January 14, 1994.
1H N M R self-diffusion and multifield 2Hspin relaxation measurements were applied in a study of the aggregation of a model associative polymer (MAP) in aqueous solution. The polymer is based on a poly(oxyethy1ene) backbone with ether-linked alkyl chains ends. The aggregation was studied also in presence of sodium dodecyl sulfate (SDS)at a high concentration. Associative polymers self-assemble in aqueous solution into what is generally believed to be micelle-like aggregates with the hydrophobic end groups situated in the micellar core. In binary solutions of polymer and water such polymer aggregates were found to display an extensive polydispersity which increased with polymer concentration, as based on experimental self-diffusion data. Corresponding measurements on mixed solutions of high SDS concentration, on the other hand, indicate that SDS micelles act as seeds for aggregation, promoting a markedly lower polydispersity for these mixed aggregates. 2Hspin relaxation data on SDS molecules in mixed aggregates were found to be consistent with a two-step motional model for chain reorientation. The fast local anisotropic motions of the SDS molecules inside the aggregates were found not to be particularly influenced by the addition of polymer, whereas the slow isotropic motions of the SDS molecules, such as aggregate tumbling and lateral diffusion of SDS over the curved aggregate surface, were considerably retarded. The increased size of the mixed aggregates upon addition of polymer is probably the main reason for this retardation of reorientational dynamics. However, the motion of the polymer in the mixed aggregates and in single-component polymer aggregates could not be described by the same motional model; instead a three-step motional model had to be applied. The additional very slow motion component was interpreted to be a reptational or exchange motion of the polymer inside or between aggregates. Introduction
the oxyethylene parts adsorb onto the micellar surfaces in the case of anionic surfactants, and protrude into the solution in the During the past decade,structure-formingassociativepolymers case of non- or cationic surfactants.5*6J2 For mixed aggregates (AP) have found a major application in water-based paints and of low molecular weight APs in concentrated ethoxylatedsulfate are starting to gain wider interest in other applications such as, surfactant solutions, a recent study suggests that the best e.g., enhanced oil recovery. The advantage in using APs is the viscosifying properties and viscoelastic behavior are s u p p e d to possibility of meeting the requirement of viscosity enhancement be related to the increase in the hydrodynamic radius when APs and more Newtonian flow behavior over a larger range of shear form loops starting and ending in a surfactant micelle.16 rates than possible with traditional high molecular weight A particular type of commercial APs, HEUR thickeners, are thickening agents. poly(oxyethy1ene)-based and hydrophobically modified by for A vast number of investigations have been carried out in order instance diisocyanatesand terminally attached alcohols.1~*J7 We to obtain informationabout the association mechanism of various have previously studied such HEUR thickeners,7J4but since these thickeners. Macroscopic rheological properties as well as properAPs usually display an extensive polydispersity already at the ties at molecular level have been studied, both for simple model nonaggregated stage, a model associative polymer (MAP) was systems and for formulated paints. In addition to viscosity developed for this study. The MAP in question is a polymeasurements,1-l0staticand dynamic fluorescence~6~I1.l2dynamic (oxyethylene didodecyl ether) of markedly lower polydispersity. light scattering,3Al3surface tension,3.4 and NMR ~elfdiffUsion7~12-~~ Investigations of mixed aggregates of MAP and SDS,at were applied as tools for the investigation of the AP aggregation concentrations far beyond thecriticalmicelleconcentration(cmc), mechanism. It is generally believed that the rheological effects as well as single-component MAP aggregates were carried out of APs originate from assembly into micelle-like aggregates at through a combinationof 'H NMR self-diffusion and multifield low concentrationsand a gradual formation of networks at higher 2H spin relaxation measurements. One should recall that the concentration. It has also been found that increased concentration self-diffusion of a polymer at the NMR time scale quantifies the of polymer leads to a widened aggregate size distribution.4s7J3 lateral displacement of a single chain in the laboratory frame, AP association and the rheological behavior is very much whereas multifield spin relaxation measurements may provide a influend by additives like surfactants. Depending on the relative quantificationof local chain motions and overall tumblingmotions concentration of polymer and surfactant, as well as the polymer of aggregates. The two-step motional model has been found to architecture, the formation of a certain aggregate type can be provide a good description of such motions of micellized promoted. As an example, nonmodified poly(oxyethy1enes) and ~urfactants.~*.*~ An alternative model, often used to interpret sodium dodecyl sulfate (SDS) are believed to form complexes, NMR relaxation in macromolecules is termed the model-free where SDS molecules are not isolated along the polymer chain approach28and is discussed further below. In the two-step model, but rather gathered into micelle-like aggregates along the polymotions on two different time scales are considered responsible (oxyethylene) structural framework.15 Studies of APs also exist for the spin relaxation. There is a fast local reorientation of the which show that mixed aggregates where the hydrophobic tails surfactant molecule in the micelle and a slow isotropic motion, of the APs are situated in the micellar core. On the other hand, which is the combined effect of micellar tumbling and lateral diffusion of the surfactant molecule over the micellar surface. At the relative polymer/surfactant concentration used here the Abstract published in Aduunce ACS Abstracts, June 1, 1994.
OQ22-3654f 94f 2098-6359tQ4.50 f0
0 1994 American Chemical Society
6360 The Journal of Physical Chemistry, Vol. 98, No. 25, 1994
experimental strategy was based on that the structural element formed by SDS molecules, is., micelles, should be dominant also for the mixed aggregates. If so, the commonly used two-step motional model used to describe pure surfactant systems could also be applied in order to describe the motional behavior in mixed- and single-component MAP aggregates. Combined with NMR self-diffusion measurements a more complete picture of the MAP aggregation mechanism might thus become experimentally accessible. Experimental Section Materials. The chosen modified poly(oxyethy1ene) (MAP) has the following general structure: 12H250(-CH2CH2G)~C
1zH25
It was synthesized in our laboratory and was also made in a form that was 2H-labeled in the a-position of the end group, in order to provide a suitable probe for the spin relaxation measurements. In outline,the synthesisis as follows. A dodecylmethanesulfonate ( C ~ ~ H ~ S S O ~called C H ~mesylate, ), was synthesized according to the method described by Crossland et The poly(oxyethylene) polymer, purchased from Fluka Chemie as PEG 6000, was dissolved in toluene and all traces of water were distilled off. An equivalent amount of butyllitium (1.6 M in hexane, Aldrich Chemie) was added at room temperature together with the mesylate. The reaction mixture was refluxed at 90 "C for 3 h. The poly(oxyethy1ene) hydroxyls were reacted with at least 5 times excess mesylate in order to obtain a fully substituted product. The extent of substitution was higher than 90% for the nonlabeled MAP, as measured by lH NMR. The toluene was subsequently distilled off, and the product was finally dissolved in dichloromethane and filtered. Thereafter the product was treated with active carbon and precipitated twice in cold dried ether. The product was subsequently kept under nitrogen in a freezer in order to retard the degradation process. The molecular weights of the polymers, PEG 6000 and MAP, respectively, were determined by means of size exclusionchromatography with THF as solvent, for PEG Mw 10 000, Mw/M, = 1.05 and for the synthesized MAP Mw 9300, Mw/M,, = 1.1, Le., n = 200. Sodium dodecyl sulfate (SDS) from Fluka Chemie was recrystallized twice in ethanol before use. Surface tension measurements confirmed that no degradation products were present. a-deuterated SDS was synthesized in our laboratory as described in a previous work.30 Both types of SDS were kept in a refrigerator at 4 "C. Solutions for NMR measurements were prepared by weighing the dissolving MAP and SDS in water. Heavy water (as used as solvent in self-diffusion measurements) was purchased from Isotec Inc. (99.9%) while the source of deuterium-depleted water (as used in samples for spin relaxation measurements) was MSD Isotopes. The samples were shaken and then kept at room temperature for at least 12 h and thereafter in a refrigerator at least 24 h. They were finally equilibrated for at least 30 min at the measurement temperature (24.0 & 1.0 "C). All solutions were clear and homogeneous at room temperature. Methods. NMR Self-Diffusion. The NMR self-diffusion measurements, using the FT-PGSE method,31 were made on a JEOL FX-100 spectrometer equipped with a 5-mm 1H probe and a Bruker MSL 200 spectrometer equipped with a 10-mm shielded 'Hprobe. As for the JEOL spectrometer an internal field/ frequencylock was provided by the deuterons in the 2H20solvent. The gradient drivers for JEOL and MSL spectrometers were homemade (see ref 3 1 ) and produce gradients (g) in the range g= 10-50 mT/m. The gradient strength was calibrated by using literature data for water diffusion in ' H ~ 0 / ~ H 2mixtures.32The 0 experiments were made by varying the duration of the applied gradient pulses (6) from 20 to 260 ms at a constant radio frequency
--
Abrahmsh and Stilbs pulse interval ( 7 = A) of 300 ms. This observation time is consideredlong enough to prevent a variation of the self-diffusion coefficient (4) with the magnetic field gradient pulse interval.13.33 In this work the attenuation of the signal intensities from the ethylene oxide protons (6, = 3.75 ppm) of the polymer and from SDS terminal methyls (6, 0.9 ppm) were monitored. By using a nonlinear least-squares fitting proced~re,~' Oswas evaluated according to eqs 1-3. 2HSpin Relaxation. 2H spin relaxation measurements were made on a Bruker AM 400 operating at 61.4 and 30.72 MHz 2H frequency on a Bruker MSL 200 spectrometer. An iron magnet system was connected to the MSL system for acquiring data for deuterium frequencies between 2 and 13.8 MHz. Spin-lattice relaxation times (TI) were measured at 9-1 1 frequencies by the standard inversion recovery method, while the spin-spin relaxation time (T2)was measured at 30.72 MHz, and in some cases at still another frequency by using the Carr-Purcell-Meiboom-Gill method.
-
Methodology and Underlying Theory NMR Self-Diffusion. The FT-PGSE method can measure molecular motion by probing the change in the spin-echo attenuation in a pulsed magnetic field gradient." In case of a single diffusing species the attenuation of the signal intensities is given by34 1(6)/1(0) = exp(-kD,)
(1)
and by applying a nonlinear least-squares fitting procedure Ds can be e~aluated.~'Here I(6) denotes the signal intensity at the gradient duration 6, Z(0) the intensity in the absence of gradient, and k = (rg6)2(A- 6/3), where r represents the gyromagnetic ratio of 'H, g the gradient strength, 6 the pulse duration, and A the gradient pulse interval. As further described below, it was found that the echo decay for a range of samplescould not be well described by eq 1. Instead a stretched exponential:
was applied.7J3 In essence eq 2 takes system polydispersity into account and has the same form as the classical KohlrauschWilliams-Watts equation.3s A mean self-diffusion coefficient (Ds(mean)) may be obtained through the transformation (3) where I'(l/j3) represents the gamma function of 1/@. The parameter j3 thusdescribes the widthofthedistributionofdiffusion coefficients (0 < j3 < 1). For a monodisperse system j3 equals 1. In an early work a simpler approximation with regard to polydispersity was applied,14 and the amplitude attenuation was fitted to a double exponential yielding a fast and a slow diffusion coefficient for the free and the aggregated AP, respectively, since at that time the apparent aggregate polydispersity was suspected to originate from impurities or degradation products such as polymer molecules without hydrophobic end groups. Scaling Laws. At concentrations above the critical overlap concentration (c*) or above the critical molecular weight for entanglement (Mw*),i.e., in semidilute polymer solutions, socalled scaling laws can describe the mechanism of molecular transport in the system. Various theoretical expressions have been suggested. For polymers in good solvents de Gennes36.37 has proposed laws whereD, 0: and D, 0: N-*.O,whereas Douglas and H ~ b b a r dadvocate ~~ an expression describing spongelike motion of an amoeba type of aggregate giving Dsa N-2.3 to N-2.5. Here N represents the number of monomer units in the polymer and c the polymer concentration. An alternative, more general
The Journal of Physical Chemistry, Vol. 98, No. 25, 1994 6361
Polymer and SDS Aggregation in Aqueous Solution type of scaling law that is applicable to D, in polymer solutions in good solvents at all concentrations has been proposed by Phillies.39 This model has previously been used to describe selfdiffusion of APs.7.13 According to this model the diffusion coefficient is given by the following expression:
0.6
D, = Do exp(-arc")
0.4
which combined with another scaling lawM
D,
a CV(~)
m
(1)
(11)
0.2
results in
m
0
where DOrepresents the self-diffusion coefficient at the limit of zero concentration, y andf functions, a and Y scaling parameters, and n a coupling parameter that can be calculated according to Walderhaug et a1.7 The coupling parameter can be regarded as a measure of the coupling strength of an individual chain to its surroundings. *I4 Spin Relaxation. 2H spin relaxation rates are frequency dependent and given by the following general expres~ion:~' (4) 1 = -x2(3J(O) 3r2 R, = T2 40
+ 5J(00) + 2 4 2 0 , ) )
(5)
Here x represents the quadrupolar coupling constant, which was set to 181kHz in this study.42 The Larmor frequencyofdeuterium is represented by wo and the reduced spectral density function by J(o). Incontrast toR,, R~becomesmoresensitivetoslow motions due to the J(0) term. In the case of fast chemical exchange between an 'aggregated" and a "free" state-which normally applies for surfactants in micelles-all NMR parameters, including the self-diffusion coefficient (0,). become time-averaged according to the pertinent population in each domain: R , = PAR,,, + (1 -P,JRi,B
(6)
here R, represents the observed parameter, R,,A and Ri,B the corresponding parameter in each domain, the the relative population in domain A. In our case, as the total concentration of labeled SDS and polymer are considerably higher than the corresponding concentration of monomeric molecules, we have found it justified to ignore the spin relaxation contribution from the 'free" state. Two-step Model. The two-step model has previously been found to provide a good description of the motions of surfactant molecules in mi~elles.18-2~According to this model motions on two different time scales are responsible for the spin relaxation. The spectral density therefore becomes frequency dependent according to J(0) =
+
(1 - S2)P(O) S2S(W)
(7)
where J f ( w ) and E(w) represent the spectral densities of the fast and the slow motion, respectively, and S = l / 2 ( 3 cos 8 - 1 ) f is the local order parameter. Here 8 is the angle between the C-D vector and the normal of the surfactant aggregate and ( hdenotes that the average is taken over a time long enough to average over the fast motion and short enough that the average is not affected by the slow motion. Provided the fast and the slow motions can be described by single-exponential autocorrelation functions, the form of the
10
0
(111)
n *.(c))
20
30
Polymer concentratiod(weight9bin D,O)
Figure 1. MAP concentration dependence (weight percent polymer in D20)of the width of the self-diffusion coefficient distribution (8).
spectral density functions becomes
Pqw) =
27p 1
+ (W,f,s)Z
Here 72 represents the correlation time for the fast local reorientation of the C-D vector within the micelle from rotation around thecarbonarbon bond, torsional motions, and protrusion from the micellar surface.M The fast motions are generally found to fall within the extreme narrowing regime (UT: > Ds,bundreven a low fraction of SDS in the free state will considerably affect the measured mean value. However, it is unlikely that polymer addition should lead to an increased amount of SDS in the free state, causing increased observed self-diffusion coefficient. As for the polymer, the observed increase of Ds is probably due to an increased proportion of polymer adsorbed onto the fast diffusing micelles. As the self-diffusion of polymer is found to be described by a single Ds (i.e., (3 = l), either the amount of free polymer must be negligible or the chemical exchange between free polymer and polymer adsorbed onto the micellar surfaces must be fast on the pertinent NMR time scale (of the order of 300 ms in our experiments). At higher polymer concentrations the D, of MAP and SDS both do decrease with increased polymer concentration, and at concentrations higher than approximately 2% their D, coincide. At these concentrations, the main part of the polymer and surfactant molecules thus diffuse together, in what we believe to be mixed aggregates. Also the Ds of the polymer measured in SDS solutions and in water (zH20)are about the same, as shown in Figure 6. This would indicate that the same type of aggregates form in the solution, i.e., micelle-like aggregates containing one or several hydrophobic domains, as visualized in Figures 4 and 7. On the other hand, at low polymer concentrations, the D, in SDS solutions is higher, due to adsorption onto the more rapidly diffusing micelles. ZH Spin Relaxation in Mixed Aggregates. With Figure 4 in mind, the spin relaxation results of labeled SDS in mixed aggregates can also be understood. The initial steep increase of both correlation times (res and T;, see Figure 9) is probably due to the adsorption of the oxyethylene part of the MAP onto the micellar surface. Due to this adsorption-likeprocess, the rotation of the surfactants around the normal of the micellar surface as well as the lateral diffusion over the curved micellar surface are likely to become retarded. As a consequence, both 72 and ~ , d i f f increase. At higher polymer concentrations the surface of the
Polymer and SDS Aggregation in Aqueous Solution micelles becomes saturated with oxyethylene, and further addition of polymer will no longer affect these motions. However, at this polymer concentration level a retardation of the tumbling rate, described by ~ ~ should m , be the main reason for further increase of T ~ This ~ . further increase is likely to be due to the increased hydrodynamic radius of the aggregates produced by the oxyethylene chains that protrude into the solution. This radius is larger than the radius of the curved surface along which the molecules diffuse. From eq 11b it is obvious that such effects will have a strong influence on ~ ~ and m consequently , rea. An increased hydrodynamicradius is furthermore observed by other authors in studies of similar systems.16.22 It has been shown that the interaction between MAP and SDS are similar to ordinary PEO/SDS interaction at high relative SDS content.12.33Therefore, at low polymer concentrationsimilar results would probably be obtained with a nonmodified polymer as well. On the other hand, at higher polymer concentrations, when the micellar surface becomes saturated with polymers, links to other hydrophobicdomains could be established, leading to further increase in hydrodynamic radius of the mixed aggregate, as illustrated in lower part of Figure 4. This means that the hydrodynamic radii R in eqs 1l a and 1l b would not be identical. The radius in eq 1 l a would be the radius of the hydrophobic domain, whereas the radius in eq 11b would be the radius of the aggregate, containing several hydrophobic domains. If the diffusion of the SDS molecules over the curved surface of a hydrophobic domain is considered constant after the initial adsorption of polymer at low concentrations, further increase in upon further addition is due to an increase in the hydrodynamic radius of the aggregate according to eq 11b. This suggests that at even higher polymer concentrations,where the tumbling rate might be completely hindered, the slow correlation time would be equal to the correlation time describingthe diffusional motion at saturation grade. The second term in eq 10would then become negligible. However, in our measurements this point is not yet reached, i.e., the rCa has not attained a constant value (Figure 9). Finally, still some retardation of the slow motion could be due to increased viscosity in the surrounding solution as the polymer concentration increases, also influencing T ~ " . The aggregates will at high polymer concentration not move in an aqueous solution but rather in a "so1vent"consistingof other aggregateswith higher viscosity than water. The links formed between the hydrophobic domains, explaining both self-diffusion and spin relaxation data of mixed aggregates, do not necessarily have to be permanent; a transient system with links constantly building and breaking could very well be considered. These links could be inter- as well as intramolecular. At the relatively low molecular weight of the polymer studied, the probability of intramolcular association is probably close to the probability of intermolecular association. In a recent study on HEUR thickeners an increased viscosity in the solution is interpreted as being due to increased proportion of intermolecular association.& It was shown that a length of approximately 500 oxyethyleneunits is optimalin order toobtain the highest viscosity. Polymers with less than 500 oxyethylene units intramolecular associations are more abundant, whereas with more units the relative concentrationof hydrophobes (in constant weight percent studies) becomes to low. In addition, compuer modeling at our laboratory indicates that surfaces with attached polymer must be closer to each other than half of the extended chain length before bridging becomes important.47 If the chains are adsorbed to the surface, as they are to the micellar surface in our case, an even closer distanceshould be needed for bridging to becomeimportant. FiniteInfiNte Network? Considering a network formed in aqueous as well as in SDS solutions at high polymer concentrations, one notes that this network can not be infinite, at least not in presence of SDS. If an infinite network was to be formed, the slow motion of the SDS molecule in the mixed aggregate would
The Journal of Physical Chemistry, Vol. 98, No. 25, 1994 6365 not be isotropic and the two-step model would not suffice to describe the spin relaxation data. It has previously been found that for systems consisting of nonspherical aggregates or systems involving large aggregates, as for example infinite networks, the simple two-step model no longer applies to experimental data,Z7 since motions will become nonisotropic and slow motions will be present. In such systems even slower motions are present. A plausible explanation for the absence of a third step in our spin relaxation data, which would appear if a third very slow motion was present, is that themixed micelles in thisconcentration range experience a homogeneous and isotropic environment leading to an isotropic motion of the aggregate.2* One can, for example, imagine that the mixed aggregates experience the homogeneous environment of a network formed by aggregated polymer. However, this model is inconsistent with the fact that the polymer and the surfactant experience the same self-diffusion. On the other hand, the MAP in a huge network would experience a slower self-diffusionthan SDS and MAP in the mixed aggregate. From this reasoning we can exclude the possibility of an infinite dynamic network as proposed by Jenkins et al.48 The absence of a yield stress, which was observed by this group, would then be due to the fact that the network is finite and the shear thickening measured for certain AP systems would originate from the additionallinks between aggregates that are formed upon shear.49 However, the possibility that the mixed aggregates of MAP and SDS are large enough to contain more than one hydrophobic domain cannot be excluded, as was discussed in the previous section. The mixed aggregate could in fact be viewed as a finite network, which need not necessarily be spherical. With regard to the interpretation of our own data one should note that the two-step model gives a good description of the field dependence of the relaxation rates of spheroids, both prolate and oblate, of axial ratio up to 2.50 Aggregate and Polymer Motion. The model proposed by Douglas and Hubbard seems to be the most reasonable scaling model to describe this type of system.38 They model concentrated solutions of high molecular weight polymers through an ensemble of "amoeba-shapedl entangled chain regions, which rearrange in response to sustained stress. In this model, the diffusion coefficient molecular weight exponent in three dimensions is predicted to fall in the interval -2.3 to -2.5, including the value of -2.4 we observed for the pure MAP aggregates in water. In that case we suppose that the size of our aggregates increase with increased polymer concentration. Therefore a scaling law where Dsa Nu might give a more correct description of our system than a law of the type Dsa F . The model proposed by Nystrbm et al., on the other hand, is a model of empirical type, that through the coupling parameter (n) may assist describing the interaction phenomena.13 The coupling parameter increases as a decrease in D,is observed, as seen in Figures 2 and 3. Hence, an increase in aggregate size leads to an increase in the coupling between polymers in the aggregates. The concentrationdependenceof n can be compared with literature data,7J3leading to the conclusion that n increases steadily with concentration with about the same slope measured by these groups. The motion described by the scaling relations is the motion of the MAP aggregates or mixed aggregates. Diffusion measurements show that the main part of the MAP molecules move at the same speed as the main part of the SDS molecules in mixed solutions, i.e., SDS and MAP molecules move mainly together in mixed aggregates. Consequently, the aggregated SDS and MAP molecules are expected to undergo similar motions, at the same rate, like overall tumbling and local reorientations of the C-D vector. This is indeed observed for MAP molecules both in mixed and pure aggregates. Both polymer and surfactant undergo fast motions on the 10-11-s time scale and slow motions on the 10-9-l W-stime scale. In addition, the polymer doesappear
6366 The Journal of Physical Chemistry, Vol. 98, No. 25, 1994 to undergo an additional very slow motion on the 10% time scale. We propose that this additional slow motion is a reptational or exchange motion of the polymer, inside or between aggregates. Since an interpretation along the lines above was the obvious choice on physicochemical grounds, no attempt was made to interpret the spin relaxation data of labeled MAP with the type of models often used to describe motions of linear nonmodified polymers.28~51 Alternatively, for example, the so-called model-free approach, which has often been used to interpet spin relaxation data for flexible macromolecules, could be employed.2s In this model the total correlation function is factorized into a product of overall and internal correlation functions. This factorization is exact for isotropic rotation and independent motions, and it has proved to be a good approximation also in the anisotropic case. However, the origin of the calculated correlation times is not considered within this model. Horii et al.sl have taken the interpretation of their spin relaxation data one step further. For PMMA in CDCl3 13C spin relaxation were measured and various models tested. For the chosen model motions of the polymer chain with the correlation times of the orders of 10-12, 10-10, and 10-9 s were evaluated and assumed to originate from diffusional rotation, libational motion in a cone, and isotropic random reorientation of the chain, respectively. These motions are not on the same time scaleas those discussed aboveand furthermore do not describe the motions that the end group undergo. As the motion fo the end group, in and between aggregates, bears more resemblance to the normal surfactant motion discussed above, these models can probably not be directly applied here. Anomalous Polymer Self-Diffusion at High Concentrations. Finally it should be noted that an observation during the study of this systems is an increase of the self-diffusion coefficient as a function of polymer concentration, at high polymer concentrations (30% for pure MAP in water and 10% for MAP in mixed aggregates, not presented), a phenomena observed also by 0thers.~J4952 We interpret this increase in terms of a change in the very nature of the diffusion process. A change from a pure micellar structure to a cubic liquid crystalline structure could be possible. For MAPS of molecular weight 2000 and 4000 g/mol, X-ray studies show that a cubic (simple or body centered) structure is present at polymer concentrationsabove approximately 25%.53 In such concentrated systems the hopping of polymers between aggregates could be considered. A hydrophobic core of a micelle consisting of SDS and MAP hydrophobes or only MAP hydrophobes can be imagined. At a certain polymer concentration this core might be filled, i.e., the hydrophobic domain reaches an asymptotic aggregation number. If the hydrophobic domains then are sufficiently close to each other to permit links between different cores, the nexCeSSnMAPendgroups, whichcannot beincorporated into in the hydrophobic domain, could jump from domain to domain at a speed much faster than the original aggregate motion. As the aggregate motion becomes slower, at high polymer concentration, this motion might be dominant. This type of intermicellar exchange is discussed, among others, by Phillies and Kato.54.55 Another possible explanation as to why an increase in selfdiffusion is observed is that the coiled dimension of the aggregate being observed becomes larger than the random walk distance, Le., R2 > 2 D ~ . ~In~that 9 ~case ~ the PGSE experiment will not record the true center-of mass motion, the measured self-diffusion coefficientwill contain (probablynon-Fickian)contributionsfrom segmental mechanisms, includingcooperativerotations and gellike motions.
Conclusions Increased concentration of MAP leads to an increased width of the aggregate size distribution. At concentrations higher than
Abrahmstn and Stilbs a critical concentration (c*), when the mean aggregate size has reached the critical molecular weight for entanglement (Mw*), the self-diffusion coefficient decreases dramatically. However, the addition of polymer to solutions of high SDS concentrations (4 wt 5% of aqueous phase) leads to more monodisperse mixed aggregatesthan for MAPin aqueous solution. SDS micelles thus act as seeds for the MAP aggregation. At concentrations of MAP c 1 2% the SDS and MAP molecules diffuse mainly together in mixed aggregates. A two-step motional model well describes the motion of surfactant molecules in mixed aggregates. The fast local motion of the surfactant in the aggregate is influenced by the addition of polymer only at low polymer concentrations. On the other hand, the slow isotropic motion, composed of aggregate tumbling and lateral diffusion of the surfactant molecule over the curved surface of the hydrophobic domain, is considerably retarded with increased polymer concentrationin the whole concentrationrange. The lateral diffusion of the surfactant molecule is probably almost totally hindered due to addition of polymers that adsorb at the micellar surface. The isotropic rotational tumbling of the aggregates is retarded markedly at increased polymer concentration due to the increased mixed aggregate size and probably also to some extent due to increased viscosity of the surrounding solution. In binary polymer/water solutions like in ternary solutions also containing surfactant the motion of the polymer is described by a model taking motions on three time scales into account. The polymer experiences fast and slow motions on the same time scales as those of surfactant molecules in the mixed aggregates. An additional very slow motion is experienced exclusively by the polymer. It is presumably related to exchange or reptational motion of the polymer inside or between aggregates.
Acknowledgment. This work was supported by the Swedish National Board for Industrial and Technical Development (NUTEK) and Swedish National Sciences Research Council (NFR). Dr. Ann-Charlotte Hellgren is thanked for skilled MAP synthesis work and Dr. Ulf Henriksson and Maria TBrnblom for practical assistance and valuable discussionsin the field of NMR. References and Notes (1) Fonnum, G. Ph.D. Thesis, The Norwegian Institute of Technology, Trondheim, Norway, 1989. (2) Jenkins,R. D. Ph.D.Thesis,Lehigh University, Bethlehem, PA, 1990. (3) Maechlin-Strasser,C.; Franpis, J.; Clouet, F.; Tripette, C. Polymer 1992, 33, 621. (4) Maechlin-Strasser,C.; Franpis, J.; Clouet, F.;Tripette, C. Polymer 1992, 33, 1021. (5) Binana-Limbele, W.; Clouet, F.; Franpis, J. Colloid Polym. Sci. 1993, 271, 8. (6) Binana-Limbele, W.; Clouet, F.; Franpis, J. Colloid Polym. Sci., submitted. (7) Walderhaug, H.; Hansen, F. K.; Abrahmsh, S.;Persson, K.; Stilbs, P. J. Phys. Chem. 1993, 97,1143. ( 8 ) Huldh, M. Colloids Surf., in press. (9) Thibenault, J. H.; Sperry, P. R.;Schaller,E. J. ACSAdu. Chem.Ser. 213; Glass, J. E., Ed.;American Chemical Societv: Washington DC., 1986, Chapter 20. (10) Bielmann, J. H.; Riesthuis, F. J. J.; van den Velden, P. M. Polym. Paints Colours J . 1986, 176 (4189), 455. (1 1) Richey, B.; Kirk, A. B.; Eisenhart, E. K.; Fitswater, S.;Hook, J. W. J. J . Coar. Technol. 1991, 63 (798), 31. (12) Lindblad, C.; Almgren, M.; Persson, K.; Abrahmstn, S.; Stilba, P.; Walderhaug, H. Colloid Polym. Sci., manuscript in preparation. (1 3) Nystrbm, B.; Walderhaug, H.; Hansen, F. K. J . Phys. Chem. 1993, 97., 8336. ..~. (14) Persson, K.; Abrahmsh, S.;Stilbs, P.; Walderhaug, H.; Hansen, F. K. Colloid Polym. Sei. 1992, 270, 465. (15) Cabane, B. J . Phys. Chem. 1977, 81, 1639. (16) Mast, A. P.; Prud'homme, R. K.;Glass, J. E. Langmulr 1993,9,108. (17) Emmons, D. S.;Stevens, T. E.. US Patent 4 155 892, Rohm & Haas co., 1979. (18) Henriksson, U.; Jonstrbmer, M.; Olsson, U.;Werman, 0.;Klose, G. J. Phys. Chem. 1991,95, 3815. (19) Sjbbcrg, M.; Henriksson, U.;Wirnheim, T. Lungmuir 1990,6,1205. Olsson, U. J. Phys. Chem. 1987,92, (20) SBderman, 0.;Henriksson, U,; 116.
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