J. Phys. Chem. 1996, 100, 6691-6697
6691
Water Self-Diffusion in Aqueous Associative Polymer Solutions Susanna Abrahmse´ n-Alami and Peter Stilbs* Physical Chemistry, The Royal Institute of Technology, S-100 44 Stockholm, Sweden
Elouafi Alami Department of Physical Chemistry, Uppsala UniVersity, P.O.B 532, S-751 21 Uppsala, Sweden ReceiVed: October 9, 1995; In Final Form: December 14, 1995X
Water self-diffusion in aqueous model associative polymer (AP) solutions, hydrophobically end-capped poly(ethylene oxide), C12EO200C12 (AP9,) and C12EO90C12 (AP4), has been studied with the NMR-PGSE method and compared to the diffusion in nonmodified poly(ethylene oxide) PEO. It was found that it decreases monotonically with increasing polymer concentration, giving Di/D0 ≈ 0.2 at 50 wt % (D0 being the water self-diffusion coefficient in the absence of polymer), independently of polymer molecular weight and modification. In further evaluation of the data, the cell-diffusion model was used. Such an analysis suggests that up to a polymer content of about 2 wt % AP9, water diffusion is not significantly affected by the polymer. Above this concentration, up to about 10 water molecules per EO group are affected in AP9 and AP4 solutions. On increasing the temperature, water self-diffusion increases, following an Arrhenius-like equation, with Ea equal to that of pure water at low polymer content (10 wt %). The activation energy increases with polymer content, and at 50 wt %, Ea is about 30 kJ/mol, independently of polymer type. A minor difference in Ea between AP4 and AP9 solutions at intermediate polymer content is likely to originate from the ability of AP4 to form well-developed cubic phase structures. An increase in temperature was found to lead to a slight dehydration of the associative polymer EO monomers closest to the hydrophobic core.
Introduction Transport of small molecules in polymer solutions is central in many technical and pharmaceutical processes, for example as a rate-determining step for drug delivery. Solvent diffusion, in particular, has been experimentally studied in many types of polymer surfactant solutions.1-4 There the polymer and the surfactant aggregates are simply viewed as stationary obstruction units about which the solvent must diffuse, and the timeaveraged self-diffusion of the solvent will hence be reduced. In addition to obstruction the polymer or surfactant may have specific interactions with the solvent, like hydration or hydrogen bonding, which also may reduce the self-diffusion coefficient. Aqueous associative polymer (AP) solutions, like the hydrophobically end-capped oxyethylenes studied here, have in recent years attracted wide interest, both in commercial and fundamental research. At this point it is therefore interesting to deduce how the water self-diffusion in these systems varies with polymer concentration and temperature. The major technical application of APs is rheology control in water-based surface coatings. It is generally believed that the rheological effects of APs originate from assembly of their end-groups into micelle-like aggregates at low concentration and a gradual formation of network structures at higher concentration. Numerous investigations have been carried out, in order to obtain information about the association mechanism and about the aggregate size, shape, and internal structure.5-23 At elevated concentrations the AP systems have also been found to form liquid crystalline structures, simple cubics or bodycentered cubics, provided the AP molecular mass is sufficiently low, Mw < 6000.21,23 In the present work, water self-diffusion in solutions of model associative polymers of the form C12EOyC12, with y ) 200 * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, March 15, 1996.
0022-3654/96/20100-6691$12.00/0
(AP9) and 90 (AP4), was studied and compared with the diffusion in a nonmodified poly(ethylene oxide). In the interpretation of the data, the cell-diffusion model was used, which takes obstruction as well as hydration into account.24 This model has previously been used for evaluating water diffusion data in aqueous nonionic surfactant and block copolymer solutions.1-3 Experimental Section Materials. The model associative polymers used in this study have the following simple chemical structure:
C12H25O(-CH2CH2O-)nC12H25 with n equal to about 90 (AP4) and 200 (AP9), respectively. They were synthesized according to Alami et al.21 and Abrahmse´n-Alami et al.,13 respectively, and were characterized by size exclusion chromatography, using THF as solvent. The dispersity index of these polymers was found to be low (Mw/Mn < 1.1) and their molecular weights (Mw) were determined to be 4600 and 9300, respectively, hence the notation AP4 and AP9. A nonmodified analogue, that was used for comparative studies was denoted PEO10 (Mw ) 104). The degree of substitution of the terminal hydroxyl groups of the modified polymers was determined by 13C and 1H NMR measurements and UV spectroscopy and ranged from 80 to 95%.13,23 Samples for NMR self-diffusion measurements were prepared by using a combination of 10 wt % D2O (Isotec Inc., 99.9%) and 90 wt % deionized water. D2O was included for providing an internal NMR field/frequency lock signal. For equilibration all samples were always slowly stirred at least overnight before use. To provide perfect mixing, the most concentrated samples were first equilibrated for about 1 h at 50 °C. Unless indicated, all solutions were clear and homogeneous at the measurement temperature, which was 25 °C when not otherwise indicated. © 1996 American Chemical Society
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Methods. The NMR self-diffusion measurements were performed using the Fourier transform pulsed-gradient spinecho (FT-PGSE) NMR technique.25 A Bruker MSL200 spectrometer, equipped with a 10 mm shielded 1H probe was used, and the stimulated echo26 was employed for the determination of water (H2O) self-diffusion. The attenuation of the spin-echo amplitude after Fourier transformation was sampled as a function of the duration of the applied gradient pulses (0.2 < δ < 10 ms). The gradient pulse interval, ∆, was kept constant at 140 and its magnitude G (0.05 to 2.2 T m-1) was varied. Field gradient calibration was carried out by the use of known selfdiffusion standards (H2O/D2O mixtures).27 The first rf pulse interval, τ1, was fixed at 20 ms during the experiments to keep spin-spin relaxation effects on the echo amplitude to a minimum. The second rf pulse interval, τ2, was equal to ∆ - τ1. The FT-PGSE method measures molecular motion by probing the change in the spin-echo attenuation in a pulsed field gradient.25 For molecules undergoing unhindered Brownian motion, and for single diffusing species, the attenuation of the signal intensities is given by
Ii/Ii(0) ) exp(-kDi)
(1)
Here k ) (γGδ)2(∆ - δ/3), where γ represents the magnetogyric ratio of the nucleus under observation (in this case 1H) and Di the self-diffusion coefficient for species “ i ”. For systems displaying a distribution of self-diffusion coefficients, a stretched exponential can be used in the analysis of experimental data,12-14,22,28,29
Ii/Ii(0) ) exp(-(kDi)β)
(2a)
In essence eq 2a takes system polydispersity into account and has the same form as the classical KWW equation.26 A mean self-diffusion coefficient can be obtained through the transformation
Di(mean) ) Di(app)/(1/βΓ(1/β))
(2b)
where Γ(1/β) represents the gamma function of (1/β) . The parameter β thus describes the width of the distribution of diffusion coefficients (0 < β < 1). For a monodisperse system β equals 1 and eq 2a converges to eq 1. However, experimental noise and low-quality data can also result in β values artificially shifted from 1. Results In Figure 1 the reduced water (1H2O) self-diffusion (normalized to the self-diffusion coefficient of water in the absence of polymer) in AP9, AP4, and PEO10 solutions is presented as a function of the total volume fraction of EO segments (φEO) in the solution. Contrary to the diffusion data for the APs themselves,11-14,22,28-30 no experimentally significant polydispersity in the water diffusion was observed for any sample. For AP4 water self-diffusion is only measured down to 15 wt %, as the solution is phase separated below about 20 wt %.23 It should be noted that the diffusion at this content (15 wt % AP4) was measured in the polymer-rich phase of a phase-separated sample. Also included in the Figure 1 is the empirical function of Jonstro¨mer et al., describing water diffusion in PEO solutions.2 As seen, Di/D0 decreases monotonically with increasing polymer concentration, and the differences between the polymers are relatively small. At 50 wt %, Di/D0 has decreased to about 0.2 in all polymer solutions. Notably we observe no abrupt change of Di/D0 in a cubic phase of AP4 solutions.
Figure 1. Reduced self-diffusion coefficient of H2O, Di/D0, in AP4 (0), AP9 (9) and PEO10 (O) polymer solutions as a function of the total volume fraction of EO segments (φEO), together with the empirical function used to describe water diffusion in PEO solutions.1,2
TABLE 1: Evaluated Apparent Activation Energies, Ea, for Water Self-Diffusion in AP4, AP9, and PEO10 AP4
AP9
PEO10
c (wt %) Ea (kJ/mol) c (wt %) Ea (kJ/mol) c (wt %) Ea (kJ/mol)
21.8
22.16
50.3
27.1
2.0 10.0 19.8 28.5 48.4
17.4 17.7 18.5 19.8 29.6
19.8
19.0
42.4
26.0
Water diffusion increases with increased temperature. In particular, the variation of water self-diffusion with temperature follows an Arrhenius-like equation, Di ) A exp(-Ea/RT). Ea varies with type of polymer and with concentration, as presented in Table 1. The activation energy for water diffusion in pure water has previously been reported to be 17.6 kJ/mol.31 The activation energy for water diffusion in AP solutions equals that of pure water at low polymer content (e10 wt % AP9) but increases with further increased polymer concentration. At 20 wt % it is slightly higher in AP4 solutions than in solutions of AP9 and PEO10. At high polymer concentration (above about 40 wt %), on the other hand, there is no detectable difference between the experimental activation energies. Discussion The Cell-Diffusion Model. It is generally found that the diffusion of small molecules in a polymeric system is only marginally affected by the presence of polymers, even at quite high polymer concentrations.2,3,32 This seems to be valid for the present system as well, as demonstrated in Figure 1. Water self-diffusion remains at a high level even at high polymer content (Di/D0 ) 0.4 at 40 wt %) for the modified as well as for the nonmodified polymers. The observed self-diffusion coefficient is lower than that of neat water, however. The so-called cell-diffusion model assumes that this decrease is due to the combined effect of obstruction and hydration of the aggregates. This theoretical model was developed some years ago by Jo¨nsson et al.24 and simulates a system of fixed particles, among which the solvent molecules can diffuse. The model takes the shape and the concentration of the particles into account and also considers specific interactions between solvent molecules and particles. The key element of the cell model is the widely used concept of dividing a macroscopic system into smaller cells. However, contrary to many other applications of the cell model, the cell-diffusion model considers a flow of the molecules within the system. In the model the effective diffusion coefficient, Dieff, for species i diffusing in a system of spherical cells is given by
Water Self-Diffusion in Aqueous Polymer Solutions
Dieff )
Di(R) Ci(R) Ui(R) 〈Ci〉
J. Phys. Chem., Vol. 100, No. 16, 1996 6693
(3)
where R represents the cell radius, and Di(R) and Ci(R) are the diffusion coefficient and the concentration of i at the cell boundary, respectively. 〈Ci〉 represents the average cell concentration. Ui(R) is a function which at the radius r of the cell is determined from eq 4.
∂Ui ∂ ) (1 - Ui)(2 + Ui) - rUi {ln(Di(r) Ci(r))} (4) r ∂r ∂r where Ui(r) Di(r) Ci(r) is a continuous function for all r and Ui(0) ) 1. For other spheroidial geometries like prolate (rodlike) or oblate (disklike) ellipsoids, similar but slightly more complex equations can be derived.24 An effective self-diffusion coefficient of component i can be obtained from eq 3 for any DiCi profile, but for simplicity, only the step function profiles will be considered here. In this case DiCi is constant with different values in the various regions of the cells. For a two-region cell,
{
DC Di(r) Ci(r) ) D1C1 2 2
rb
(5)
b being the radius of the inner region of the cell. Ui(R) is given by
Ui(R) )
1 - βφ 1 + βφ/2
(6)
where
φ ) b3/R3
(7)
D2C2 - D1C1 D2C2 + D1C1/2
(8)
and
β)
The two-region model is really an oversimplified model of the water-polymer systems studied here. Part of the solvent molecules will interact with the hydrophilic groups of the polymer and thus do not behave as in the bulk solution. Therefore, a third region, representing the head-group shell must be introduced, Figure 2. In conclusion, this model has the advantage of making it possible to take into account the mobility of the solvent molecules in the head-group region of the aggregates, here denoted palisade layer. In addition, the finite diffusion of the aggregates (cells) is taken into account. Assuming a spherical symmetry for the AP aggregates of the present study, it is possible to calculate the water self-diffusion by subdividing each cell into the three regions, as depicted in Figure 2. Even if the aggregates not are spherical, scattering studies indicate that the hydrodynamic microdomains are more or less spherical, even at very high AP concentration.21,23 This assumption can therefore be made without introducing any serious error.24 As a first approximation, the aggregates (cells) of the present study are assumed to consist of a hydrocarbon core, surrounded by a PEO palisade, and at low AP concentration further surrounded by free, bulk, water of concentration C2 diffusing with a diffusion coefficient D2. The hydrocarbon core is assumed to be completely expelled from water, whereas the palisade layer is characterized by an average water concentration, C1 or Cx, and an average diffusion coefficient, D1 or
Figure 2. Two-dimensional cut through the cell described in the text. The central region represents the hydrocarbon core, which is assumed to be unsolvated. The intermediate area represents the palisade layer, while the last area represents the bulk solution. Also shown is the assumed concentration profile for the solvent.
Dpalisade. In the calculation, D2 is set as constant and equal to the water self-diffusion in the absence of polymer. Moreover, the micelles can be assumed to be immobile (Dmic ≈ 10-13 m2/ s), since the polymer diffusion is so much slower than that of water (D0 ≈ 10-9 m2/s). No assumptions are needed for the aggregation number of the micelles, since the calculations are based on volume fractions. For this purpose we need to know the volume of the water molecule (taken to be 30 Å3) and of the EO chains (13 600 and 6000 Å3 for AP9 and AP4, respectively). These values are based on the density of PEO in its amorphous state (1.1 g/cm3). In the crystalline state the value is slightly higher, 1.2 g/cm3 .33 It is more justified to refer to the amorphous state, as the crystallinity of the EO chain in solutions of APs has been found to be rather low.23 The volume of the two hydrocarbon parts of the AP is taken as 700 Å3, as calculated with F ) 0.8 g/cm3.34 The approach also uses the self-diffusion coefficient of water in nonmodified PEO10 at one concentration, together with one data point for the PEO diffusion evaluated from the empirical formula of Jonstro¨mer et al.2 The concentration of nonaggregated AP in the bulk was taken as the cac (critical aggregation concentration, cac ) 1.4 × 10-5 M) value as determined by static fluorescence (Lindblad, personal communication) and microcalorimetry.14 In selfdiffusion studies, the hydration is defined as the number of water molecules effectively moving with the AP aggregates as kinetic entity (Cx ) C1 ) number of H2O/EO monomer), i.e. the amount of water in the palisade layer. Contrary to some previous studies,1,3 the present cell-diffusion model does not suppose the hydrated state to be a “bound”, completely immobilized, state. Water is allowed to move in the palisade layer, like water in a solution of PEO at the same concentration (H2O/EO monomer). A similar modeling approach successfully described water diffusion in C12En water systems.2 The Amount of Water in the Palisade Layer, Cx. An analysis of the self-diffusion data as a function of polymer content is presented in Figure 3a,b for AP9 and AP4, respectively. The reduced self-diffusion coefficient Di/D0 is shown as a function of polymer concentration, together with calculated values at different values of Cx (H2O/EO in palisade layer). As observed, pure obstruction effects (Cx ) 0) do not suffice for explaining the concentration dependence of the water diffusion. In the low AP9 content range (below 2 wt %) the measured Di is about the same as in pure water. In the intermediate polymer content region 2-15 wt %, on the other hand, the measured self-diffusion coefficient typically suggests that the concentration of water in the palisade layer can be as high as 10 water molecules per EO group (Cx ) 0-10). As the hydrogenbonding capacity of EO is two water molecules (each oxygen has two free electron pairs), such a high hydration number
6694 J. Phys. Chem., Vol. 100, No. 16, 1996
Figure 3. Experimental reduced water self-diffusion coefficients, Di/ D0, as a function of polymer content and the predictions from the celldiffusion model at various amounts of water in the palisade layer (Cx). D0 represents the self-diffusion coefficient in neat water at the experimental temperature: (a) AP9 and (b) AP4. The lines represent, from the filled one and downward, Cx ) 0, 2, 4, 8, and 16 water molecules/EO monomer, respectively.
implies structured water as well as hydrogen bonding. The high values of Cx are consistent with those found in nonionic surfactant systems (8-9).2 However, as the cell-diffusion model provides the amount of water per head group, which is rather large for the AP, the estimated absolute value of the amount of water in the palisade layer is rather approximate. At higher polymer (AP9 and AP4) content, the experimental water self-diffusion coefficient is close to, but slightly lower than, the predicted value by the cell-diffusion model when all water is affected by EO. This means that no free water is present; that is, the palisade layer extends through the entire solution. This condition is represented by the lowest curve in Figure 3a,b, at the point where the lines merge. Some early studies1,3 considered the water molecules to be completely immobilized in the palisade layer. Such a model could explain the observed differences between experimental values and values predicted from the cell-diffusion model. A lowest amount of hydration water of about two to four water molecules per EO group can be estimated for AP9 solutions using this model.24 However, Jonstro¨mer et al.2 showed that modeling completely immobilized water is not realistic. The deviations in this region are therefore suggested to be within experimental error. Nevertheless, the two-region model (water in palisade layer
Abrahmse´n-Alami et al. and bulk water) does not provide a completely satisfactory description of the system. One cannot explain the very low experimental water self-diffusion coefficients at very high polymer content. The difference could be either due to experimental errors, as suggested above, or due to the fact that the concentration of water in the palisade layer near the hydrophobic core is lower. To extend the applicability of the cell-diffusion model, a distribution of water molecules in the palisade layer could be invoked. Due to sterical constraints, one can assume that that the concentration of water is lower in the EO part closest to the hydrophobic domain. Microcalorimetry measurements do in fact indicate an extensive dehydration of the EO segments close to the core upon micellation of APs.35 Therefore, the palisade layer can be divided in two: an inner and an outer region. A more correct model would assume a continuous distribution of water concentration over the EO part of the solution. A concentration profile like that of Scheujtens and Fleer36 could be used. However, such an analysis is outside the scope of the present study, and a division of the EO part in two is considered as being a satisfactory description of the system. In the high polymer content region, where no free bulk water is present, the three regions according to Figure 2 will then result, albeit with different values of Ci and Di. Water was presumed to diffuse as in nonmodified PEO in both palisade regions, but the concentration (H2O/EO) in each region was varied. Also, the concentration in the inner part was constant (Cxi), upon AP concentration increase, until the concentration in the outer part (Cxu) had decreased to the same value. Such an approach satisfactorily described the water diffusion in nonionic surfactant systems.2 However, the very low self-diffusion coefficients observed here are inconsistent with such a model. The second cell-diffusion model does not describe the concentration dependence of the water diffusion in this particular system any better than the first. This test does in fact indicate that the volume fraction of EO chains close to a hydrophobic/hydrophilic interface, which should contain less water, is too small to give any contribution. All water must therefore be considered to be influenced by the EO chains in the high-concentration region, and the deviations between experimental and calculated points must be within experimental error, Vide infra. In the low-concentration region the water selfdiffusion data are not sufficiently accurate for testing this second model. Water self-diffusion in AP4 (Figure 3b) essentially shows the same behavior as in AP9 solutions, even though the former forms a cubic phase structure in the studied concentration interval. It also is interesting to note that the dramatic decrease of the AP9 water self-diffusion coefficients does not seem to be coupled to similar changes in water diffusion rates. As shown in Figure 4, a dramatic decrease in water diffusion is instead observed at about the critical overlap concentration, c*, of the parent PEO. This has been calculated to be about 4 wt %.21 This observation is another indication that it is mainly the EO part of the AP that influences the water diffusion and that below c* of the PEO water is almost unaffected by the polymer. The clustering of the AP molecules themselves through the hydrophobic ends and the formation of a cubic phase structure will not influence the water diffusion. Again, water diffusion depends mainly on the total EO concentration and is independent of the solution structure. The Temperature Dependence of Water Diffusion and Cx. The temperature dependence of water self-diffusion in AP solutions increases with increased temperature and follows an Arrhenius behavior. In agreement with the self-diffusion
Water Self-Diffusion in Aqueous Polymer Solutions
Figure 4. Comparison between the reduced self-diffusion coefficients for AP9 (b) and PEO10 (O), and H2O in a AP9 solution (2), as normalized to the diffusion coefficient at infinite dilution, Di(0) and D0(0), respectively.
coefficients, the absolute values of the apparent activation energies, Ea, seem marginally influenced by the polymer solution structure, Table 1. At moderate polymer concentrations (20 wt %) Ea was, however, found to be slightly higher in the AP4 solution, which could be attributed to the cubic phase structure. The reason could be that even though no more water is affected by the polymer in this solution, as compared to AP9 and PEO, the water could be more tightly bound. Differential scanning calorimetry actually indicates an extensive amount of bound, nonfreezing, water in the cubic phase of an AP2 polymer (Mw ) 2600) solution.23 Malmsten et al. assumed water to be completely immobilized in the palisade layer.3 A more tightly bounded state would result in a Dpalisade/D0 even closer to zero, leading to a lower probable amount of H2O in the palisade. However, as discussed in the previous section, a picture where water is considered to move in the palisade as in a PEO solution is likely to be more realistic. For polymer AP9, on the other hand, the Ea’s do not seem to differ significantly from that of the parent PEO. In the high polymer concentration range, the differences between the Ea’s of the three polymers are smaller. Water no longer experiences an inhomogeneous environment of clusters, but rather a concentrated and more homogeneous environment of EO chains. A temperature increase often leads to dehydration of polymers or surfactants in aqueous solution, as has previously been quantified for certain EO- and PO-containing block polymers and surfactants.1-3,37-41 Activation energies for water in PEO can be utilized for calculating the water self-diffusion at various temperatures. These, in turn, can be used directly in the celldiffusion model to calculate Cx (H2O/EO) as a function of temperature, i.e. the dehydration, in a particular AP solution. The temperature dependence of the hydration (Cx) in solutions of AP9 at two different compositions and at one of AP4 is presented in Figure 5. As seen, a slight dehydration is observed upon a temperature increase, and it is most pronounced at lower polymer contents. At higher polymer contents the Cx value is already very low at 25 °C. Increased temperature probably alters the cac value and the diffusion coefficient of AP unimer in pure solvent. However, this was found not to influence the Cx value. Wanka et al.37 have found dehydration effects that coincide with the melting of the poly(propylene oxide) chain in pluronics copolymers. Dehydration in the present study seems to be a continuous function of temperature and not correlated with a melting of the EO chain, however. Instead, the lower value of Cx at higher temperatures is a consequence of the strong temperature dependence of the EO-water interaction.42 For nonionic surfactants, dehydration with increasing temperature is accompanied by a change in the liquid crystalline phase
J. Phys. Chem., Vol. 100, No. 16, 1996 6695
Figure 5. Temperature dependence of the amount of water in the palisade layer, Cx in a solution of AP9 at 20 wt % (b), and 48 wt % (O), and a 21 wt % solution of AP4 (9).
structure.39 The polymers in the present study do have large head groups, which are strongly hydrated in the whole temperature range. This results in particularly stable spherical hydrophobic domains,39 and the change in phase structure, as observed for nonionic surfactants upon a temperature increase, is therefore not observed.23 The dehydration can be considered to be confined to the inner region of the palisade layer, in favor of the outer. Jonstro¨mer et al.2 have previously observed that the dehydration of nonionic surfactant micelles starts near the hydrophobic surface of the micelle. Using the modified cell-diffusion model (Vide infra), it can be shown that an increase in temperature leads to a dehydration of the inner part of the palisade layer. Figure 6 a-d presents the concentration of an inner region (Cxi), at different relative volumes of the inner and outer region (Vi:Vu), as a function of temperature. The concentration of water in the outer region (Cxu) was held constant at the maximum value observed at 25 °C (Cxu ) 10.3 H2O/EO for 21 wt % and 4.6 for 38 wt % AP4, and Cxu ) 10.4 and 2.9 H2O/EO for 20 and 49 wt % AP9). Figure 6 clearly shows that the dehydration starts in the inner region of the palisade layer, closest to the hydrophobic core. However, the distinction of the volumes of the inner and outer regions is subtle, and the indications are therefore qualitative. To determine the dehydration quantitatively, the results from this study must be compared to absolute values of the hydration at some temperatures. It is not probable, however, that the inner region is completely expelled from water even at the highest temperature in this study. To achieve a realistic comparison of the AP4 and AP9, systems the same amount of EO monomers in the inner region for the two polymers should be chosen. The line at a relative volume 1:5 for AP4 is equivalent to the line at 1:13.3 for AP9. As observed, the same general feature prevails. From the discussion above, it is evident that the spherical core-palisade model is a very simple model for the AP systems. However, although a more advanced model would provide a more detailed and realistic picture of the system, it is not likely to provide any additional information on the state of hydration. Water diffusion depends only weakly on the AP solution structure. It is instead more dependent on the absolute concentration of the EO monomers of the associative polymer. Conclusions The present results indicate that the hydration of the EO groups is very much system-independent. It was found to be governed only by temperature and the concentration of EO groups in the system.
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Figure 6. Temperature dependence of the amount of water in the inner palisade region (Cxi) when the concentration in the outer region (Cxu) is kept constant at the maximum value observed at 25 °C: (a) AP9 at 20 wt %, (b) a 21 wt % solution of AP4, (c) AP9 at 48 wt %, and (d) a 49 wt % solution of AP4, with various relative volumes in the inner and outer region, Vxi:Vxu, ) (b) 0:1, (4) 1:1, (O) 1:2, (0) 1:3, (3) 1:5, (]) 1:13.3, respectively.
Modeling of the water self-diffusion data through the celldiffusion model suggests that up to 10 water molecules per EO group are affected in AP solutions. As water self-diffusion in these systems is mainly determined by the total EO concentration in the solution, it is unaffected by the AP molecules below the critical overlap concentration of the parent PEO. Clustering of the AP9 molecules, which occurs below this concentration, and the formation of the cubic phase structure in AP4 solutions do not influence the water self-diffusion to any significant extent. Upon increased temperature, water self-diffusion increases and follows an Arrhenius-like equation, with Ea equal to that of pure water at low polymer content (10 wt %). Ea increases with polymer content, and at intermediate polymer content (20 wt %) Ea in AP4 solutions deviates slightly from that of AP9 and PEO10 solutions. This small difference could originate from the ability of AP4 to form well-developed cubic phase structures. Increased temperature does affect the amount of hydrated water, which decreases with temperature, and more so at a lower polymer content. The dehydration was found to be continuous as a function of temperature and is likely to primarily be a dehydration of the EO chains closest to the hydrophobic domain. Acknowledgment. The work was financially supported by the Swedish Natural Science Research Council, NFR. Dr. B. Jo¨nsson is thanked for valuable discussions and for putting the cell-diffusion computer program at our disposal. Dr. A.-C. Hellgren, F. Isel, and Dr. G. Beinert are acknowledged for skillful synthesis work.
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