Electrostatic and Hydrophobic Interactions in NaCMC Aqueous Solutions: Effect of Degree of Substitution

The rheology of water-soluble polyelectrolytes at intermediate and high concentrations is controlled by entanglement, hydrophobic, and electrostatic interactions, whose influences are difficult to isolate. We investigate the rheology of semidilute solutions of sodium carboxymethyl cellulose (NaCMC) with molecular weight Mw ≃ 2.5 × 10 g/ mol and varying degree of substitution (DS) as a function of polymer concentration in various solvent media: salt-free water (long-ranged electrostatic interactions), 0.5 M aqueous NaCl (screened electrostatics), and 0.5 M aqueous NaOH (screened electrostatics, diminished hydrophobic interactions) in order to selectively examine the role played by these different interactions. Decreasing DS is found to decrease solubility and induce partial aggregation and eventual gelation. In salt-free and 0.5 M NaCl solution, NaCMC with DS ≃ 1.2 exhibits hydrophilic polyelectrolyte and neutral polymer in good solvent behavior, respectively. Decreasing DS to ≃0.7−0.8 leads to hydrophobic behavior in both media, becoming weak gels at high concentrations. In 0.5 M NaOH (pH = 13.5) the viscosities of solutions with different DS become identical when plotted against the overlap parameter, which we interpret as resulting from the solubilization of unsubstituted cellulose blocks. Small-angle neutron scattering (SANS) data indicate that the polymer conformation is not strongly affected by hydrophobic interactions. By varying DS, ionic strength, and pH, we demonstrate the tuning of NaCMC−solvent interactions, controlling separately the electrostatic and hydrophobic effects on the solution rheology.


■ INTRODUCTION
Water-soluble polyelectrolytes play a crucial role as rheology modifiers, stabilizers, and functional ingredients in a range of formulations. 1 Significantly, electrostatic forces promote solution stability and result in expanded polymer conformations. Further, hydrophobic groups on the polymer chains promote transient interchain associations, 2 which lead to enhanced viscosities, 3 longer relaxation times, 4−9 aggregate formation, 10−13 and conformational transitions. 14−16 While cellulose, the most abundant polymer on earth, 17 is insoluble in water (and most aqueous salt solutions, including NaCl), several of its derivatives may be dissolved at a molecular or colloidal level. 18 Sodium carboxymethyl cellulose (NaCMC) is an anionic, weak, semiflexible, water-soluble polyelectrolyte widely used as a thickener and rheology modifier. 19−23 The degree of substitution (DS, the number of carboxymethyl groups per glucose unit) of NaCMC is defined in Scheme 1 and usually varies between 0.7 and 1.2 in commercial materials, which qualify them as strongly charged polyelectrolytes. 19 Weakly substituted NaCMC generally exhibit hydrophobic interactions in aqueous solution due to the presence of unsubstituted cellulose blocks, for which water is a nonsolvent. 24,25 Addition of NaOH is known to promote unsubstituted cellulose solubilization in aqueous solution and is therefore expected to remove hydrophobic interactions in weakly substituted NaCMC.
Despite a large number of experimental investigations on the NaCMC/water/salt solutions (summarized in the next section), the degree of solubility of NaCMC in semidilute solution and the influence of different interactions (entanglement, electrostatic, hydrophobic) on the flow behavior of NaCMC solutions are not yet fully resolved.
In this article, we study the rheology of NaCMC solutions of varying degree of substitution (DS = 0.7, 0.8, and 1.2) as a function of polymer concentration, from approximately the overlap concentration (c*) to 100c*. All three DS have an effective charge spacing set by the Bjerrum length of ≃0.71 nm in DI water estimated from conductivity data in semidilute solution. 26 Three solvent media are considered to systematically screen different interactions: (i) DI water (pH ≃ 7) for nonscreened interactions, (ii) 0.5 M NaCl (pH ≃ 7) providing excess salt, and thus screening of electrostatic forces, and (iii) 0.5 M NaOH (pH ≃13.5), for which electrostatic interactions are screened and unsubstituted cellulose is solubilized, hence diminishing both electrostatic and hydrophobic interactions. Polymer chains and counterions contribute to the screening of electrostatic, excluded volume, and hydrodynamic forces in all solvent media. The relative strength of these interactions is therefore not only a function of the solvent choice but also polymer conformation. All NaCMC samples are fully neutralized, and hence we do not expect significant further charging of the carboxymethyl groups at pH = 13.5 compared to pH = 7 aqueous media. 27 Further, at high pH, the OH groups in the cellulose backbone are not expected to increase the linear charge density of the polyion either. We employ a combination of rheological and small-angle neutron scattering (SANS) measurements to rationalize the interplay between network conformation, solubility, and flow response in these model conditions.

SOLUTION RHEOLOGY
Polymer solutions are classified into three concentration regimes: dilute, semidilute, and concentrated. In dilute solution, chains do not overlap and chain dimensions vary as R ∝ N ν , where N is the degree of polymerization and ν is the Flory exponent. The overlap concentration c* marks the crossover to semidilute solution: where b is the monomer length; B is the ratio of the chain's end-to-end distance in dilute salt-free solution to the fully stretched chain length, 21,28 which is found to be B ≃ 1 for NaCMC and other semiflexible polyelectrolytes, consistent with the fact that the persistence length 27 for NaCMC with 0.75 < DS < 1.25 is far larger than b = 0.515 nm. 21,29,30 In salt solutions, c* can be estimated as the reciprocal of the intrinsic viscosity, obtained from the Huggins equation. For salt-free solutions the Huggins equation does not apply, 31 and the estimate η sp (c*) = 1 20,32 can be used instead. Above c* chains overlap, and excluded volume (and hydrodynamic) interactions are screened for length scales larger than the correlation length: which reduces to ξ = (B/bc) 1/2 in salt-free solution (ν = 1). The specific viscosity and relaxation times of the solution can be described by the Rouse model: where the specific viscosity is η sp = (η − η s )/η s , η is the viscosity of the solution at zero shear rate, and η s is that of the solvent. Equation 4 reduces to η sp = N(cb 3 ) 1/2 B −3/2 in salt-free solution.
Above the entanglement concentration (c e ), the longest relaxation time and viscosity vary as Eqs 5 and 6 are the scaling predictions for entangled solutions of flexible polyelectrolytes with and without salt present. Polyelectrolytes with added salt are analogous to neutral polymers in good solvent, for which eqs 5 and 6 also apply. For neutral polymers in theta solvent, which is not considered here, a different scaling applies 33 in entangled solutions. Excluded volume interactions become fully screened at c D , the crossover to the concentrated regime. Polyelectrolytes and neutral polymers are then expected to show similar conformational and rheological behavior, which is to some extent observed. 34−38 c D should correspond to the concentration at which ξ reaches the value of the thermal blob or intrinsic persistence length (l 0 ) and therefore be independent of M w ; for NaCMC, l 0 = ξ corresponds to a value of ≃0.14 M in salt-free solution. 21 Experimentally, it has been found that two crossover concentrations exist beyond the semidilute unentangled regime: above a certain concentration c e , a dependence of η sp ∼ N 1.8 c 1.5 is observed, and above a second crossover concentration (c**), η sp ∼ N 3 c 3.4 is found for NaCMC in salt-free solutions scales, reminiscent of entangled neutral polymer behavior in good solvent. 20 While c** has been widely interpreted as a crossover to the concentrated regime, the N dependence of c** ∝ N −0.6 suggests c** may correspond instead to an entanglement transition. 20 Both the η sp ∼ N 1.8 c 1.5 and the η sp ∼ N 3 c 3.4 regimes disagree with the scaling prediction for entangled, salt-free polyelectrolyte solutions (eq 6). In this study, we opt to identify c e and c** solely from the concentration dependence of η sp , and it is not at this point clear whether c e or c** marks the crossover to the entangled regime. Using a crossover function between η sp ∼ c 0.5 and η sp ∼ c 3.4 yields a value between c e and c**, detailed in the Supporting Information of ref 20.
Solution Rheology of Hydrophilic NaCMC (DS ≳ 1). Salt-free solutions of highly substituted NaCMC (DS ≳ 1) have been found to exhibit typical polyelectrolyte behavior. 20,21,39−41 A weak, near Fuoss, power law dependence of the viscosity with concentration (η sp ∼ c 2/3 ) is observed in semidilute unentangled solutions followed by stronger (η sp ∼ c 3.5 ) power law at high concentrations, characteristic of neutral polymer behavior. 20,21,41,42 The mesh size (or correlation length) has been reported to scale as ξ ∝ c −1/2 in the semidilute regime, 21 in agreement with eq 2. 28,43 The absence of thixotropy and gelling indicates that any aggregates or hydrophobic interactions do not significantly affect its macroscopic properties. 21 Addition of NaCl has been found to decrease the viscosity of NaCMC solutions except at high polymer concentrations, 20,22 for which electrostatic interactions are highly screened by free counterions even in the absence of added salt. In excess salt, the viscosity of entangled NaCMC solutions has been reported 1,22 Macromolecules Article to scale as η sp ∝ N 3.8 c 4.1 , similar to neutral polymers in good solvent and in moderate agreement with eq 6 for ν = 0.59.
Solution Rheology of Hydrophobic NaCMC (DS ≲ 1). While the average DS has been reported not to significantly affect rheological properties if substitution is random, 44−46 heterogeneity has been found to lead to stronger exponents of the viscosity with concentration 47,48 and longer relaxation times. 49,50 Concentrated solutions of heterogeneous samples are reportedly thixotropic 51−55 and can form gels. 46−48,56−60 Fuller and co-workers 61 inferred from rheo-optical measurements that for DS ≤ 1 semidilute and concentrated NaCMC solutions are highly aggregated.
Elliot and co-workers, 45,51 Francis 44 (DS ≃ 0.7), and Enebro et al. 49 (DS ≃ 1) reported that samples with similar average degree of substitution but different regularity show markedly different properties. Concentrated solutions (1−3 wt %, M w ≃ 1.5 × 10 5 g/mol 62,63 ) of "blocky" samples exhibited thixotropy and crystallinity, while the regularly substituted ones only showed pseudoplasticity. After centrifugation, the obtained gel phase displayed highly thixotropic flow while the solution phase displayed nonthixotropic pseudoplastic flow. These observations suggest that unsubstituted regions, acting as temporary cross-links, are the cause of thixotropy and gelation. 45,46 Francis 44 and Yang 64 reported that the viscosity of NaCMC aqueous salt solutions depends on whether the polymer or the salt is dissolved first, the viscosity being higher in the former case, and the effect was found to be stronger for lower DS samples.
Equations 3−6 do not take into account attractive interactions between polymer chains, 65,66 which lead to stronger power law exponents for the concentration dependence of the viscosity and relaxation times 66 and may cause a dependence of η sp ∼ exp(c α ), with α ≃ 0.6. 65 In the following, we will apply eqs 2−6 to the data presented while, for completion, the Supporting Information considers the possible exponential dependences of the viscosity which may arise from attractive interactions ( Figure S10).

■ METHODS
The main characteristics of the three NaCMC samples (Sigma-Aldrich) investigated are summarized in Table 1. The DS of the samples was measured by converting the polymer into its acid form, dissolving it in aqueous NaOH, and titrating the excess NaOH with HCl using phenolphthalein as an indicator. The characterization of sample CMC1.2 was reported previously. 20,21 Water was obtained from a Milli-Q source (resistivity of 18 μS/cm), and D 2 O (99.8% D content) was purchased from Cambridge Isotopes. SANS experiments were carried out at SANS2D (ISIS pulsed source, U.K.) with a scattering wavenumber (q) range of 0.0045−0.8 Å −1 and at D22 (ILL, France) with λ = 6 Å and sample−detector distances of 1.5, 5.6, and 17.6 m yielding a q range of 0.003−0.6 Å −1 . Quartz Hellma cells of path length 5 or 2 mm were employed, depending on polymer concentration.
Rheological measurements were carried out on two stresscontrolled rheometers: a TA hybrid using a cone and plate geometry of diameter 40 or 60 mm and angle of 1°or 2°and a Malvern Kinexus pro with a 40 mm, angle 1°, and cone and plate geometry. Selected viscosity measurements were carried out on a LV-DVI-Prime Brookfield viscometer with a Couette geometry, at a shear rate lower than the onset of shear thinning.

■ RESULTS AND DISCUSSION
Small-Angle Neutron Scattering (SANS).   the local maximum in the scattering intensity. The scattering intensity shows a I ∝ q −1 dependence for q > q* as expected for polyelectrolytes in salt-free water (ν = 1), while a stronger dependence seen at very high q arises from the finite lateral dimensions of the chain, with a radius of r p ≃ 3−4 Å. 21 Details of the fitting procedure are provided in the Supporting Information ( Figures S1−S4). The peak position as a function of concentration for the three samples studied, in salt-free water, is shown in Figure 2. A power law of q* ∝ c 1/2 is observed for all samples, consistent with eq 2 for ν = 1 (ξ = 2π/ q*). We do not expect a local collapse at high concentrations, as observed for hydrophobic flexible polyelectrolytes due to the relatively high intrinsic rigidity of the NaCMC chains. 8,9,67 The correlation length of flexible polyelectrolyte solutions has been reported to vary with charge density. 68 This occurs because as the charge density increases, the electrostatic blob (ξ T ) decreases in size, leading to chain unfolding locally. Fitting eq 2 to the data presented in Figure 2 yields B ≃ 1.1 ± 0.1 for sample CMC1.2 and B ≃ 1.2 ± 0.1 for samples CMC0.8 and CMC0.7 as expected for locally rigid polyelectrolytes. Since it is unlikely that NaCMC can fold locally given its intrinsic persistence length of ≃5 nm (or 10 monomers), it is possible that the marginal increase in B with decreasing DS results from a smaller number of chains contributing to the network. This may occur due to partial lateral aggregation for example. However, within experimental error, we cannot rule out that chains are fully soluble and no conformational change occurs in the DS range studied. Taking only the high concentration regime (c ≳ 0.09 M) and assuming the CMC1.2 sample is fully soluble, we can calculate the percentage of chains not contributing to the mesh size to be ≃10−15% for the CMC 0.8 and CMC0.7 samples. This result indicates that most chains are molecularly dispersed for the weakly substituted samples, with a small fraction possibly aggregated and/or collapsed.
An upturn at low q, characteristic of polyelectrolyte solutions 9,69−73 is also observed. Low q power laws have been speculated to be related to the mesoscopic clustering of polyelectrolyte solutions, whose dynamic origin remains controversial. 72,74−77 For CMC1.2, a power law of I(q) ∝ q −3.6 , independent of polymer concentration was found in an earlier study. 21 CMC0.7 and CMC0.8 show similar behavior at low concentrations (c ≲ 10−15 g/L). At high concentrations, a weaker power law of I(q) ∝ q −1 is observed, which could be related to the formation of fringed micelles. 18,46,78−81 These supramolecular structures, which are common for cellulose derivatives, consist of a core of laterally aggregated (perhaps crystalline) chains, out of which dangling chains emanate. This hypothesis is consistent with the results for the correlation length outlined above. Fitting the low q upturn is challenging because of the large number of free parameters required to describe fringed micelle aggregates and the added difficulty of fitting both a polydisperse population of aggregates and a soluble chain polyelectrolyte mesh simultaneously over a limited q range (as detailed in Figure S4).
In summary, SANS data indicate that in salt-free D 2 O aCMC is molecularly dispersed with an extended local conformation for the DS range investigated in this study. We next report the rheological properties of these samples to understand the effect of different interactions on their flow behavior.

Macromolecules
Article where η(0) is the zero shear rate viscosity, γ̇is the shear rate, τ is the relaxation time, and n the power law exponent of the apparent viscosity in the shear thinning regime. For samples that did not exhibit shear thinning, an average over all viscosity values was taken as η(0). Fits to the Cross and the Carreau− Yasuda models (the Carreau model is a particular case of the latter) are considered in the Supporting Information ( Figures  S5−S8). The different models for the shear rate dependent viscosity yield similar values of η(0), but different values for τ and n. The generalized Carreau−Yasuda model fits the data well at all concentrations but the estimates of τ are less reliable due to the additional free parameter required. The Cross model fits the data well, but it gives values of τ and n which differ significantly from other models as well as from model-free estimates of these parameters. We have opted to use the Carreau model as it provides a reliable estimate of the different flow properties with a limited number of fit parameters. Salt-Free Solutions. Representative viscosity data as a function of shear rate along with fits to the Carreau model for sample CMC0.7 in D.I. water are plotted in Figure 3a. The concentration dependence of the specific viscosity at zero shear rate is plotted in Figure 3b, along with the scaling predictions for the semidilute unentangled (η sp ∝ c 1/2 ), semidilute entangled (η sp ∝ c 3/2 ), and concentrated (η sp ∝ c 15/4 ) regimes. Table 2 compiles c* and c e (calculated from the onset of the η sp ∝ c 3/2 dependence) and c** (calculated from the onset of the η sp ∝ c 15/4 dependence) for the different samples studied.
The stretching parameter B may be calculated from viscosity data in the unentangled regime using eq 4 (B η = η sp −2/3 N 2/3 (cb 3 ) 1/3 ) 82 or from correlation length data using eq 2 (B ξ = bcξ 2 ) obtained from SANS. Figure 4 compares B ξ and B η for the three samples studied. We note that since the η sp ∝ N dependence predicted by eq 4 is not observed experimentally, 20 B η effectively becomes N dependent. This dependence is not real but simply reflects a shortcoming of the scaling model. For all three samples B η /B ξ ≃ 2.3−3. The values observed for other polyelectrolyte systems differ: Dou and Colby 36 find B η /B ξ = 2.7 and B η /B ξ = 1 for quaternized poly(2-vinylpyridine) in ethylene glycol and N-methylformamide, respectively; Di Cola et al. find B η /B ξ = 0.9−1.3 for a range of maleate copolymers in aqueous solution, and data for sodium polystyrenesulfonate gives B η /B ξ ≃ 0.5. 32,83,84 The differences observed likely arise due to the neglect of prefactors in the calculation of the Rouse and Zimm times and due to the use of the static correlation length to estimate the crossover length scale at which hydrodynamic interactions become screened. 28 We consider the SANS estimate of B to be more reliable as it directly probes the mesh size of polyelectrolyte solutions without making assumptions about their hydrodynamic properties.
The specific viscosities of the three samples are plotted as a function of polymer concentration in Figure 5a, and the same    best fit power law exponent (0.68 ± 0.05) is observed for all samples in the semidilute unentangled regime, somewhat higher than the eq 4 value of 1/2 for ν = 1 and in agreement with earlier results, presented in Figure S7 of ref 20. For consistency, we opt to determine the crossover concentrations c e and c** from the intersections of the predicted power laws, as shown in Figure 3. In Figure 5 we show both the best fit and predicted power laws. We note that the exact criteria used does not have a significant effect on the resulting crossovers. 21 In entangled solutions, stronger power law exponents for the concentration dependence of the specific viscosity are observed for samples CMC0.7 and CMC0.8 than for CMC1.2. The longest relaxation times, estimated by τ in eq 7 and plotted in Figure 5b, also increase for the less substituted samples. These two observations are interpreted as resulting from associations between chains, 65 which arise due to unsubstituted patches along the cellulose chain. 49,85 The flow index for the three samples, plotted in Figure 5d, appears to be unaffected by hydrophobic interactions. The values of n ≃ 0.1−0.2 in the unentangled regime are lower than the predicted value of n = 0.5 by Colby et al. 86 and may reflect the limitations of our fits given the restricted experimentally accessible shear rate range.
The terminal modulus, which can be estimated as G ≃ η/τ, follows an approximately linear relation with concentration, given by G ≃ k B Tc/10N. The factor of 1/10 is probably the result of the polydispersity of the samples and the method used to estimate the terminal modulus. While the zero-shear rate viscosity corresponds to an average over all chains, the relaxation time is identified from the onset of shear thinning and therefore corresponds to the highest molar mass fraction, yielding artificially low values of G. CMC0.7 and CMC0.8 deviate to lower values at high concentrations, which we interpret as arising due to chain association and coupled relaxation, thereby decreasing the number density of chains in solution.
We observed no change in the viscosity of a CMC0.7 solution with c ≃ 0.05 M after filtering through a 0.2 μm size filter. Light scattering data confirm the removal of aggregates, which results in a large decrease of the scattered intensity at low angles and a decrease in the amplitude of the slow mode decay in the intensity correlation function. It appears that supramolecular structures (possibly fringed micelles) do not significantly affect the rheological behavior of NaCMC solutions. The increase of viscosity at higher concentrations (which we are not able to filter) probably has a different origin, namely, temporary associations between dissolved chains and/ or the formation of a polymer network.
NaCl and NaOH Solutions. Having assessed the rheology in DI water, we now turn to solutions containing excess salt (0.5 M), i.e., solutions with many more added salt ions than free polyelectrolyte counterions. Under these conditions, the Debye screening length is κ −1 ≃ 0.4 nm, meaning electrostatic forces become short-ranged and analogous to excluded volume forces in neutral polymer solutions. 87,88 The solution viscosities for which the salt was dissolved before the polymer were found to be identical to those where the salt was added to the dissolved polymer for all samples, in contrast to previous reports by Francis 44 and Yang and Zhu. 64 We interpret this difference as due to incomplete dissolution of their samples. The electrostatic interactions are highly screened, and thus neutral polymer in good solvent behavior is observed; the viscosity varies as η sp ∝ c 1.3±0.1 in the semidilute unentangled regime, in good agreement with eq 4 for ν = 0.59. Figure 6 compares the specific viscosity as a function of polymer concentration for the three NaCMC samples in DI water as well as 0.5 M NaCl and 0.5 M NaOH aqueous solutions. As expected, addition of salt decreases the solution viscosity at low concentrations for all samples and electrolytes. This behavior is the result of screening of repulsive forces between charged groups along the polymer chain 20,28 which leads to reduced chain dimensions. At high concentrations, the viscosities of the salt-free solutions and the 0.5 M NaCl solutions converge as salt does not contribute to further screening.
Highly substituted CMC1.2 displays very similar solution viscosities in NaCl and NaOH. For CMC0.8 and CMC0.7, by contrast, the viscosities in the presence of NaOH are significantly lower than in NaCl at high polymer concentrations. We interpret this decrease in viscosity in the presence of NaOH as resulting from the solubilization of unsubstituted cellulose blocks. 89 The onset of hydrophobic interactions may be identified in the plots of η sp vs c[η] as the point where the viscosities in NaCl and NaOH diverge. This is seen to occur around c ≃ 5− 10c* for samples CMC0.7 and CMC0.8 in Figure 7. We observe power law exponents for the viscosity dependence with concentration of m ≃ 4.3 for CMC1.2 and m ≃ 5.5−7 for samples CMC0.7 and CMC0.8 in NaCl, compiled in Table 3. By contrast, in NaOH, all points collapse onto the same curve, as expected for polymers with the same polymer−solvent interactions, only differing in molecular weight. 1,43  (8) where the term in square brackets is the viscosity dependence predicted by the Rouse model for semidilute unentangled solutions and η sp (c*) is the specific viscosity at the overlap concentration. Equation 8 interpolates eqs 4 and 6 when α = 1/(3ν − 1) and β = 2α. Additionally, data were fitted to an expanded Huggins equation: 1,90 where k H is the Huggins coefficient, B′ is a parameter related to the onset of entanglement, and m gives the power law exponent of the specific viscosity with concentration in the entangled regime. The viscosity at the overlap concentration is given by η sp (c*) = 1 + k H + B′ ≃ 1 + k H . The parameters from fits to eqs 8 and 9 are collected in Table 3. The entanglement parameters for NaOH solutions are similar for all three samples. The concentration dependence of the viscosity in entangled solution varies as η sp ∝ c 4.2±0.2 . The ratio of the entanglement to overlap concentration is found to be c e /c* ≃ 6−7, in agreement with an earlier report in 0.1 M NaCl. 20 Computing this ratio from the compilation of Heo et al. for flexible, neutral polymers, 91 we find c e /c* ≃ 3−15. Note that we have adjusted their values to match our fitting methods. 92 The similar range of values is consistent with NaCMC in 0.5 M NaOH behaving similarly to a neutral polymer in good solvent.
A value of the melt entanglement molecular weight M e ≃ 3900 g/mol was reported by Horinaka et al. 93 where N e (1) is the number of Kuhn segments 94 between entanglements in the melt, 95 gives c e /c* ≃ 1. This value Figure 7. Specific viscosity as a function of the overlap parameter for solutions of the three NaCMC samples studied (CMC1.2: red circles; CMC0.8: blue rhombuses; CMC0.7: black triangles) in (a) 0.5 M NaOH. Black line is a fit to eq 9, using parameters for CMC0.7 given in Table 3. (b) 0.5 M NaCl (open symbols correspond to solutions in DI water, as in this range the data in DI and 0.5 M NaCl converge; 20 the value of [η] corresponds to the one in NaCl for all points) The full black line is the same as in part (a); the dotted line is the eq 9 fit to CMC0.7 data, with fit parameters in Table 3. a The Huggins coefficient was fixed at k H = 0.45 for all fits to eq 9. Fits to eq 8 used exponents α = 1.3 and β = 2.6 predicted by scaling theory for neutral polymers in good solvent.

Macromolecules
Article disagrees with our observations in solution. We do not at the moment have an explanation for this disagreement. Oscillatory Rheology. The hydrophobic character of sample CMC0.7 was further quantified by oscillatory shear rheology experiments. Figure 8b plots the loss and storage modulus for a solution of ≃0.35 M in DI water. The sample displays a weak gel-like behavior, with G′ ≥ G″ over the entire frequency (ν, in s −1 ) range. We note that the observed behavior does not satisfy some common definitions of gels in that a plateau in not observed for G′; additionally, G′ is never much larger than G″. At these high concentrations, it is not possible to obtain a value for η(0). Measurements a few days after preparation and after one year yield very similar results ( Figure  S9), indicating the gel structure is stable. Shearing at 100 s −1 results in a decrease in the solution viscosity and of G′ (but not G″). We did not observe a recovery of the viscosity following the shearing step, which therefore does not qualify this sample as thixotropic in the time range studied (≃ 30 min after shearing), detailed in Figure S9. In NaOH (Figure 8c), the solution displays a lower viscosity and the variation of G″ and G′ with oscillation frequency is characteristic of an entangled polymer solution. Solubilization of the unsubstituted cellulose blocks by NaOH therefore turns the gel into a solution. A c ≃ 0.4 M CMC1.2 solution in DI water is also a viscoelastic liquid (Figure 8a), demonstrating that the hydrophobic interactions in this sample are significantly weaker, as anticipated from the concentration dependence of the viscosity. The samples studied obey the Cox−Merz rule, as shown in the bottom panels of Figure 8.

■ CONCLUSIONS
We have examined the effect of the degree of substitution on the structure and rheology of NaCMC in aqueous solutions. SANS and rheology data were interpreted in the framework of the de Gennes, Pfeuty, and Dobrynin scaling models of polyelectrolyte solutions. Despite some shortcomings, discussed throughout the text, these models allow us to identify the key crossover concentrations and resolve the contributions of different interactions to the flow behavior of NaCMC.
Lowering DS below ≃1 is found to favor polymer−polymer interactions, resulting in hydrophobic behavior; in turn these associations cause increased viscosities and eventual gelation. The correlation length is found to be largely unaffected by DS, within experimental uncertainty, indicating that these interactions do not significantly alter, on average, chain conformation (e.g., the persistence length) or polymer solubility in the semidilute regime. Hydrophobic interactions have an increasingly large effect on the solution rheology as the polymer concentration increases.
Addition of NaCl screens electrostatic interactions, decreasing the solution viscosities at low polymer concentrations; at higher concentrations (≳0.1 M), electrostatics are largely screened by counterions and addition of NaCl does not contribute significantly to further screening. Addition of NaOH Figure 9. (a) Schematic of the structure of NaCMC solutions as a function of polymer concentration, DS and pH. For c ≲ 5c*, neither NaOH nor DS has a strong effect on solution structure; this is supported by the SANS data presented. At high concentrations, weakly substituted (DS ≃ 0.7) NaCMC contains a large number of interchain associations which lead to increased viscosities and gelation c ≳ 0.2 M in DI water. By contrast, highly substituted NaCMC shows standard (nonassociative) polymer behavior. Addition of NaOH solvates the unsubstituted cellulose backbone (red lines) and has an effect that is similar to increasing the DS. At low DS, addition of NaOH is sufficient to suppress association, resulting in a structure as show in the left column.

Macromolecules
Article diminishes hydrophobic as well as electrostatic interactions, resulting in a decrease in solution viscosities at high polymer concentrations for weakly substituted samples (0.7−0.8). At lower polymer concentrations, NaOH decreases solution viscosities by a similar amount as NaCl. A summary of the effects of electrostatic and hydrophobic forces on NaCMC solutions is shown schematically in Figure 9.
Hydrophobic interactions result in a viscosity increase at high (c ≳ 5c*) concentration. Electrostatic interactions primarily affect solution viscosity at low concentration due to repulsion, leading to chain expansion, while at high polymer concentrations these interactions are screened (even in the absence of salt). The role of entanglement is manifested at c > c e and is not significantly affected by salt.
This work provides mechanistic insight into the rheological behavior of NaCMC under representative solution environments enabling quantitative control of flow properties of this ubiquitous water-soluble cellulose derivative.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00178.
Detailed analysis of the SANS data, including the low q upturn; fits to different models (Carreau, Cross, Carreau−Yasuda) to shear rate dependent viscosity (PDF)