Influence of divalent counterions on the solution

Cellulose manuscript No. (will be inserted by the editor)

Influence of divalent counterions on the solution rheology and supramolecular aggregation of carboxymethyl cellulose Carlos G. Lopez · Walter Richtering

Received: date / Accepted: date

Abstract Divalent counterions promote attractive forces between polyelectrolyte chains via electrostatic bridging, which play a significant role in the conformation of ionic biopolymers. Further, counterion valence is known to affect the flexibility and aggregation properties of polyelectrolytes in solution. The present study seeks to resolve the effect of counterion valence and type on the structure and flow properties of a model semiflexible polyelectrolyte. We report rheology and light scattering data for the Na+ , Mg2+ , Ca2+ , Mn2+ , Co2+ , Ba2+ salts of carboxymethyl cellulose in aqueous solutions. The Na+ and Mg2+ counterions do not interact specifically with the carboxylate groups, and their CMC salts form clear solutions in the concentration (c) range studied (0.001M < c < 0.3M), which spans from the dilute to the entangled regimes. The other salts form clear solutions at low concentrations and become turbid at higher ones. The specific viscosity as a function of molar polymer concentration falls into a single curve for all divalent salts, with small differences occurring only for c > 0.2M. Compared NaCMC, divalent salts display a lower viscosities at low concentrations (in the non-entangled regime), suggesting less expanded chains, in agreement with earlier experimental results on flexible polyelectrolytes. Above the entanglement crossover (c ' 0.07M), solutions with divalent cations display viscosities up to an order of magnitude larger than NaCMC, possibly because interchain crosslinks form by electrostatic bridging. Dynamic light scattering measurements on semidilute non-entangled solutions reveal a bimodal decay function, where the Carlos G. Lopez · Walter Richtering Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, D-52056 Aachen, Germany E-mail: [email protected]

relative amplitudes of the two modes vary with counterion valence, size as well as with the filter size employed and the time after filtration. These variables (except for counterion valency) do not strongly affect the solution viscosity, indicating that polyelectrolyte clusters only contain a small fraction of the total number of chains in solution. Keywords Carboxymethyl cellulose · Divalent Counterions · Light scattering · Aggregation · Viscosity

Graphical Abstract

1 Introduction The interaction of soft matter with oppositely charged multivalent species is of interest in polymer physics (Muthukumar, 2017; Dobrynin and Rubinstein, 2005), for example with regards to the phase behaviour(Prabhu et al., 2003, 2001) and structural transitions (Schweins et al., 2006; Lages et al., 2010) of polyelectrolytes. The

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conformation of important biological macromolecules, for example DNA or intermediate filaments, is also affected by these interactions (Horkay et al., 2012; Geissler et al.; Horkay et al., 2018; Hmonnot et al., 2015). Recently, polyelectrolyte brushes in the presence of mulitvalent ions have received much attention for their role in joint lubrication (Yu et al., 2018; Brettmann et al., 2017; Hao et al., 2016). From an application point of view, the interaction of multivalent counterions with polyelectrolytes plays an important role in self-assembly (Stewart et al., 2017), the design of stimuli responsive materials (Huynh et al., 2016; Yin et al., 2008; Horkay and Basser, 2004; Koovan et al., 2015) drug delivery (Malmsten, 2006; Tønnesen and Karlsen, 2002), detergent formulations (Smulders and Sung, 2000; Tsarkova et al., 2018; Lopez et al., 2018b) or water purification (Rud et al., 2018; Cheng et al., 2018). Addition of low molar mass salts to polyelectrolyte solutions leads to chain shrinking(Eich and Wolf, 2011; Xiong and Wolf, 2014; Spiteri et al., 1996), and in certain cases aggregation and phase separation(Sinn et al., 2004; Goerigk et al., 2007; Schweins et al., 2006; Lages et al., 2010, 2007). Phase separation occurs at high added salt concentrations (' molar amounts) in the case of non-specifically interacting counter-ions or at much lower concentrations (Hansch et al., 2018; Schweins et al., 2003) if specific interactions occur. Studies on flexible polyelectrolyte polystyrene sulfonate (PSS), have shown that its soluble divalent salts (e.g. MgPSS or CaPSS) display a greater degree of local collapse (higher mass per unit length(Dubois and Boué, 2001)) and smaller overall dimensions than its monovalent salts (e.g. NaPSS or KPSS).(Zhang et al., 2001; Dubois and Boué, 2001). PSS with divalent counterions displays a correlation length approximately twice larger than with monovalent ones. (Zhang et al., 2001; Combet et al., 2005, 2011; Dubois and Boué, 2001). Polyelectrolyte chains with divalent counter-ions are more flexible than those with monovalent ones(Dubois and Boué, 2001; Chremos and Douglas, 2016), and under certain conditions, they adopt a non worm-like chain conformation (Dubois and Boué, 2001). Some of these effects may arise due to intra-chain electrostatic bridging, a phenomena that is not well understood. Analogous data are not available for semiflexible polyelectrolytes, but it is likely that their intrinsic rigidity will prevent the local collapse(Lopez et al., 2015, 2018a) observed for their flexible counterparts, therefore leading to different behaviour. The impact of divalent ions on the conformation, supramolecular association and solubility of polyelectrolytes in turn affects their flow behaviour, which can be advantageous when tailoring the rheological prop-

Carlos G. Lopez, Walter Richtering

erties of polyelectrolyte solutions. In the case of nonspecific interactions, addition of a salt will typically lead to a decrease of the solution viscosity due to reduced intrachain electrostatic repulsion. On the other hand, gelation of ionic polysaccharides such as alginate or pectin can be achieved by complexation of the polymer chains with specifically interacting Ca2+ ions. (Dumitriu, 2004; Nakauma et al., 2017; Gao et al., 2017) For some entangled polyelectrolyte systems, addition of either a monovalent or a divalent salt can lead to an increase in solution viscosity.(Donnelly et al., 2015; Wyatt et al., 2011; Wyatt and Liberatore, 2010; Qiao et al., 2013) Polyelectrolytes in salt-free solution display an upturn in the low wave-vector region of their scattering profile and a slow mode(Sedlák, 1999) on the dynamic light scattering (DLS) correlation function. Both of these experimental observations suggest the presence of polyelectrolyte clusters, implying attractive forces between chains, and in contrast with the strong interchain repulsion expected by different theories(De Gennes, P.G. et al., 1976; Dobrynin et al., 1995). Early studies established the influence of counterion valency(Drifford et al., 1996; Drifford and Dalbiez, 1985; Zhang et al., 2001), polymer concentration(Sedlak, 1996; Sedlák and Amis, 1992b,a) and solvent quality(Ermi and Amis, 1997, 1998) on these clusters as well as their stability(Sedlák, 2002b,a), but an understanding of their physical origin remained elusive. Recently, their origin has been assigned to attractive dipole interactions between sections of the chains with condensed counter-ions(Muthukumar, 2016) or to the preferential solvation of counterions over polymer segments(Chremos and Douglas, 2017, 2018b). While the conformation and solution structure of flexible polyelectrolytes with divalent counterions has received some attention in earlier literature as outlined above, data on their dynamics and flow behaviour are lacking. In this article, we study the effect of different divalent counter-ions on the aggregation and flow behaviour of carboxymethyl cellulose (CMC) in solutions with no added salt. The paper is organised as follows: We next review the current knowledge of the interactions of various ions with CMC and then present steady and oscillatory shear data to characterise the flow behaviour and conformation of different salts of CMC. We conclude by showing that aggregation in unentangled polyelectrolyte solutions (quantified through dynamic light scattering) does not affect strongly their flow behaviour. Sodium carboxymethyl cellulose (NaCMC) is an anionic, weak, semiflexible polyelectrolyte, extensively used as a structuring agent and texture modifier in food products(Xin et al., 2018; Nicolae et al., 2016; Gibis

Title Suppressed Due to Excessive Length

et al., 2017), to prevent the crystallisation of tartaric salts in white wines (Bajul et al., 2017; Guise et al., 2014) and as a viscosity modified in oil drilling fluids(Feddersen and Thorp, 1993; deButts et al., 1957). Other applications include its use in as a dirt suspender detergents or as a structuring agent in toothpaste formulations(Agarwal et al., 2004; Garlick and Miner). Its calcium salt is used as a disintegrant in pharmaceutical formulations such as tablets(Porsch and Wittgren, 2005). Table 1 lists some of the typical characteristics of commercial grades of NaCMC.

Table 1 Typical range of molecular parameters for commercial grades of NaCMC. M0 = 162 + 71 × DS is the monomer molar mass. * Defined as the ratio of the weight averaged molar mass (Mw ) to the number averaged molar mass (Mn ). Property Molar mass (Mw ) M0 Polydispersity* D.S. Purity

Range 105 − 106 g/mol 220-260 2-4 0.7-1.2 99.5 wt% (food or cosmetic grades)

Fig. 1 a: Schematic representation of carboxymethyl cellulose monomer. The number of R = CH2 COONa per monomer is the degree of substitution (DS). b: Calcium counterion shared between two adjacent groups (green) and an interchain cross-link formed by calcium bridging (blue).

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The degree of substitution (DS) of NaCMC is defined as the number of carboxymethyl group substituted per glucose unit, out of a maximum value of 3, see Figure 1a. High DS (& 1) NaCMC displays approximately homogeneous substitution. By contrast, grades with DS . 0.9 exhibit blocks of unsubstituted cellulose region being present along the chain backbone (Lopez et al., 2018a). These unsubstituted blocks promote temporary associations between chains which lead to enhanced viscosities at high concentrations and eventual gelation(Lopez et al., 2018a; Barba et al., 2002). 1.1 The interaction of carboxymethyl cellulose with salts. Addition of monovalent salts to NaCMC leads to a decrease of the solution viscosity at low polymer concentrations due to the screening of electrostatic repulsion which decreases the persistence length and excluded volume strength, leading to reduced chain dimensions (Lopez et al., 2016). The effect becomes less pronounced as the polymer concentration increases(Lopez et al., 2016; Clasen and Kulicke, 2001; Kulicke et al., 1996). No precipitation of NaCMC by monovalent cations is observed with three exceptions: H+ (Dieckman et al., 1953; Hakert et al., 1989), which binds to the chain due to the low pKa of the carboxylate groups, Ag+ (Feddersen and Thorp, 1993), which displays strong specific interactions due to its high coordination number(Ezhova and Huber, 2014, 2016; Urbanski et al., 2018), and counter-ions with large hydrophobic regions (e.g. dodecyltrimethylammonium)(Guillot et al., 2003; Trabelsi et al., 2007; Wu et al., 2009; Sardar et al., 2012). Francis(Francis, 1961) found the decrease of the viscosity of a 10 g/L NaCMC solution upon addition of different divalent salts (CoCl2 , CaCl2 and BaCl2 ) to be independent of the cation type, from which he concluded that specific interactions between the carboxylate groups and the cations were unlikely and the viscosity reduction was solely due to electrostatic screening. Later studies by Matsumoto and co-workers investigated the binding of different alkaline earth cations to NaCMC in aqueous solution, at a ' 1:1 molar ratio of carboxylate groups to metal cations. They found the percentage of COO− groups bound to a metal cation to be Ca2+ (97%) > Ba2+ (92%) > Sr2+ (71%) > Mg2+ (53%), in line with the osmotic pressure data of Inagaki et al (Inagaki et al., 1957). Haug et al found that the binding of different alkaline earth cations relative H+ increases steadily with the molar mass of the cation(Haug and Smidsrød, 1970). Clasen and Kulicke(Clasen and Kulicke, 2001) report that the viscosity of NaCMC upon addition of CaCl2 first drops and then increases,

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reaching a peak at [Ca2+ ]/[COO− ] ' 1, before decreasing again up to eventual precipitation. Such behaviour was not observed in other studies(Yang and Zhu, 2007; Francis, 1961; Heinze et al., 1994). Matsumoto and co-workers(Matsumoto and Zenkoh, 1991) performed SAXS measurements on aqueous NaCMC solutions with different amounts of added CaCl2 . They observed an increase in the radius of gyration (obtained from fitting the low wavevector data) with increasing salt concentration, from which it was concluded that NaCMC chains are stiffened by addition of CaCMC. The size extracted from their fits however likely corresponds to the size of multi-chain clusters and not to single polymer dimensions. Figure 1b outlines a possible scenario for the cross-linking of chains via divalent cation bridging. Al3+ salts have been found to lead to an increase in the viscosity of NaCMC due to the formation of crosslinks between the chains, promoting gel formation in several studies (Ishii et al., 2013; Francis, 1961; Yang and Zhu, 2007; Elliott; Feddersen and Thorp, 1993). Heinze and co-workers(Heinze et al., 1994) by contrast report a decrease in solution viscosity of NaCMC upon addition of AlCl3 . This discrepancy may occur because the measurements of Heinze and co-workers were carried out at a single shear rate of 500 s−1 , at which solutions are deep into the shear thinning region of their flow curves. The current manuscript presents a systematic study of the solution properties of carboxymethyl cellulose with divalent counterions in salt-free solution over a wide polymer concentration range, covering the dilute to entangled regimes. We seek to resolve the impact of counterion valency and type on the conformation, dynamics and supramolecular aggregation of CMC, which serves as a model semiflexible polyelectrolyte.

2 Materials, Methods and Data Evaluation 2.1 Materials A sodium carboxymethyl cellulose sample with nominal Mw = 2.5 × 105 g/mol and DS ' 1.21 was purchased from Sigma-Aldrich. Dyalisis membranes with a molecular weight cutoff of 12-14 kg/mol or 6-8 kg/mol were purchased from Spectrapor. Deionised (DI) water was obtained from a mili-Q source. NaCl (VWR, ACS Reagent, ≥ 99%), MgCl2 ◦6H2 O (VWR, ACS, Reagent) and CaCl2 ◦2H2 O (Sigma Aldrich, ACS, Reagent) and MnCl2 ◦4H2 O (WVR, ACS, Reagent), CoNO3 (Sigma 1

This value is quoted on the analysis certificate of the batch. The general value for the product is DS = 1.15-1.35.

Aldrich, Puriss p.a. ACS Reagent, ≥ 99.0%), BaCl2 (Sigma Aldrich, 99.9%) HCl (0.1 and 1 M aqueous solutions, VWR) and NaOH (0.1 and 1M aqueous solutions, VWR) were used as received. Supor filters of various pore sizes were purchased from VWR.

2.2 Sample preparation The NaCMC sample was purified by dialysing a ' 30 g/L solution of the as received sample against DI water to remove any salt impurities. To prepare the different divalent salts of CMC, NaCMC solution of ' 30-40 g/L in a five to tenfold molar excess of the corresponding salt was dialysed against DI water with frequent water exchanges for 5-10 days. In excess MnCl2 , CaCl2 , CoCl2 , BaCl2 CuCl2 the solutions turns turbid and a precipitate forms. The dialysis bag was therefore lightly shaken at regular intervals to promote re-dissolution of the polymer as the dialysis proceeded. The solutions turned clear after a few days and water exchanges except for the CuCMC salt, which remained insoluble even after several days of dialysis agains DI water. The above method was preferred over the more common approach of transforming NaCMC into its acid form, washing with water/ethanol mixtures to remove excess ions and neutralisation with the corresponding base because washing the acid form can lead to changes in the DS of the polymer, as highly substituted HCMC displays limited solubility in aqueous ethanol. Samples were prepared gravimetrically, assuming no change in volume of the components upon mixing. Vials were placed on a roller-mixer or a vortex mixer for a 1572 hrs to dissolve the polymer.

2.3 Determination of degree of substitution Approximately 0.5 g of the unpurified NaCMC was dissolved in 20 mL DI water. 1 M aqueous HCl was added to the solution to adjust the solution to pH ' 0.8. The solution was transferred to a dialysis bag and dialysed against DI water with frequent exchanges to avoid prolonged exposure of the membrane to low pH. The dialysis bag was then transferred to a 2.5 L bath of 0.008 M HCl ([H + ]/[COO− ] ' 10), which was exchanged twice over the course of three days. The concentration of HCl chosen to be low enough as to not damage the dialysis membranes. Finally the bath was changed to DI water to remove excess acid and any salt impurities. The solution was then freeze dried. A portion of the HCMC was dissolved into ' 10 mL of 0.1 M NaOH titrated with 0.1 M HCl to pH = 8. The degree of substitution was then calculated following reference [1]:


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3 Results and discussion DS =

0.162(VN aOH [N aOH] − VHCl [HCl]) m(1 − 0.0584{VN aOH [N aOH] − VHCl [HCl]}/m)

where V is the volume of HCl or NaOH and m is the mass of HCMC. 2.4 Rheology Rheological measurements were performed on a stress controlled Kinexus-Pro rheometer with cone and plate geometries of diameter of 40 mm or 60 mm and an angle of 1◦ . The temperature was controlled with a Peltier plate. A solvent trap was used to minimise sample evaporation. Oscillatory measurements are carried out in the linear viscoelastic region. 2.5 Light scattering Dynamic light scattering measurements were carried out on an ALV-5000 instrument with a laser of wavelength λ = 633 nm. Disposable glass cuvettes were rinsed with freshly distilled acetone to remove dust. All samples were filtered before transferring them to the cuvettes. The first few drops of filtered solution were discarded. Intensity correlation data were fitted to a bimodal second order modified cumulant expansion (Burchard and Richtering, 1989): h µ2,1 t2 µ2,2 t2 i2 g1 (t, q) = B1 e−Γ1 t (1 + ) + B2 e−Γ2 t (1 + ) 2 2 (1) where Bi is the amplitude of the decay mode, Γi is the inverse decay time, µ2,i is the second cumulant and the subscript refers to the fast mode (i = 1) and the slow mode (i = 2). The decay times obtained in Equation 1, neglecting concentration effects, varies as a function of the scattering vector as:

The molar mass of the sample was determined from the intrinsic viscosity in 0.1 M NaCl ([η] ' 220 M−1 ) and the MHS relation given in reference [66] to be Mw ' 2.1 × 105 g/mol. The degree of substitution was estimated as DS ' 1.3, in reasonable agreement with the manufacture’s specifications. 3.1 Phase behaviour The addition of the various salts in tenfold excess leads to phase separation except for the sodium and magnesium cations, see Table 2. All the salts of CMC except for CuCMC form clear solutions at low polymer concentrations in DI water. CaCMC, MnCMC and BaCMC become turbid as the concentration is increased above a critical value (∼ 0.06 M for MnCMC and CaCMC). We could not clearly determine the clear-to-turbid transition of CoCMC in salt-free solution, due to its deep pink colour. These observations are in agreement with the results of Feddersen et al(Feddersen and Thorp, 1993), who observed precipitation of NaCMC (DS ' 0.7) by the addition of excess divalent cations (e.g. Ca2+ , Fe2+ , Zn2+ ) except for Mg2+ . The Cu2+ salt forms a fibrous precipitate that did not dissolve when dialysed against DI water for 10 days. Table 2 Solubility of aqueous NaCMC (c ' 0.1 M) in 10 fold molar excess of added salt. Added salt HCl NaCl MgCl2 CaCl2 MnNO3 CoCl2 BaCl2

Appearance Turbid Clear Clear Turbid/Precipitated Turbid Turbid/Precipitated Turbid/Precipitated

3.2 Rheology Γ q −2 = (1 + Kq 2 )

(2)

where K is a constant dependent on the size and shape of the particles, with units of length squared. The apparent diffusion (D) coefficient is calculated as D = limq→0 (q 2 Γ ), and the hydrodynamic radius is evaluated using the Stokes-Einstein equation: RH =

kB T 6πηs D

(3)

where kB is the Boltzmann constant, T the absolute temperature and ηs the viscosity of the solvent.

3.2.1 Shear rate dependence of viscosity Viscosity data were fitted to a horizontal line and to a power-law at low and high shear rates respectively, see the supporting information. The intercept between the two lines provides a measure of the longest relaxation time of the system. For some samples, the Newtonian plateau could not be reached, and we therefore extrapolated the data to zero shear rate. For this purpose, the data were fitted to the generalised Carreau-Yasuda model:

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η(γ) ˙ =


η(0) [1 + (τ γ) ˙ b ]n/b

(4)

where γ˙ is the shear rate, η(0) is the solution viscosity at zero-shear rate, τ is the longest relaxation time of the solution, n is the power law of the viscosity with shear rate at high shear, and b is a parameter which modifies the shape of the cross-over between the Newtonian and power-law regions, and is dependent on sample polydispersity(Clasen and Kulicke, 2001). We fit the shear rate dependence of the viscosity only for flow curves for which the viscosity at high shear rates decreases to at least 0.6η(0). Extrapolation to γ˙ = 0 never lead to values of η more than a few percent greater than the lowest measured datapoint, indicating that while some of our measurements do not fully reach the Newtonian plateau region, the recorded shear rate range is sufficient to provide an accurate extrapolation to η(0).

Figure 2 shows the viscosity of NaCMC (part a) and CaCMC (part b) as a function of shear rate for different polymer concentrations. Eq. 4. Fits to the Newtonian plateau and a power law are presented in the supporting information (Figure S2). Some samples display an upturn at low shear rates, which is not considered when fitting the viscosity to Eq. 4. 3.2.2 Concentration regimes The specific viscosity as a function of concentration is plotted in Figure 3 for NaCMC and CaCMC, along with best fit power laws that identify the different concentration regimes. We observe three regions: I: η ∼ c0.68−0.78 , II: η ∼ c1.5 and III: η ∝ c3.4−5.5 . Table 3 compiles the crossover concentrations for these regimes. Two estimates for the onset of entanglements, ce (' 0.02 M) and c∗∗ (' 0.08 M), corresponding to the onset of regimes II and III are considered, see reference [66] for a discussion on this topic. Table 3 Crossover concentrations for NaCMC and CaCMC, inferred from viscosity data, as shown in Figure 3. a The crossovers for the different divalent salts are within experimental uncertainty the same as for CaCMC. Sample NaCMC CaCMCa

c∗ (M) 6 × 10−4 1.9 × 10−3

ce (M) 2.2 × 10−2 1.9 × 10−2

c∗∗ (M) 8.2 × 10−2 7.9 × 10−2

The overlap concentration (c∗ ) is estimated from ηsp (c∗ ) = 1. This criterion has been shown to provide an accurate measure of c∗ , in agreement with that obtained form other methods (Boris and Colby, 1998; Colby, 2010; Bordi et al., 2004). The entanglement crossovers (ce and c∗∗ ) differ only by a factor of ' ×1.25 between mono- and divalent salts, consistent with earlier observations that electrostatics do not have a strong impact on the entanglement crossover(Lopez et al., 2016). 3.2.3 Chain conformation The overlap concentration is found to be ' ×3 lower for NaCMC than CaCMC. Polymer chains are space filling at c∗ and therefore(Ying and Chu, 1987; Colby, 2010): c∗ '

Fig. 2 Viscosity as a function of shear rate for aqueous solutions of NaCMC (a) and CaCMC (b). Lines are fits to Eq. 4 or to a flat line in the Newtonian region.

M N ∼ 2 R3 L

(5)

where R = N ν is the end-to-end size of a chain in dilute solution, with N the degree of polymerisation and ν the solvent quality exponent, and L is the effective contour length of the chain(Lopez et al., 2015, 2018a; Dobrynin et al., 1995). In the second equality, we have assumed a rod-like conformation of the polyelectrolyte


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The power law for the specific viscosity in the unentangled regime is found to be ηsp ∝ c0.68 for NaCMC and ηsp ∝ c0.76 for the divalent salts. Both values are larger than the Dobrynin et al(Dobrynin et al., 1995) prediction: ηsp ' (c/c∗ )1/(3ν−1)

Fig. 3 Specific viscosity as a function of polymer concentration for NaCMC (a), and CaCMC (b). Dobrynin et al’s theory predicts ηsp ∝ c0.5 for the semidilute unentangled regime, ηsp ∝ c1.5 for the semidilute entangled and ηsp ∝ c3.9 for the concentrated regime. The agreement between the prediction for the semidilute entangled exponent and the observed exponent of 1.5 is likely accidental (Lopez et al., 2016). The crossover concentrations are compiled in Table 3.

chain (ν = 1), which is in agreement with experimental evidence for NaCMC (Lopez et al., 2015, 2016). Using Eq. 5, the difference in c∗ implies that R for NaCMC is ' 70% larger than for CaCMC. Due to the semiflexible nature of the cellulosic backbone, it is unlikely that CMC can fold on short (' 5 − 10 nm) length-scales and the decrease in R likely occurs due to an increase in long-range flexibility. The scaling of c∗ with molar mass, which, to the best of our knowledge has not been measured for any polyelectrolyte with divalent counterions, should provide a clue as to whether polyelectrolyte chains with divalent counterion ions maintain a rod-like (or directed random walk) configuration in dilute solution.

(6)

which for ν = 1 leads to a power law of ηsp ' c1/2 . The larger than predicted exponents may result from the non-negligible contribution of the intrinsic persistence length to the flexibility of the chain(Lopez et al., 2015, 2016). This contribution becomes more significant as the electrostatic contribution decreases, which would explain the higher exponent observed for the CaCMC salt compared to NaCMC. For c > c∗∗ , CaCMC displays a power law of ηsp ∼ c5.62 , which is larger than the typical values of 3.4-3.8 observed for highly substituted NaCMC polymers(Lopez et al., 2015, 2016, 2018a), and possibly signals interchain bridging by the divalent cations. Figure 4 compares the specific viscosity of the different salts of CMC. All the divalent salts collapse into a single curve, with only minor differences occurring at high polymer concentrations (c & 0.2 M) between MgCMC and the other samples. This collapse is surprising given the different phase behaviour observed between the divalent cations and suggest that the conformation of CMC is not affected by specific counterion interactions in the concentration range studied. Given the polydispersity in DS of commercial NaCMC samples, it is likely that the turbidity observed for solutions at high concentrations is caused by the fraction of chains with a lower DS, while the more substituted fraction remain soluble. Throughout the unentangled regime, NaCMC displays viscosities approximately twice as large as the divalent salts, again signalling more expanded (less flexible) chains, in line with the results of Zhang et al(Zhang et al., 2001) and Dubois et al(Dubois and Boué, 2001) for polystyrene sulfonate.

3.3 Entangled dynamics At high polymer concentrations the trends observed in the unentangled regime are reversed and the viscosities of the different M2+ CMCs are larger than for NaCMC by nearly an order of magnitude. These enhanced viscosities may occur due to electrostatic bridging interactions between chains, which create temporary cross2 The exponent of 5.6 is obtained from fitting the highest concentrations in Figure 3b. Consideration of a wider concentration range yields lower exponents of ' 5

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Fig. 4 Specific viscosity as a function of polymer concentration for the different salts of carboxymethyl cellulose considered in this study. NaCMC (•), MgCMC (◦), CaCMC (4), CoCMC (), MnCMC (), BaCMC (O).

links. The observed behaviour is reminiscent to that observed in weakly substituted NaCMC, where interchain associations between unsubstituted regions of the cellulose backbone lead to strong power laws of the viscosity with polymer concentration. For weakly substituted NaCMC, these associations eventually lead to gelation, as DS is lowered or the concentration is increased(Lopez et al., 2018a). In order to further compare these behaviours, we studied the oscillatory response of the different M2+ CMC samples. Figure 5 plots storage (G0 ) and loss moduli (G00 ) of NaCMC and CaCMC solutions in the entangled regime a function of frequency (ω). The lines indicate the typical slopes observed at low frequency for monodisperse polymer solutions: G00 ∝ ω 1 and G0 ∝ ω 2 .(Rubinstein and Colby, 2003) The latter power law is not observed for the samples studied,which display G00 ∼ ω 1.4 , in line with other studies on polydisperse cellulose polymers (Chen et al., 2011, 2018; Lv et al., 2012). It is likely that the G00 ∝ ω 2 will only sets in at lower frequenciesLu et al. (2013); Wang et al. (2014).. The crossover between G0 and G00 provides a measure of the plateau modulus (GOsc ) and the longest relaxation time of the system (τOsc ). The Cox-Merz rule holds for all the samples studied. Table 4 compares the various rheological parameters extracted from fitting the steady and oscillatory shear rheology data for selected samples. The two estimates for longest relaxation times obtained from steady shear data differ by a factor of τInt ' 2 − 3τCY . Earlier studies(Boris and Colby, 1998; Lopez and Richtering, 2018) on solutions of monodisperse polyelectrolytes

Fig. 5 Storage (hollow symbols) and loss (full symbols) modulus as a function of frequency for NaCMC (part a, c = 0.25 M) and CaCMC c = 0.2 M. Measurements were taken at T = 1◦ C (circles) and T = 25◦ C (diamonds) and adjusted to the latter temperature via time temperature superposition.

have shown that both methods(Note 1, 2018; Lopez and Richtering, 2018) agree well. The differences observed in this study therefore may be assigned to the polydispersity of the CMC samples, which leads to a broadening of the flow curve. In order to evaluate which method provides a more accurate estimate, we compute the plateau modulus from steady shear data as G ' η/τ (Rubinstein and Colby, 2003), and compare it with the crossover point between the G0 and G00 curves in oscillatory shear. The latter method is known to underestimate the value of G00 plateau by around an order of magnitude (Liu et al., 2006) for systems with polydispersity of Mw /Mn ' 2 − 4. For most samples, we observe GCY /GOsc > 1 and GInt /GOsc < 1 , and


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we therefore conclude that the Carreau-Yasuda model (Eq.4) gives a better estimate of the plateau modulus of our samples than the intercept method, although it probably underestimates by a factor of 2-5.

entanglement density (Rubinstein and Colby, 2003), and is expected to scale as Gp ' c3/2 for polyelectrolytes in salt-free solution and Gp ' c2.3 for neutral polymers in good solvent. The latter agrees with the values observed for NaCMC and CaCMC. Following Eq. 7, the higher values of Gp observed for the divalent salts may result from temporary cross-links between chains. In contrast to the behaviour observed for NaCMC of varying degree of substitution, where Gp decreases as interchain associations become more significant (Lopez et al., 2018a), electrostatic bridging leads to the opposite effect, implying a different type of interchain associations in entangled solution. The reptation model predicts the longest relaxation time to vary with polymer concentration as: τ ∝ c3(ν−1)/(3ν−1)

Fig. 6 Longest relaxation time (a) and plateau modulus (b) obtained from Eq. 4 as a function of polymer concentration for different CMC salts. Lines best fit power laws for c > c∗∗ . The symbols have the same meaning as in Figure 4: NaCMC (•), MgCMC (◦), CaCMC (4), CoCMC (), MnCMC (), BaCMC (O).

Figure 6 plots the longest relaxation time and plateau modulus of the various salts studied as a function of polymer concentration. The data for the divalent salts largely fall onto the same curve. The plateau modulus provides a measure of the density of elastically active strands (µ) in solution (Rubinstein and Colby, 2003): Gp ' kB T µ

(7)

In semidilute entangled solutions without associative interactions between chains µ is determined by the

which leads to τ ∼ c0 for polyelectrolytes in salt-free solution and τ ∼ c1.6 τ ∼ c2.3 for neutral polymers in good and θ solvents respectively. For both monoand divalent salts the observed exponents do not match scaling predictions. The variation of τ ∼ c2.8 for the various divalent salts could be interpreted as either signalling that : I. Chains are near their ideal dimensions in the concentration range studied and therefore follow a power law close to θ solvents (2.3) or II. The power-law arises from a combination of entanglements and electrostatically bridged interchain associations. The first scenario seems unlikely since under that assumption we would expect the divalent datasets to converge with NaCMC at high concentrations, which is not observed. A c ' 0.3 M BaCMC sample does not show a Newtonian plateau at low shear rates and the apparent viscosity increases steadily as the shear rate is decreased (see Figure S4), which may correspond to the onset of gelation. The Cox-Merz rule is obeyed over the entire shear rate ranges studied. Figure 7 compares the flow index obtained from Eq. 4 as a function of concentration for the different CMC salts. In entangled solution, divalents salts display larger exponents, indicating greater degree of shear thinning. The data approach the value of n = 0.82 predicted for entangled polymer melts. Following Kulicke and co-workers(Clasen and Kulicke, 2001), we fit n as a function of polymer concentration to the expression: n = 0.82 − k1 ek2 [η]c

(8)

where k1 and k2 are dimensionless constants, compiled in Table 7. We approximate [η] = 1/c∗ . Analogous fits to n obtained form the intercept method are presented in the supporting information and display similar trends.

10


Table 4 Rheological parameters for entangled solutions of CMC. Sample Cation c (M)

η(0)

τCY (s)

nCY

bCY

Steady shear GCY (Pa)

Na+ Na+ Na+ Na+ Na+ Na+

0.25 0.18 0.14 0.097 0.063 0.044

3.8 1.3 0.48 0.17 0.057 0.029

0.011 9.2×10−3 7.1×10−3 4.2×10−3 4.8×10−3 3.2×10−3

0.74 0.62 0.51 0.43 0.25 0.21

0.62 0.72 0.82 0.85 1.4 1.3

340 140 67 40 12 9.0

0.022 1.8 × 0.013 8.5 × 4.8 × 4.5 ×

Ca2+ Ca2+ Ca2+ Ca2+ Ca2+

0.20 0.16 0.13 0.094 0.064

9.3 2.6 0.75 0.22 0.060

2.2×10−2 1.0×10−2 5.7×10−3 2.31.910−3 2.2×10−2

0.78 0.71 0.59 0.53 0.32

0.56 0.59 0.66 0.61 0.82

414 252 132 97 31

8.6 3.3 1.6 8.3 5.2

Mg2+ Mg2+ Mg2+ Co2+

0.22 0.16 0.08

6.2 1.95 0.13

0.0125 0.0079 0.0020

0.78 0.68 0.44

0.60 0.62 0.70

496 247 66

0.028 0.02 0.0077

0.16

2.96

0.015

0.66

0.66

0.66

Mn2+

0.16

3.1

0.017

0.66

0.65

177

τInt

Oscillatory shear τOsc (s) GOsc (Pa) 2.8 × 10−3 230 1.1 × 10−3 210

nInt

GInt (Pa)

10−3 10−3 10−3

0.65 0.59 0.44 0.35 0.25 0.19

172 72 37 20 12 6.4

-

10−2 10−2 10−2 10−3 10−3

0.58 0.56 0.46 0.37 0.23

110 79 48 27 11

0.67 0.55 0.3

221 98 17

200

0.029

0.03

0.58

× × × × ×

Equation 8 applies to data for different molecular weights for NaCMC samples in 0.01 M NaCl aqueous solution (as well as other polysaccharides) with a single set of k1 and k2 values (Clasen and Kulicke, 2001; Storz et al., 2010). For salt-free solutions, it is likely that k1 and k2 are Mw dependent since the entanglement and overlap crossovers are not proportional(Colby, 2010).

10−2

Comparison GCY /GOsc GInt /GOsc

-

1.47 0.67 -

0.75 0.34 -

5.6 × 10−3 2.9 × 10−3 -

247 158 -

1.7 1.6 -

0.44 0.50 -

0.0025 -

345 -

1.43 -

0.64 -

102

0.0021

230

0.88

0.45

103

0.0029

170

1.05

0.61

Table 5 Fit parameters to Eq. 8 for NaCMC and CaCMC samples. n is extracted using the two methods explained in the text.a Obtained from fitting data from reference 65 to Eq. 4 (Mw ' 3.2 × 105 g/mol, DS = 1.2), see also Ref. 66. b In 0.01M NaCl aqueous solution. Values from Refs. (Clasen and Kulicke, 2001; Kulicke et al., 1996). Obtained from a range of NaCMC samples of different molar masses 0.21 ≤ Mw × 10−6 ≤ 2.29. Sample DS NaCMC 1.3 NaCMC 1.0

Carreau-Yasuda [η] (M−1 ) k1 1.65 × 103 0.86 3 3.7 × 10 0.71

k2 0.0047 0.0030

Intercept method k1 k2 0.79 0.032 -

a

NaCMC 1.2 b

CaCMC 1.3

Fig. 7 Flow index as a function of polymer concentration for different CMC salts. Lines are fits to Eq. 8 to the NaCMC and CaCMC data. Symbols have the same meaning as in Figure 4: NaCMC (•), MgCMC (◦), CaCMC (4), CoCMC (), MnCMC (), BaCMC (O).

3.4 Dynamic light scattering Figure 8 shows the correlation functions for a 0.008 M CaCMC solution filtered through different pore sizes along with fits to Eq. 1, which describes the data well. All curves show a bimodal decay function. As the filter size is decreased, the slow mode becomes less prominent. Measurements on these solutions were carried out within a few hours after filtration. Dapp = Γ/q 2 for the fast mode is q independent. For the slow mode, Dapp varies linearly with q 2 and we obtain the translational

0.16 − 1.4 × 103 5.6 × 102

0.758 0.049

-

-

1.4

1.0

0.015

0.028

diffusion coefficient by extrapolation to zero angle via Eq. 2, see Figure S1. Figure 9a plots the diffusion coefficient of the fast mode (Df ast ) as a function of filter size for the CaCMC sample considered in Figure 8. For large pore sizes, the correlation functions are dominated by the slow mode (particularly at low angles) and it is therefore difficult to extract Df ast reliably. For the 0.1 and 0.2 µm filters on the other hand, Df ast can be evaluated with reasonable accuracy to be ' 1.8 ± 0.7 × 10−6 cm2 /s, about four times lower than that of the Ca2+ ion, indicated by the red line. Equation 3 calculates the hydrodynamic size of a particle from its diffusion coefficient assuming particles in solution, experience a drag force (F ) from the solvent viscosity of F ∼ vηs R, where v is the velocity of the particle and R is its size. This approximation is expected to hold when the particle size is much smaller than the mesh size of the polymer solution, so that diffusion is unhindered by the polymer chains. For NaCMC, the mesh size is ξ ' 21 nm at c ' 8 × 10−3 M(Lopez et al., 2015), which is much smaller than the size of the aggregates responsible for the slow mode (see Table 6). We therefore expect Eq. 3 will yield more reasonable estimates for the particle size using the solution viscosity


11

Fig. 8 Correlation function at scattering angle of θ = 150◦ for 0.008 M CaCMC in DI water, along with fits to Eq. 1. The curves correspond to different filter sizes, from bottom to top: 0.1 µm, 0.2 µm, 0.45 µm, 0.8 µm. Each curve is shifted upwards by constant value of 0.5 with respect to the one below for clarity.

instead of the solvent viscosity. While we do not have a direct measurement of the correlation length of the divalent salts, it is unlikely that it will increase to a value commensurate with the size of aggregates. Figure 9b compares the hydrodynamic diameter calculated using d0H = 2RH ηs /η, where RH is calculated using Eq. 3, for different CMC salts as a function of the pore size of the filters (dP ). The aggregate’s hydrodynamic diameter of Mg2+ , Mn2+ , Ba2+ and Ca2+ salts, approximately track the filter size for c . 200 nm, indicating that the aggregate size is restricted by the maximum size that can pass through the filter. For larger pore sizes, aggregates display values of d0H that are systematically lower than dP and we therefore expect these to approximately correspond to the ‘nonfiltered’ size of the aggregates. The size of the Co2+ and Na+ salts continues to increase as dP increases, signalling the presence of larger aggregates. The relative amplitude of the fast mode in the q = 0 limit, obtained by linear extrapolation of B1 /(B1 + B2 ) as a function of q 2 , is plotted in Figure 9c. Decreasing the filter size decreases the relative amplitude of the slow mode, which signals a smaller fraction of aggregated chains. The measurements presented above were carried out within hours after the sample was filtered into the cuvette. Significant changes on the aggregate size and

Fig. 9 DLS results as a function of filter pore size a: Fast diffusion coefficient Red line is the diffusion coefficient of Ca2+ . b: Estimated diameter of aggregates, line indicates d0H = dP . c: Relative amplitude of the fast mode. Red line is a guide to the eye to CaCMC data. Symbols have the same meaning as Fig 4: NaCMC (•), MgCMC (◦), CaCMC (4), CoCMC (), MnCMC (), BaCMC (O).

slow mode amplitude were found for selected samples re-measured approximately one week after, see Table 6. These changes reveal the non-equilibrium nature of the aggregates, and are in line with results obtained for NaPSS by Sedlak(Sedlák, 2002b). The effect of the total

12


Table 6 Ionic radius and diffusion coefficient of the various counter-ions considered. b Extrapolated to the q = 0 limit. a The values inside the brackets refer to measurements taken 7-10 days after filtration and the ones outside to measurements taken within 24 hrs after filtering. b Insoluble salt of CMC. Ion Cation Atomic Number Na+ 11 Mg2+ 12 Ca2+ 20 Mn2+ 25 2+ Co 27 Cu2+ 29 Ba2+ 56

Ionic Radius (˚ A) 1.02 0.72 1.00 0.83 0.745 0.87 1.35

6

D × 10 (cm2 /s) 13.3 7.06 7.92 7.12 7.32 7.14 8.47

6

Df ast ×10 (cm2 /s) 4.9 1.5 1.6 1.5 1.0 -b -

Polyelectrolyte 0.8 µm filter 0.2 µm filter a 0 RH,slow (nm) dH /dP RH,slow (nm)a d0H /dP B1 /(B1 + B2 )a 2000 750 800 (1900) 880 1200 750

solution agen (i.e. including the time from dissolution to filtration) was not investigated. The viscosity of a 0.008 M CoCMC solution was measured for filtered and non-filtered solutions. No changes in the viscosity could be observed within the error range (' ±5%) of our measurements. This suggests that clustering does not strongly affect the viscosity of CMC solutions, which agrees with earlier results by Reed and co-workers on NaPSS(Michel and Reed, 2000). Further evidence for this comes from the fact that despite the varying slow mode amplitudes and decay times for the different divalent salts of CMC, all display approximately the same viscosity as a function of concentration. Cellulose based polymers are known to assemble into supramolecular structures even in the absence of ionic groups along the chain(Schulz et al., b; Burchard, 2001, 2003; Schulz et al., a), and we therefore do not know to what extent the observed aggregates are of electrostatic origin. Douglas and co-workers have studied the impact of ion solvation(Chremos and Douglas, 2017, 2018b,a) on the aggregation properties of polyelectrolytes, concluding that it is essential feature to understand the origin of polyelectrolyte clustering. Water-ion solvation can be quantified through a dispersion energy W −Ion , which scales with the (experimentally accessible) Born radius of the ion (rB ) as W −Ion ∼ 1/rB . We do not observe any clear correlation between the ionic radius (' rB ) and the aggregation CMC, but this could arise from other effects (e.g. the degree of counterion condensation) which do not correlate strongly with rB affecting cluster formation. A recent theory by Muthukumar suggests that dipoles along the chain backbone can lead to physical crosslinks between different chains, which generate aggregates responsible for the slow mode (Muthukumar, 2016). Polyelectrolytes are then expected to display a critical micelle concentration above which they become highly aggregated. The conformational and rheological properties of non-entangled polyelectrolytes in salt-free solutions are reasonably well described by the Dobrynin model(Lopez

0.81 0.47 0.50 0.55 0.75 0.47

200 500 450 (370) 510 500 580

0.37 1.3 1.1 1.3 1.2 0.97

0.2 0.081 0.046 (0.137) 0.12 0.081 '0

and Richtering, 2018), which assumes no polyelectrolyte aggregation. For example, the terminal modulus of NaPSS in salt-free water is found to be in quantitative agreement with the scaling prediction of kB T c/N over a wide range of molar masses. Results for NaCMC, while more scattered, are in line with this observation(Lopez et al., 2016; Note 5, 2018) Highly aggregated and/or crosslinked solutions would be expected to depart from this behaviour. Overall, we conclude that current experimental evidence points towards polyelectrolyte clusters containing only a small fraction of chains, and hence affecting the macroscopic properties of polyelectrolyte solutions to a small degree.

4 Conclusions We have studied the impact of different counterions on structure and flow behaviour of semiflexible polyelectrolyte carboxymethyl cellulose. Divalent counterions shrink the chain dimensions compared to monovalent ones and, at high concentrations promote interchain associations via electrostatic bridging which lead to viscosity enhancements of up to an order of magnitude. We find that the type of divalent counterion has a significant impact on the phase behaviour and supramolecular aggregation of CMC. However, the flow properties (viscosity, relaxation times etc) are largely unaffected by counterion type. Our results suggest that clusters play only a small role in the macroscopic solution properties of carboxymethyl cellulose.

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