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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Intrinsic Viscosities of Polymer Blends: Sensitive Probes of Specific Interactions between the Counterions of Polyelectrolytes and Uncharged Macromolecules Maria Bercea*,† and Bernhard A. Wolf*,‡ †

“Petru Poni” Institute of Macromolecular Chemistry of Romanian Academy, 41-A Grigore Ghica Voda Alley, 700487 Iasi, Romania Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany

‡

Macromolecules Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 09/17/18. For personal use only.

S Supporting Information *

ABSTRACT: In joint dilute aqueous solutions of pullulan (PUL) and poly(sodium 4-styrenesulfonate) (PSS-Na) the Na+ ions of the polyelectrolyte interact so favorably with the monomeric units of PUL that isolated coils containing both types of macromolecules are formed upon dilution. When water is replaced against a 1 M solution of NaCl, this effect dies out because of the large surplus of Na+ ions. On the other hand, if the water contains increasing amounts of the respective counterpolymer instead of NaCl, the formation of mixed isolated coils is fostered, where a further diminution of the intrinsic viscosities is caused by the lower the solvent quality. The molar mass of PSS-Na plays an important role for the viscosities of the solutions in pure water. The reason lies in the different extent of the electrostatic selfshielding as a function of the polyelectrolyte concentration.

1. INTRODUCTION The intrinsic viscosities of polymer blends in a common solvent yield helpful information about the compatibility of polymers and raises some hope to obtain even quantitative access to polymer/polymer interaction parameters.1 Deviations of [η] from additivity have been reported for numerous polymer blends and can be interpreted as manifestation of highly favorable interactions between the macromolecular solutes. Examples for the typical behavior of blends (intrinsic viscosities less than additive) were reported for mixtures of poly(ethylene oxide)/poly(ethylene glycol),2 poly(3-hydroxy butyrat)/poly(ε-caprolactone),3 dextran/pullulan,4 and polystyrene/poly(4-vinylpyrridine).5 Blends of poly(vinylidene fluoride) and polystyrene,6 poly(vinyl chloride) and poly(εcaprolactone),7 poly(vinyl alcohol) and poly(styrenesulfonic acid),8 etc., testify that the intrinsic viscosity of the blend may result larger than the sum of the binary coils. There are also reports on an inversions of the sign of the deviation as a function of blend composition, as for example poly(ether sulfone) mixed with poly(vinylidene fluoride) or poly(styrene),9 carboxymethylcellulose/polyacrylamide, polyvinylpyrrolidone/methylcellulose,10 poly(vinyl alcohol)/sodium polystyrenesulfonate,8 chitosan/poly(vinyl alcohol),11 and more. The present study was performed to gain additional knowledge on the behavior of blends between charged and uncharged macromolecules in dilute solution. In particular, we wanted to investigate the role of the molar mass of the polyelectrolyte (because the spatial extension of this class of macromolecules is considerably more sensitive to M as © XXXX American Chemical Society

compared with uncharged polymers). Another item of interest concerned the effects resulting from the presence of solvent additives, namely either NaCl or the respective counterpolymer. To obtain the information we are looking for, relative viscosities were measured as a function of polymer concentration for the different ternary and quaternary systems and modeled quantitatively by means of a relation that contains three adjustable parameters, out of which one or two can normally be set zero. For this study we have chosen aqueous solutions of pullulan (PUL) and two samples of sodium polystyrenesulfonate (PSS-Na) differing largely in their molar mass. Pullulan is a water-soluble polysaccharide, stable to changes of temperature and pH, nontoxic, inert to most metals and ions, biodegradable and biocompatible with adhesive and prebiotic properties, and extensively used for biomedical, pharmaceutical, food, and cosmetic applications. Its structure consists of a linear glucan having three glucose units connected by α-1,4 glycosidic bonded maltotriose connected through α1,6 glycosidic linkage. Sodium polystyrenesulfonate was extensively used as a model polyelectrolyte system, and it was widely used for basic studies for understanding the polyelectrolyte features in aqueous solution.12−15 This polymer demonstrated also multiple functions for a wide variety of applications such as flocculation, personal care, and pharmaceutical products. It modulates the electrophoretic behavior Received: July 5, 2018 Revised: August 29, 2018

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DOI: 10.1021/acs.macromol.8b01422 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules disposable microfluidic devices by dynamic modification of the surface properties16 or enhances the monovalent selectivity of anion exchange membranes.17 PSS-Na is used in the treatment of hyperkalemia, even for the pediatric population18 when a close monitoring of serum electrolytes is required.19 In addition, many applications involve a good knowledge of their properties in solution when the electrostatic repulsive interactions between the ionized groups determine a stretched conformation of PSS-Na rods not only at infinite dilution but also at increasing polymer concentration.13 Thus, the viscosity in aqueous solutions evolves in an unpredicted manner when a neutral polymer is located in the environment of the charged coils.

ln ηrel =

1 + 2αc ̃ + (αβ − γ )c 2̃ {η} = [η ] (1 + βc ̃ + γc 2̃ )2

ln ηrel = c ̃ + (α − β)c 2̃ + (β 2 − αβ − γ )c 3̃ − (β 3 − αβ 2 − 2γβ + αγ )c ̃4... ln ηrel = c ̃ + M 2c 2̃ + M3c 3̃ − M4c ̃4...

M 2 = α − β ; M3 = β 2 − αβ − γ ; M4 = −β 3 + αβ 2 + 2γβ − αγ

(8)

(2)

The above considerations refer to binary systems, i.e., to solutions of a given polymer in a single solvent. Here we are also interested in the behavior of ternary systems consisting of solutions of a binary polymer blend in a single solvent. Under typical conditions infinite dilution will exclusively lead to the coexistence of isolated A coils and isolated B coils due to the unfavorable interaction between the blend components. This yields the following average value for the intrinsic viscosities of the blend:22,23

(3)

Sometimes c̃ is in the literature addressed as coil overlap parameter; this is, however, not permissible due to the fact that the spatial extension of macromolecules normally changes with concentration; for the typical case of thermodynamically favorable solvents the coils shrink as c rises. Because of this situation, the coil overlap Ω needs to be calculated using {η} (accounting for this effect) instead of [η] {η}c ≡ Ω

(7)

The leading term of the expansion is unity and stands for isolated solute molecules, and the factors M2, M3, and M4 quantify the contributions of binary, ternary, and quaternary interactions; their numerical value can be calculated from the system specific parameters as specified below:

By definition, [η] and {η} represent hydrodynamic specific volumes of macromolecules in solution. For better comparison of the effects of variable composition, polymer concentrations are often modeled in terms of c̃, the dimensionless reduced concentration, defined as [η ]c ≡ c ̃

(6)

The fact that eq 5 contains some of the system specific parameters in the denominator impedes their direct molecular interpretation. For that reason we perform a series expansion with respect to the reduced concentration up to the forth power in view of the dilute nature of the present solution. This procedure yields the following relations:

(1)

where η is the viscosity of the polymer solution at constant temperature, pressure, and shear rate γ̇, ηrel = η/ηsolvent stands for the relative viscosity, and c (mass per volume) denotes the polymer concentration. Equation 1 complies with the traditional designation and can be applied to any type of polymer solutions. Its great advantage lies in its ability to give access to unadulterated [η ] values for polyelectrolytes in the absence of extra salt. As compared with the traditional methods for the determination of [η] (like plots of (ηrel − 1)/c or ln ηrel/c versus c; please cf. SI2 of the Supporting Information), eq 1 has the great advantage of avoiding the “zero divided by zero” situation leading to infinitely large errors as c approaches zero. To relinquish the limitation of vanishing polymer concentration in the evaluation of viscosity data formulated in eq 1, one can introduce a generalized intrinsic viscosity20 {η} as i ∂ ln ηrel zy i ∂ ln η yz zz zz {η} ≡ jjj = jjjj z c ∂ k {c , T , p , γ ̇ k ∂c {c , T , p , γ ̇

(5)

The parameters α, β, and γ are system specific parameters and depend on the variables of state. Equation 5 is applicable over the entire range of polymer concentrations from the solvent up to the polymer melt and can even model the glassy solidification of polymer solutions. For uncharged polymers and the composition range of present interest (0 < c̃ < 2) at least one of the above parameters can be normally set zero. Equation 2 in combination with eq 5 offers the possibility to quantify the composition dependence of the hydrodynamically active specific volume of the polymers. If the generalized intrinsic viscosity {η} is normalized to [η] and the reduced polymer concentration is used as the independent variable, this relation reads

2. THEORETICAL BACKGROUND Application of the tools of phenomenological thermodynamics has led to the following alternative definition20 of the intrinsic viscosity of polymers in a given solvent: i ∂ ln ηrel yz i ∂ ln η yz zz zz [η] ≡ lim jjj = lim jjjj c→0 c 0 → ∂c z{T , p , γ ̇ γ→ γ→ ̇ 0 k ∂c {T , p , γ ̇ ̇ 0k

c ̃ + αc 2̃ 1 + βc ̃ + γc 2̃

[η] = wA*[η]A + wB*[η]B

(9)

However, for solutions of sufficiently favorably interacting polymers the situation may become different. In this case there exists a possibility to lower the Gibbs energy of the system by incorporating one A and one B molecule into isolated coils. If we denote the intrinsic viscosities measured for such cases as [η], the following inequality holds true:

(4)

The determination of [η] and of {η} according to eqs 1 and 2 requires precise modeling of the concentration dependencies. The following comparatively simple relation, formulated in terms of reduced concentration, has proven to be very versatile:21

[ η ] ≠ [η ̅ ]

(10)

The [η] values calculated according to the approach outlined above refer to the special situation that isolated coils contain one macromolecule A and one macromolecule B at the same B


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Macromolecules Table 1. Characteristics of the PUL and PSS Samples Used in the Present Study

binary stock. After the magnetic stirring, the mixtures were kept for 3 days at room temperature to guarantee thermodynamic equilibrium. The viscosities of the solutions were measured at 25 °C by using an Ubbelohde capillary viscometer (capillary diameter of 0.53 mm, type 0a) in combination with an automatic measurement system (Lauda Instruments, Germany). All samples were freed of dust by means of filters with a pore diameter of 0.45 μm. By successive dilution of the stock solutions, different polymer concentrations were prepared directly inside of the viscometer. After dilution, prior to the measurements, each solution was kept at 25 °C for at least 20 min. Kinetic energy corrections were taken into account. Flow times were determined at least eight times with errors less than 1%. Because of the fact that the intrinsic viscosities are according to eq 1 determined from the slope of ln ηrel vs c (and thus do not suffer from the “zero divided by zero” situation associated with the traditional methods), the precision of the viscosity measurement remains much less consequential than with traditional evaluation methods. Table 1 shows the formulas of the polymers and some characteristic parameters.

time. To quantify the deviation of the intrinsic viscosities measured for different blend compositions from additivity, we use the following expression: ε=

[η ] − [η ̅ ] [η ̅ ]

(11)

The ε values measured for the present system can be well modeled by means of the following power law: ε = E(wA*)a (wB*)b

(12)

where the w* values are the weight fractions of the components in the pure blend; E, a, and b are adjustable parameters.

3. MATERIALS AND PROCEDURES Poly(sodium 4-styrenesulfonate) (PSS-Na) samples with average molecular weights of 70 kg/mol (supplied by Polymer Standards Service GmbH, Mainz, Germany) and 1000 kg/mol (purchased from Sigma-Aldrich) were used as received. Even if moderate remainders of extra salt in these samples would not devaluate the central message of this study, we are in Supplement 1 demonstrating that the solvent salinity caused by extra salt contained in the present polymer samples remains well below 10−3 M/L. The pullulan (PUL) sample was purchased from TCI Europe N.V. and dialyzed against deionized water for 24 h at room temperature by using a dialysis membrane with molecular weight cutoff 20 kg/mol (deionized water was exchanged three times). The dialysate was filtered with a 0.45 μm filter to remove the precipitated material and freeze-dried. The molecular weight of pullulan was determined by size exclusion chromatography and viscometry as being 300 kg/mol. To check whether the sample contains noteworthy amounts of extra salt, we have determined the conductivity of its aqueous solutions using a Zetasizer Nano ZS (Malvern Instruments, UK) with a red laser 633 nm (He/Ne). For cPUL = 0.01 g/dL we have obtained 8 × 10−7 S/cm, and for cPUL = 1 g/dL we measured 1.92 × 10−6 S/cm as compared with 5 × 10−7 S/ cm for Millipore water. Binary stock solutions of PSS-Na (1 g/dL for PSS-Na 70 and 0.5 g/dL for PSS-Na 1000) and of PUL were prepared in Millipore water by magnetically stirring of the mixtures; the homogeneous solutions were then kept for 24 h at room temperature. The PUL/PSS mixtures of desired composition were prepared by using different ratios of the

4. RESULTS AND DISCUSSION 4.1. Single Solvent Water. Figures 1 and 2 show the evaluation of the viscosities measured for the pure polymers (PUL, PSS-Na 1000, and PSS-Na 70) and their blends in different solvents according to eq 5. The shape of the curves shown in the last two graphs differs fundamentally. For PSS-Na 1000 the dependencies interpolate smoothly between the curves for the pure polymer, whereas they intersect in the case of PSS-Na 70. This dissimilar behavior is caused by the differences in the [η] values of the blend components. The ratio of these values is about 30 in the former case, whereas it is only ∼3 in the latter. Higher intrinsic viscosities led to much lower self-shielding effects than lower [η] values.24 For that reason the viscosity of PSS-Na 70 can at higher polymer concentrations fall below that of PUL 300. The intrinsic viscosities obtained (eq 1) from the curves shown in Figures 1 and 2 are in Figures 3 and 4 depicted as a function of blend composition. The preceding graphs demonstrate that the intrinsic viscosities of the mixtures PUL + PSS-Na 70 and PUL + C


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the two PSS-Na samples qualitatively equal, despite the pronounced differences in the variation of ln ηrel with polymer concentration (intersection of lines for different blend composition) discussed earlier. This is, however, not surprising in view of the fact that intrinsic viscosities characterize the infinitely dilute state. The evaluation of the results according to eq 11 in Figure 5 demonstrates that the intrinsic viscosities of the blend may fall

Figure 1. Plot of ln ηrel as a function of polymer concentration (sum of PUL and PSS-Na) for blends of PUL 300 + PSS-Na 1000 of the indicated compositions and for the pure polymers.

Figure 5. Dependence of ε (eq 12) for pure water as a function of blend composition for the two PSS-Na samples with the molecular weights of 70 and 1000 kg/mol. The curves are modeled according to eq 12.

to half their value expected from eq 9, which corresponds to a reduction of the radius of gyration of the mixed isolated coil by ca. 20%. The curves shown in Figure 5 were calculated by means of power functions; in view of the comparatively large experimental errors for the PSS-Na rich blends, the results for both polyelectrolyte samples were evaluated conjointly (dotted green line). The present results are tentatively interpreted as an indication that the normalized deviation of the measured intrinsic viscosities from additivity as a function of blend composition do not depend on the molar mass of the polymers. Figure 6 shows how the parameters of eq 5 vary with w*. In all cases the parameter α is not required for the modeling of the results. The signs of β and of γ are identical for PUL and for PSS-Na, but the absolute values are much larger in the

Figure 2. As Figure 1 but for PSS-Na 70 instead of PSS-Na 1000.

Figure 3. Intrinsic viscosities of the blend PUL 300/PSS-Na 1000 as a function of w*, its composition.

Figure 4. As Figure 3 but for PSS-Na 70 instead of PSS-Na 1000. Figure 6. Dependence of the parameters β and γ (eq 5) on w*, the composition of the blend, for pure water (open symbols); α = 0 in all cases except for PSS-Na 1000 in pure water. Full symbols: PSS-Na solutions in 1 M NaCl; γ = 0.

PSS-Na 1000 deviate strongly from additivity (cf. eq 9). This behavior proves thermodynamically very favorable interactions between the two types of polymers. The coil shrinkages are for D


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Macromolecules latter case. This is due to the electrostatic interactions which modifies the viscosities of the solutions as a function of polymer concentration. Figure 6 also displays the β values for the PSS-Na solutions in 1 M NaCl. It is interesting to note that they are for both molar masses of the polyelectrolyte markedly lower than the values for pure water. This behavior results from the shielding of the electrostatic repulsion, which is due to salinity of the solvent. To gain some molecularly interpretable information about the viscometric effects, the contributions of binary to quaternary intermolecular contacts between the solute were also calculated eq 8. The results are shown in Figure 7.

Figure 8. Coil shrinkage as a function of the reduced polymer concentration c̃ for the two PSS-Na samples of different chain length calculated according to eq 6 by means of the parameters β and γ.

4.2. Mixed Solvents. In the previous section we have dealt with the intrinsic viscosities of polymer blends in pure water. Now we are shifting our attention to the behavior in solvents that contain salt or a certain constant amount of either polymer A or polymer B. In the former case we study the effects of electrostatic shielding; in the latter we want to know how the additional interaction between the two types of macromolecules modifies the intrinsic viscosity of the blend. Water + NaCl. The typical polyelectrolyte effects observed with water vanish if the solvent contains sufficient amounts of extra salt. Normally the saturation behavior as a function of the concentration of extra salt (following a Boltzmann sigmoid25) is reached as the salinity becomes on the order of 1 M as exemplified in SI1 of the Supporting Information. The results of measurements with 1 M NaCl are shown in Figure 9.

Figure 7. Mi parameters of eq 8 as a function of blend composition for solutions in pure water.

With the discussion of the Mi values it should be kept in mind that these parameters have a clear-cut molecular meaning only for binary systems. Table 2 lists their values for the solutions of PUL or PSS-Na in pure water. Table 2. Parameters of Eq 8 Resulting for Solutions of the Specified Polymers in Pure Water PSS-Na 70 PSS-Na 1000 PUL 300

M2

M3

M4

−2.52 −1.29 −0.13

6.76 1.61 0.02

−18.05 −2.00 0.00

The first member of the series expansion, M1, is unity in all cases and quantifies the effect of isolated coils. For the uncharged PUL the higher members are small and need only be considered up to the third order. For the PSS-Na samples the results depend markedly on their molar mass. The M2 and M3 values have the same sign as for PUL, but their absolute values are larger by at least an order of magnitude. The parameter M4 is only required for polyelectrolytes. The common reason for all the special effects observed with polyelectrolyte solutions in pure water lies in the phenomenon of self-shielding, which depends on their molecular mass.24 Figure 8 exemplifies this effect in terms of the dependence of the generalized intrinsic viscosity {η}, normalized to [η], on the reduced polymer concentration. Because of the higher segmental concentration in the shorter chain PSS-Na coils, the electrostatic shielding increases more rapidly as c̃ rises. From Figure 8 it can be read that the reduced concentration required for a halving of {η} amounts to 0.17 for PSS-Na 70 but 0.31 for PSS-Na 1000.

Figure 9. Plot of ln η rel as a function of polymer concentration for 1 M NaCl solutions of the neat polymers and blends (w* = 0.5) of PUL and PSS-Na.

Figure 10 exhibits the intrinsic viscosities obtained from these measurements. For both representatives of PSS-Na the results for the blends lie on the straight line connecting the values of the corresponding neat polymers; in other words, the [η] values are additive and obey eq 9. This result implies that the isolated coils contain either one macromolecule PUL or one macromolecule PSS-Na in contrast to situation encountered in the absence of extra salt. The evaluation of the results shown in Figure 9 with respect to the viscometric interaction parameters of eq 5 discloses that the β (the only required parameter) remains practically unchanged if pure water is replaced with 1 M NaCl solution. For the PSS-Na samples the effect depends on chain length. E


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intrinsic viscosity with respect to additivity for the present system leads to an [η] value of ∼1.8 dL/g. To explain the still lower values observed here, we require an additional effect. According to phenomenological consideration, this effect should be caused by the different solvent quality of the mixed solvent containing the counter polymer as compared with pure water. If we follow this reasoning, the present findings imply that the ternary coils interact unfavorably with the polymers contained in the mixed solvent and therefore shrink accordingly and the more so the higher its concentration becomes. This way of thinking would be consistent with the observation that similar intrinsic viscosities are reached in the limit of very large counter polymer concentrations in the mixed solvents.

Figure 10. Intrinsic viscosities of the blends PUL 330/PSS-Na 1000 and PUL 330/PSS-Na 70 as a function of w* for a saline solvent (1 M NaCl).

5. CONCLUSIONS AND OUTLOOK All experimental observations reported in the literature concerning the deviation of the intrinsic viscosities of blends can be convincingly explained in terms of the formation of mixed isolated coils, which is caused by highly favorable interactions between the solute molecules. The present results for mixtures of a polyelectrolyte with an uncharged polymer demonstrate that this effect cannot only be brought about by Gibbs energetically preferred contacts between the segments of the polymer backbones. The driving force may also consist of favorable interaction between the counterions of the polyelectrolyte and the monomeric units of the uncharged polymer. To the best knowledge of the authors, this is a phenomenon that was not yet reported in the literature. The only observation that points in this direction concerns the triggering of a reversible stiffness transition of poly(ethylene glycol) by K+ ions.26 In the case studied here it is the favorable interaction of the Na+ ions of PSS-Na with the monomeric units of PUL that causes the deviation of the intrinsic viscosities from additivity. The driving force for the establishment of PUL-Na+ contacts is obviously so large that the polymer backbone of PSS-Na is forced stay in the immediate vicinity of PUL even in the case of infinite dilution. The experimental observation that the intrinsic viscosities of the blends are additive in the presence of sufficient extra NaCl proves this interpretation. Under such conditions the favorable interactions can be established independent of PSS-Na due to the overabundance of free Na+ ions. The measured composition dependence of ε (the reduced deviation of the intrinsic viscosity of the blend from additivity, eq 12) as a function of the blend composition can be well modeled by means of power function. According to the present data the influence of different molecular weights of PSS-Na on this normalized quantity is little or absent. In contrast to this situation, the influences of the molar mass of the polyelectrolyte on ln η rel as a function of polymer concentration are significant. They are quantified and discussed by means of the system specific parameters β and γ (eqs 5 and 8). They enable the rationalization of the experimental observations in terms of the dissimilar coil shrinkage associated with an augmentation of the polymer concentration. Because of the higher charge density in isolated coils of the lower molecular weight sample, the self-shielding is much more pronounced than for the higher molecular weight sample. This means that viscosity increase with rising polymer concentration is in the former case much more subdued than in the latter case.

The presence of extra salt reduces β in the case of PSS-Na 70 by ∼8%, whereas the reduction amounts to ca. 47% in the case of PSS-Na 1000. This difference is caused by the fact that the extent of self-shielding is much more pronounced for the lower molecular weight sample, which reduces the contribution of salt shielding. With respect to the parameter γ the situation is more difficult because this parameter encloses contributions from binary and from ternary intermolecular contacts according to eq 8. Water + PUL or Water + PSS-Na 70. The last section described the changes in the viscometric behavior of the blend solutions resulting from the replacement of pure water as the solvent for the blends by water containing 1 M NaCl per L. Here we replace water by an aqueous solution of either PUL or PSS-Na of constant composition. In this manner we can study how the intrinsic viscosities are influenced by the presence of the counterpolymer in the solvent. Figure 11 shows the results for PUL 300 and PSS-Na 70.

Figure 11. Influence of the concentration of the counterpolymer in the mixed solvent on the intrinsic viscosities of PSS-Na 70 and of PUL 300.

In the absence of the counterpolymers in the solvent, we naturally measure the corresponding intrinsic viscosities for pure water. In the presence of counterpolymer, some ternary isolated coils will form (as discussed earlier) and some binary isolated coils will remain. Under the reasonable assumption that the fraction of ternary coils will increase as the counterpolymer concentration in the mixed solvent rises (law of mass action), we can explain the decline of [η] as the polymer content in the mixed solvent grows. However, from the results for polymer blends in pure water we know (Figures 4 and 5) that the largest reduction of the F


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In addition to mixed solvents consisting of water plus NaCl, we have also measured the intrinsic viscosities of the PUL and of PSS-Na in mixed solvents containing different amounts of the counterpolymer (PSS-Na in the case of PUL and PUL in the case of PSS-Na). It turns out that the fraction of mixed isolated coils containing both polymer components rises with an increasing content of the counterpolymer in the mixed solvent. Because of unfavorable interaction of these ternary coils with either PUL or PSS-Na of the mixed solvent, the intrinsic viscosities reached for high concentration of the counterion result only slightly larger than in very saline solvents. The radii of gyration of polyelectrolytes dissolved in pure water are normally governed by their concentration. In case of joint solutions of charged and uncharged polymers they may also be changed by the concentration of the uncharged component as demonstrated here. This phenomenon is due to the opportunity of the two different high molecular solutes to form coils that contain both components even in the infinitely dilute state. The details of the interactions between the polymers are not only of interest in the field of basic research; they should also have biological consequences, for instance, for the tailoring the size of macromolecules in solution or for the regulation of the concentration of certain ions, like Na+ in the present case. So far the effects of larger differences between the degrees of polymerization of the two macromolecules on the formation of mixed isolated coils have been ignored. It appears, however, reasonable to assume that more than one molecule of the shorter chain component may be incorporated if the interaction is so favorable that it compensates the loss in mixing entropy associated with that process.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01422. SI 1: solvent salinity caused by extra salt contained in the poly(sodium 4-styrenesulfonate) samples; SI 2: feasibility of evaluating viscosity measurements with respect to intrinsic viscosities in terms of Huggins plots for polyelectrolyte solutions in the absence of extra salt (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.B.). *E-mail: [email protected] (B.A.W.). ORCID

Bernhard A. Wolf: 0000-0002-4051-7114 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are very grateful to Dr. L. Nita (Petru Poni Institute of Macromolecular Chemistry, Iasi, Romania) for performing the conductivity measurements reported here. Furthermore, we thank Prof. H. Kunz (Institute of Organic Chemistry, University Mainz, Germany) for drawing our attention to special interactions between polysaccharides and different ions. G


Article

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