Rheological investigation on the associative properties of poly(vinyl alcohol) solutions

Poly(vinyl alcohol) (PVOH) is a water-soluble polymer largely used in the polymer industry. Typical applications involve the textile, paper, food packaging, coating, and adhesive industries [1]. PVOH is characterized by high chemical and thermal stability, low manufacturing cost, and high optical transparency in water [1]. Given its biocompatibility and biodegradability, PVOH has also gained much interest in biomedical applications, specifically for tissue engineering [2–8]. Poly(vinyl alcohol) is mainly obtained by means of hydrolysis of its hydrophobic precursor, poly(vinyl acetate) [9]. However, 100% hydrolysis to the PVOH homopolymer makes aqueous solutions prone to crystallization; most commercial PVOH is 75–90% hydrolyzed. The possibility of obtaining PVOHs with various degrees of hydrolysis (DH) has conferred to these systems unique properties, which have stimulated many fundamental studies as well [10–17]. Of particular interest here are the associative properties of aqueous PVOH solutions. Importantly, PVOHs that are not fully hydrolyzed in water exhibit a lower critical solution temperature (LCST) that strongly depends on the DH, in addition to mass concentration and weight-average molecular weight [18,19]. Increasing the acetate content decreases the LCST, preventing good solubility of PVOH in water at low temperatures [18].

Among the large body of literature, it is worth highlighting the following findings. Isasi et al. [20] studied PVOH solutions through infrared and NMR spectroscopy, demonstrating that the sequence distribution of acetate-vinyl alcohol within the polymer chain controls the hydrogen bonds. For block copolymers, hydroxyl-hydroxyl bonds are preferred, whereas in random copolymers hydroxyl-hydroxyl and hydroxyl-carbonyl associations compete. However, herein we present evidence that the latter seem to lead to stronger hydrogen bonds with longer lifetimes. Many studies revealed that the Huggins viscosity coefficient is a good indicator of polymer associations [21–30].

The Huggins coefficient should be small (k_H < 0.5) for good solvation of high molecular weight chains, as has been confirmed experimentally [21,31–36]. Lower % hydrolysis raises the Huggins coefficient above 0.5, which is attributed to temporary associations between PVOH chains in water. Lewandowska et al. [21] also observed that the higher the content of acetate, the higher the Huggins coefficient, similar to earlier work [28]. These observations tend to confirm the finding of Isasi et al. [20], for which the hydroxyl-carbonyl hydrogen bonds control the strongest associations. On the other front, for very high DH, recent atomistic molecular dynamics simulations [17] report that the intrachain hydroxyl-hydroxyl hydrogen bonds are very stable, resulting in a major driving force for crystallization and the formation of aggregates. This explains the typical insolubility of PVOH at high degrees of hydrolysis and low temperatures.

Flow curves are also good indicators of polymer associations. Three remarkable aspects are as follows: (i) An unusual Cox–Merz rule failure, where the steady-state value of the shear stress-growth coefficient is larger than the complex viscosity [37–41], opposite to the effect of edge fracture, which invariably lowers the apparent shear viscosity [42]. (ii) The transition between the Newtonian and the shear thinning power-law regime is much broader compared to nonassociating polymer solutions [37,43]. (iii) Stronger concentration dependences of the zero-shear viscosity and chain relaxation time above the chain overlap concentration than nonassociating polymer solutions, as theoretically predicted by Rubinstein and Semenov [44–46].

In this work, we use intrinsic viscosity and flow curves for a set of five industrial PVOHs, with varying molecular weight and DH, dissolved in either water or DMSO, to assess interchain associations. Data obtained in water agree with those reported in the literature, and a broad collection of results is presented. Remarkably, we demonstrate that by dissolving PVOH samples in DMSO, a strong hydrogen bond acceptor, polymer chain associations are fully prevented. Despite the vast realm of studies on PVOH, the present investigation provides the key strategies to detect polymer chain associations and control them by means of DMSO.

The five poly(vinyl alcohol) samples used in this work were provided by Procter and Gamble. Number- (M_n) and weight- (M_w) average molecular weights are provided by the company and reported in Table I, together with the polydispersity and the DH. The sample code reflects the M_w in kg/mol (k) and the DH, expressed in %. Our own solution ¹H NMR measurements in D₂O confirm the degrees of hydrolysis.

Solutions in water were prepared by adding cold (∼5 °C) deionized water (Milli-Q) into a glass vial containing a weighed amount of PVOH powder and stirring for at least 24 h, and a maximum of 72 h depending on the concentration, at 25 °C. For high concentration solutions (>15 wt. %), some gentle heating was required, not exceeding 40 °C. A final stir was also provided via a spatula to assess homogeneity. Solutions in DMSO were prepared with a similar procedure but dissolved far more readily. Room temperature DMSO was added to weighed PVOH powder and stirred. High concentration solutions (>15 wt. %), again, required temperatures up to 40 °C to achieve proper mixing.

Intrinsic viscosity measurements were performed using a Cannon Ubbelohde viscometer (CUC-75). The temperature control was ensured by a water bath using a Boekel Grant temperature controlling unit to hold the water at 25 °C. For each concentration, three runs were performed, their times averaged, and the viscosity of the solution taken from the average.

Rheology measurements under steady-shear conditions were performed with two strain-controlled rheometers. For pourable solutions, a Rheometrics Fluids Spectrometer (RFS-III) was used, equipped with a force rebalance transducer and a circulating water bath to control the temperature at 25 °C. Two concentric cylinder geometries were used, depending on the concentration, see Table II. A stress-controlled Discovery Hybrid Rheometer DHR-3 (TA instruments) was also used for high concentration solutions (>15 wt. %) where loading of a viscous sample into a concentric cylinder was not possible. A cone and plate geometry with a diameter of 20 mm and a cone angle of 1° was used with temperature control via a Peltier bottom plate.

After loading each sample, a thermal equilibration followed for at least 30 min. Each sample was presheared at 100 s⁻¹ for 1 min, to erase any mechanical history of the sample. No aging was observed for any of the solutions tested. Water evaporation was minimized by ensuring a water-saturated environment around the sample. Flow curves were obtained by means of ascending shear rate sweep experiments in the range 0.01–1000 s⁻¹. Each shear rate ran until steady-state conditions for the shear stress-growth coefficient were attained. The minimum shear rate was limited by the torque resolution of the rheometers, whereas the maximum shear rate was controlled either by the maximum torque resolution of the rheometer (RFS-3 equipped with concentric cylinder) or by edge fracture while using the DHR-3 with cone and plate geometry.

The obtained flow curves were then fitted to the Carreau model [47] (see Fig. S1 in the supplementary material) [57] in order to estimate the zero-shear viscosity η₀ and the chain relaxation time τ.

Owing to the high precision of its measurement, the intrinsic viscosity [η] is often used to determine various characteristics of polymer coils in dilute conditions; for instance, associations strength, solvency conditions, and coil size, without any polymer adsorption interfacial effects [48,49]. We used the methods of Huggins [Eq. (1)] and Kraemer [Eq. (2)] to determine [η] in water and DMSO,

where $ηr$⁠, the relative viscosity, is the ratio between the viscosity of the solution and that of the solvent; k_H is the Huggins coefficient; c is the concentration; and $ηsp=ηr−1$ is the specific viscosity. Both equations are limited to the second term, therefore including only single coil and two-body interactions. This is supported not only by the linear trend exhibited in the experimental results but also by the results obtained by Lewandowska et al. [21] on aqueous PVOH solutions who investigate the effect of including higher order terms in Eqs. (1) and (2), leading to negligible differences. The viscosities of pure water and DMSO were measured separately.

Figure 1 shows the Huggins and Kraemer plots in both water and DMSO. Table III lists the extracted intrinsic viscosity [η], Huggins coefficient k_H, and overlap concentration as c* = 1/[η], from Fig. 1. The Huggins coefficient was utilized as an indicator of polymer chain associations. To this end, a remarkable finding is that the Huggins coefficient drops considerably when PVOH samples are dissolved in DMSO. In particular, we highlight the 49k-75 sample, with the highest acetate content, which exhibits a drop of about a factor of 5. Milder is the drop in k_H displayed by the PVOHs with larger DH, suggesting the key role of the acetate groups in dominating chain-chain associations. A similar result was also observed by Lewandowska et al. [21].

Interestingly, the 49k-75 sample is also characterized by the lowest LCST among the investigated samples (not shown), suggesting that the vicinity of a phase boundary may also be crucial for a polymer solution to exhibit association effects [50].

Our k_H data are also reported in Fig. 2 as functions of the intrinsic viscosity (left panel) and DH (right panel). These agree well with the extended sets of data found in the literature, also shown in Fig. 2 [21,23,24,26–28,36,51,52]. This representation allows for drawing two important conclusions: (i) Huggins coefficient k_H ≤ 0.5 is normal for nonassociating polymer solutions (observed for PVOH in DMSO) but larger k_H > 0.5 and smaller intrinsic viscosity in water indicate aggregation [31]. Dilute coils of associating polymers adhere for some time when they collide, with M doubling but hydrodynamic volume R³ does not increase by as much as a factor of 2, making [η] ∼ R³/M decrease for an associating polymer solution [31]. (ii) The PVOHs with lower DH and intrinsic viscosity are more sensitive to associations, which we hypothesize is caused by more acetate groups, which dominate associations, presumably because the acetate-alcohol hydrogen bond is strongest (with the longest lifetime).

Equally interesting is the molecular weight dependence of the intrinsic viscosity shown in Fig. 3. In good solvency conditions, the intrinsic viscosity scales with molecular weight to the power of 0.76, whereas in theta solvent the power-law exponent is 0.50 [48]. Our observed data, as well as other data sets from the literature [21,23,26,52,53], display power-law exponents in the range 0.65–0.75, suggesting marginally good solvency conditions. The 49k-75 sample (lowest DH) exhibits a lower intrinsic viscosity compared to the 48k-88 sample, having the same M_w, but a higher DH (less acetate content). If both samples are dissolved in DMSO, they do exhibit the same intrinsic viscosity, as expected if associations are indeed prevented (see Fig. 3). It should be noted that, despite the strong suggestion for which DMSO prevents chain-chain associations, there is still an effect of DH on the intrinsic viscosity. In fact, the data of Schurz et al. [26] (open triangles) and Dieu [23] (vertical short lines), respectively, at 99% and 97% DH, display higher values of [η]. As $[η]∼b3$ [48], where b is the Kuhn monomer length, we hypothesize that strongly hydrolyzed PVOH may adopt a larger b value, owing to intramolecular helix formation which, in turn, favors crystallization, known to occur by hydrogen bonding in high-DH PVOHs [17,26]. An additional aspect we need to highlight is that the data from Ref. 52, despite being aqueous solutions, overlap with our DMSO data (no associations). We tentatively attribute the deviation from our aqueous solutions to the possible difference in the sequence distribution of acetate-vinyl alcohol within the polymer chains, which plays an important role in interchain associations [20]. The distribution of the acetate content was not the object of the present investigation, but certainly deserves more attention in the future.

Figures 4 and 5 depict typical flow curves for PVOH samples in water and DMSO, respectively. Various concentrations are reported in different panels. Additional flow curves and analysis are reported in Figs. S2 and S3 in the supplementary material [57]. It is known that strong shear flows promote chain associations, manifested as an abnormal Cox–Merz rule failure, where the complex viscosity is lower than the steady-state value of the shear stress-growth coefficient in the shear thinning regime [37]. An example of a Cox–Merz failure is shown in Fig. 6, for the 144k-88 sample at 16 wt. % in water. In addition, as clearly shown by Regalado et al. [37], associating polymers exhibit a broader transition between the Newtonian and the power-law shear thinning region compared to that of nonassociating polymers. To this end, we show in Fig. 7 flow curves normalized by the zero-shear viscosity, for samples 144k-88 and 171k-80 in both water and DMSO at the same mass concentration. It is remarkable the effect of chain-chain association on the Newtonian to power-law shear thinning transition region. Moreover, the solutions in DMSO allow for the estimation of the shear thinning slope, which is equal to −0.5, expected for polymer solutions [37,54,55].

Within the hypothesis that each carbonyl group is a potential sticker, we consider the case for which the number of monomers between adjacent stickers N_s is smaller than the number of monomers in both a correlation blob, g, and an entanglement strand, N_e; N_e > g > N_s. In other words, there are many stickers in each entanglement strand, and even many in each correlation volume (sticky blob, see schematic in Fig. 8). In this limit, most associations are intramolecular (as the blobs are effectively right at their overlap concentration and hence inside the blobs is quite like dilute solution) since inside the correlation blobs there is only one chain. One can further assume that each sticky blob contributes to of order one intermolecular association so that the number of monomers between intermolecular associations $Ns≅g$⁠. The number of monomers in a correlation volume writes [48]

where ϕ = c/c* is the polymer volume fraction and $ν$ is the Flory exponent. The concentration dependence of the number of monomers in an entanglement strand is [48]

The Flory exponent ν is equal to 0.59 in athermal solvent [48]. Note that both solutions give a concentration dependence of $Ne(ϕ)∼ϕ−1.3$⁠. It follows that the number of intermolecular associations per chain is

where N is the degree of polymerization of the polymer chain. The relaxation time of the chain, based on the solution of the reptation model, writes [48]

with τ_s being the lifetime of a sticker, which we assume does not depend on concentration. By substituting Eqs. (3) and (4) into Eq. (6), we obtain

The concentration dependence of the entangled terminal modulus for both good and θ solvency conditions is [48]

It follows that the concentration dependence of the viscosity can be written as

An additional indicator of associating polymer features is, therefore, represented by the concentration dependence of the viscosity and chain relaxation time [Eqs. (7) and (9)] [44,45]. Figure 9 presents the specific viscosity (panel A) and the chain relaxation time normalized by the viscosity of the solvent (panel B) as functions of concentration normalized by the overlap concentration (see Table I), for the samples investigated in this work. Figure 9(b) only reports the comparison between the two highest molecular weight 171k-80 and 144k-88 samples. Poly(ethylene oxide) (PEO) [48] and 100% hydrolyzed PVOH [56] data taken from the literature are also added in panel A for comparison. For c/c* < 1, solutions are below their overlap concentration, and there are only subtle differences in $ηsp$ between solutions in water or DMSO, or PEO in water [shown in Fig. 9(a) and the subtle differences are better shown by intrinsic viscosity and Huggins coefficient discussed previously]. Above the overlap concentration (c/c* > 1), remarkable differences between associating and nonassociating polymers start to emerge. For the latter, a slope of 2 is predicted in the region between the overlap (c/c* = 1) and the entanglement concentrations [c_e/c* ∼ 7 in DMSO, see Fig. 9(a)], in θ conditions [48]. Above the entanglement concentration, a slope of 4.7 indicates the viscosity scaling in θ solvent for entangled DMSO solutions [48]. In the same regime, the concentration dependence of the chain relaxation time in DMSO follows a power law with exponent 2.3, as also expected for entangled solutions in θ conditions [see open symbols in Fig. 9(b)]. For semidilute solutions, it is vital to note that θ conditions often apply even in good solvent, if the thermal blob is sufficiently large [48]. Note also that 100% hydrolyzed PVOH [56] follows the predicted trend for nonassociative polymers [see X symbols in Fig. 9(a)], as the acetate content, dominating the interchain associations, is zero.

On the other hand, associating polymers exhibit an even stronger concentration dependence of both specific viscosity and relaxation time, above the overlap concentration. In Fig. 9(a), a slope equal to 7.6 was observed, consistent with the prediction of Eq. (9) and corroborating the sticky-blob argument introduced above. Similarly, the chain relaxation time, within the same entangled concentration regime, scales as $τ∼(c/c∗)5.3$⁠, in good agreement with Eq. (7), for θ conditions. The Mark–Houwink exponents in Fig. 3 suggest good solvency conditions in dilute solution so the finding of θ-solvent scaling in entangled solution simply suggests a large thermal blob for PVOH in both water and DMSO. The solution correlation length decreases as the concentration is raised and reaches the thermal blob size at c**, above which the entire chain has an ideal conformation. Figure 9(a) suggests c** ≈ 8c* for PVOH in water, making all entangled solutions involve chains that are random walks.

By using the DMSO solutions as a reference for nonassociating PVOH chains, it is possible to quantify the time delay exerted by the interchain associations observed in aqueous solutions. This is done by dividing the chain relaxation time of the aqueous solutions by that of the DMSO ones at the same concentration. The terminal relaxation time for nonassociating entangled polymers in solution, here called τ_DMSO, writes [48]

with τ_e and τ₀ being the relaxation times of an entanglement strand and of a Kuhn monomer, respectively. It follows that the ratio between Eqs. (7) and (10) is

The monomer relaxation time τ₀ in DMSO is proportional to the viscosity of DMSO, while the association lifetime τ_S is proportional to the viscosity of water.

Figure 10 depicts the ratio of the relaxation times in water and DMSO normalized by the solvent viscosities, to quantify the concentration dependence of the delay from associations in Eq. (11), as a function of the polymer volume fraction for samples 171k-80 and 144k-88, reasonably assuming that the density of water and DMSO is nearly the same and equal to 1 g/cm³. The observed data seem to agree well with the scaling prediction for the interchain associations time delay in θ conditions, reported in Eq. (11). Remarkably, the data observed for the 171k-80 sample are larger than those for the 144k-88 one, suggesting once again the importance of the carbonyl groups in dominating interchain associations. To this end, Fig. 10 can also be used to determine in an elegant way the effective association energy (E) for the slowest associations of the two highest molecular weight samples with different acetate content. In fact, the sticker lifetime τ_s can also be written as a product between an attempt time τ_attempt and the effective energy barrier of one interchain association [46],

The attempt time is assumed to be the monomer time in water, written as

where τ₀ is the monomer time (attempt time) in DMSO. By combining Eqs. (11)–(13), it is possible to write

For θ conditions, we can write

The dashed lines in Fig. 10 correspond to E/kT = 6.8 for 171k-80 and E/kT = 6.0 for 144k-88. This further supports our hypothesis that acetate groups are involved in the strongest associations and 6 < E/kT < 7 is expected for hydrogen bonding. The vertical shift between the two data sets is equal to ∼2, which can be explained both in terms of activation energy difference, $e(6.8−6)=2.2$⁠, and with the ratio of acetate content in the two samples, $20/12≅1.7$⁠. Such an analysis shows the power of having two solvents for the same polymer, one in which the polymer associates (water) and the other where no associations are present (DMSO) as that enables the estimation of association energy with just isothermal data. Future work will study the temperature dependence of terminal relaxation times to further test Eq. (15).

We have shown that aqueous solutions of PVOH (presumably random copolymers of vinyl alcohol and vinyl acetate with DH between 75% and 88%) exhibit clear signatures of associative polymers. Associations are dominated by either hydroxyl-carbonyl hydrogen bonds or acetate-acetate hydrophobic interactions; the lower the DH, the stronger the interchain association effect. However, the observation that the hydrogen bond acceptor DMSO eliminates interchain associations strongly suggests that alcohol groups are involved in water, so the alcohol-acetate hydrogen bonds are likely the dominant associations. Chain associations emerged in various ways: (i) the Huggins coefficient takes values larger than 0.5, (ii) the specific viscosity and the chain relaxation time exhibit a strong concentration dependence, (iii) the Newtonian-shear thinning transition region of a flow curve is very broad, and (iv) the Cox–Merz rule is violated in an unusual way in Fig. 6.

We proposed a “sticky-blob” model that should apply quite generally weakly to associating polymer solutions with many repeat units having a sticker so that there are many stickers present within each correlation volume. We then assumed that each sticky blob contributes to an interchain association. This simple model leads to strong concentration dependences of both specific viscosity and relaxation time, in the entanglement regime, which agrees very well with our observed data for poly(vinyl alcohol) in water.

When the same PVOH samples were dissolved in DMSO, polymer chain associations were prevented, and all the features of nonassociative polymers were unambiguously restored. This is a fortuitous result that allows direct comparison with aqueous solutions to quantify association effects in water. At any entangled concentration, the ratio between the relaxation times of aqueous and DMSO solutions represents the time delay due to interchain associations. The sticky-blob model proposed in this work is able to capture quite well the concentration dependence of this time delay in Fig. 10. That allowed estimation of an effective association energy, which is found to increase with acetate content. If the associations were stronger, perhaps dynamics with so many stickers would be described by Ref. [58], but there is no evidence of strong aggregation in PVOH/water solutions. Future work should focus on better ways to quantify the relaxation time of sticky-blob polymer solutions, as the crossover from zero-shear viscosity to power-law shear thinning becomes too broad for existing models to fit the flow curves when every correlation volume is a sticker.

The seed idea for this work and the work itself were supported by Procter & Gamble. The authors thank the student Melisa Slye for helping with flow curve measurements. The authors declare no competing financial interest.

The authors have no conflicts to disclose.