Hydrogen-bonded polymer complexes (HBPCs) form upon association of macromolecules via multiple intermolecular hydrogen bonds. The transient nature of their hydrogen bonding enables their responsiveness to external stimuli such as pH, temperature, and solvents or external fields. Here, hydrogen-bonded assemblies were obtained via the complexation of a triblock copolymer Pluronic® F127, with poly(methacrylic acid) (PMAA). Various rheological material functions of PMAA/F127 complexes, including dynamic properties, relaxation modulus, and shear viscosity, were characterized using steady torsional, oscillatory shear, step strain, compressive squeeze, and capillary flows. The structure of the HBPCs involves agglomerates of the hydrogen-bonded complexes, i.e. nanoclusters, connected by hydrogen bonding interactions. The strengths of the hydrogen bonds in the HBPCs could be manipulated via the exposure of these complexes to aqueous solutions at different pH levels and/or cosolvent concentrations, resulting in changes in the elasticity and viscosity of the HBPCs. Especially the ionization degree, the resultant ratio of the polyacid to F127, and the development of micro- and nanoscale porosity played significant roles in the manipulation of the rheological behavior of the HBPCs. Under low pH conditions, the PMAA/F127 HBPCs could be extruded from capillary dies with relatively small diameters (800–1500 μm) and high length over diameter ratios (40–60). Upon exit from capillary dies, the extrudates preserved their shape, albeit exhibiting flow instabilities and the associated bulk distortions at high shear rates. Under low pH conditions, the generalized Maxwell model described the relaxation modulus in the linear regime, and the Kaye-Bernstein, Kearsley and Zapas model was effective in the prediction of the shear viscosity of the HBPC. The self-healing behavior of PMAA/F127 complexes was demonstrated and linked to the pH-controllable hydrogen-bonding interactions between PMAA and F127.
Polyelectrolyte complexes have long been recognized as versatile materials for promising applications in the biomedical [1,2], energy , and pharmaceutical  industries. Polyelectrolyte complexes include the electrostatically paired assemblies and the hydrogen-bonded polymer complexes (HBPCs). Electrostatically paired assemblies are entropically driven and involve polyelectrolyte chains of opposite charge, which on assembly release counter ions . On the other hand, hydrogen-bonded complexes, HBPCs, form from the association of macromolecules via multiple intermolecular hydrogen bonds [6–15]. Hydrophobic interactions can be utilized to stabilize HBPCs [14,16–19]. HBPCs exhibit a transient nature of bonding which enables their responsiveness to external stimuli such as pH, temperature, solvents, or external fields (shear, electric and magnetic fields) . Hydrogen-bonded structures permit the tailoring of material properties in a reversible manner via changes in the strength of the hydrogen bonds [20–22]. A recent investigation has shown that hydrogen bonding can be employed to program shape memory in materials without the use of external triggers .
There is a significant body of investigations, which probe the rheological behavior and functional properties of polyelectrolyte solutions and polyelectrolyte gels [24–27], as well as the processability of electrostatically paired polyelectrolyte complexes [2,28–31]. However, in spite of the greater responsiveness and versatility of HBPCs, as compared to their electrostatically assembled counterparts, relationships between the hydrogen bonding interactions, rheological behavior, and functional properties of HBPCs are poorly understood. This poor understanding is a handicap for the shaping of the hydrogen-bonded assemblies and generally, restricts their processing to the layer-by-layer deposition technique [32–37]. A notable exception is the recent work of Li et al., that involves the labor-intensive preparation of HBPCs of poly(acrylic acid) and polyethylene oxide (PEO), which could be converted to fibers at appropriate pH levels . The utility and industrial applicability of hydrogen-bonded polymers would increase significantly if their processability window could be widened, especially if they could be shaped via standard polymer processing methods, including injection molding, transfer molding, and extrusion. A recent example of the importance of the shapeability of hydrogen-bonded polyelectrolytes is the proposed use of a pH-sensitive and elastic HBPC in a gastric device .
Recent studies have shown that hydrogen-bonded nanostructured complexes can be prepared based on block copolymer micelles (BCMs) . BCMs contain hydrophobic pockets, enabling the loading of bioactive payloads that can be released via environmental stimuli such as changes in solvent, pH, temperature or light [24–28]. One block copolymer that is especially interesting for the formation of hydrogen-bonded assemblies is the Pluronic® block copolymer, i.e., poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) (PEO-b-PPO-b-PEO). Pluronic block copolymers form micelles in dilute aqueous solutions, or micellar nanostructured gels in concentrated solutions under physiological temperatures , and are widely investigated as pharmaceutical delivery systems on the basis of their temperature sensitivities [40–44]. A recent study has reported that Pluronic F127 triblock copolymer (F127) can form nanostructured hydrogen-bonded complexes with weak polyacids that are responsive to pH and temperature . However, the rheological behavior and the processability of these novel HBPC assemblies, and the relationships between their rheological material functions and structure have not been investigated.
Here, the linear viscoelastic material functions, i.e. the storage and loss moduli, the magnitude of complex viscosity, and relaxation modulus of F127 and poly(methacrylic acid) (PMAA), complexes were characterized as functions of the pH and the cosolvent concentration. The dynamic properties of PMAA/F127 complexes were correlated with the ionization of PMAA and the composition of the HBPCs as quantified by Fourier transform infrared spectroscopy (FTIR). The PMAA/F127 complexes were found to be extrudable at pH = 2. Steady torsional, oscillatory shear, step strain, compressive squeeze, and capillary flows were used, and the material functions of PMAA/F127 complexes at pH = 2 were elucidated by using a Kaye-Bernstein, Kearsley and Zapas (K-PKZ) type nonlinear viscoelastic constitutive equation . Finally, the ability of the Pluronic/PMAA complex to self-heal was demonstrated using small-amplitude oscillatory shear.
PMAA (Mw 150 kDa) was procured from Scientific Polymer Products, Inc. Pluronic F127 consisted of PEO98–PPO67–PEO98, and had a Mn of 12.5 kDa (Sigma-Aldrich), Safranin O, N-hydroxysulfosuccinimide sodium salt (sulfo-NHS) and the cosolvent dimethyl sulfoxide (DMSO) were obtained from Sigma-Aldrich. CF400-Cu-UL 400-mesh ultrathin transmission electron microscopy (TEM) grids were supplied by Electron Microscopy Sciences. Lab-Tek® 155411 8 Chambered #1.0 Borosilicate and 1-ethyl-3-[3-dimethylaminopropyl]carbodiimide hydrochloride (EDC) were purchased from Thermo Scientific, and Alexa Fluor 488 hydrazide (Alexa-488) was obtained from Invitrogen Co., CA. The substrates for FTIR were 525 ± 25 μm thick, n-doped (110) silicon wafers that were received from Virginia Semiconductor, VA. Ultrapure Milli-Q water (Millipore) with a resistivity of ∼18 MΩ-cm was used in all experiments.
B. Preparation and composition/structure characterization of HBPCs
All polymers were used as 20 mg/ml solutions in Milli-Q water. Typically, PMAA/F127 complexes were prepared by adding ultrapure water and 20 mg/ml F127 solution to a 20 mg/ml PMAA solution at room temperature to achieve an ultimate PMAA/F127 mass ratio of 1.5/1. The final concentration of F127 in the mixture solution was 0.5 wt. %. The pH of the solution was adjusted to pH 2 using 1 M HCl. The precipitated complexes were collected by centrifugation at 4000 rpm for 10 min, rinsed with water at pH 2, and stored at pH 2. A PMAA/F127 mass ratio of 1.5/1 was selected based on our prior results . Specifically, this is the lowest PMAA/F127 mass ratio at which the precipitation of complexes occurred. At a high total content of PMAA in the mixture the ratio of PMAA/F127 in the precipitates remained constant.
The polyelectrolyte complex samples were exposed to aqueous buffer solutions at different pH and to different solvent concentrations following the procedures that are outlined in Appendix A. The fractional mass values of hydrogen-bonded complexes that survived the exposure to different pH and solvent concentrations were determined using weight measurements. FTIR spectra of the HBPCs were deconvoluted, and specific spectroscopic bands characteristic of PMAA and F127 components were calibrated using PMAA/F127 of known concentrations to allow the quantitative determination of the ratio of F127 to PMAA, the degree of ionization and the cosolvent DMSO content within the complexes. Fluorescently labeled PMAA solutions, PMAA* (∼25 μg/ml) were prepared, and TEM and confocal microscopy imaging of the HBPC samples were carried out following procedures that are provided in Appendix A.
C. Rheological characterization
The details of the apparatus and the procedures used for the characterization of various rheological material functions of the HBPCs are presented in Appendix B. The characterization methods included small-amplitude oscillatory shear, step strain, steady shearing using parallel plate and cone and plate geometries, squeeze flow, and capillary rheometry.
III. RESULTS AND DISCUSSION
A. Effects of exposure of the HBPC to aqueous buffer solutions at different pH
The overall effects of the pH level (without the use of a cosolvent) on the storage modulus and the magnitude of complex viscosity, determined via small-amplitude oscillatory shearing, are shown in Fig. 1. As the pH increases from 2 to 6, the elasticity and the viscosity of the HBPCs diminish. The reduction of the viscosity renders the processing of the HBPCs easier, considering that the pressurization requirements for shaping would be reduced. However, the reduction of the storage modulus signals a reduced ability of the HBPCs to maintain their shapes upon processing. A sharp transition in elastic and viscous behavior occurs at pH = 5.5. The pH associated with the sharp transition is close to the pKa of the PMAA of 6–6.5 . However, a direct correlation is not expected . The transition pH is dependent not only on the pKa of a weak polyacid but also on the strength of hydrogen bonding between the polyacid and the polybase. What causes the decrease of elasticity and viscosity with increasing pH?
By imaging the fluorescence of labeled PMAA*/F127 complexes using confocal laser scanning microscopy (CLSM) in the wet state, it was observed that the porosity of the PMAA*/F127 increased when the pH was increased [Figs. 2(a) and 2(b)]. The TEM images of the PMAA/F127 at pH 2 and 5 are indicative of the network structures that prevail in the complexes that were dried from the solution at pH = 2 and 5. The structure consists of agglomerates of the hydrogen-bonded complexes, i.e. nanoclusters, connected with hydrogen bonding interactions while exhibiting an open network structure. Figure 2(b) indicates that the HBPCs develop significant microscale porosity upon the breakdown of the network after exposure to the buffer at pH 5 (the CLSM data were collected while the samples were immersed in a buffer solution). Hydrogen-bonded complexes of weak polyacids are known to weaken upon the increase of the pH of the solution as a result of enhanced ionization of the polyacids [39,47], and the reduction in the hydrogen bonding interactions between the micelles of the F127 block copolymer and PMAA. These effects are likely to contribute to the observed greater porosity of the hydrogen-bonded complexes at pH = 5 (Fig. 2).
In order to understand better the effects of pH on the complexation of PMAA/F127, FTIR spectroscopy was used to determine the component ratio in the pH-treated complexes [Fig 3(a)]. The 1700 and 1730 cm−1 bands are associated with >C = O stretching vibrations of PMAA and the bands at 1065 and 1104 cm−1 are associated with the asymmetric and symmetric –C–O–C– stretching vibrations of F127. The ratio of PMAA/F127 remaining in the HBPCs after a 12-h exposure to the aqueous buffer solution at a given pH was determined from the ratio of the sum of the intensities (obtained via integrations of areas under the curves) at 1700 and 1730 cm−1 bands over the sum of the intensities associated with the bands at 1065 and 1104 cm−1. The FTIR calibration curve of the PMAA and F127 mixture at various PMAA/F127 ratios is available . The mass ratio of PMAA to F127 is determined to be ∼1.5/1 at pH 2 and decreases to ∼1.2/1 at pH 5 [Fig. 3(b)]. The FTIR analysis of the PMAA/F127 complexes also indicated that the increased pH resulted in the deprotonation of PMAA as evidenced by the emergence of the 1570 cm−1 band associated with asymmetric stretching vibration of the deprotonated carboxylic group  [Figs. 3(a) and 3(c)] and diminished hydrogen bonding between PMAA and F127. Therefore, the integrities of the PMAA/F127 complexes were reduced due to the smaller number of intermolecular hydrogen bonds, and higher amounts of PMAA were lost during the dissociation of the complexes at high pH buffer.
Spectral deconvolution of the FTIR data enables the determination of the degree of ionization of PMAA in the PMAA/F127 complexes, i.e. the fraction of the carboxylic groups of PMAA that dissociates in the aqueous solutions at various pH values. The ionization degree of PMAA in HBPCs was determined from the ratio of the band intensity at 1570 cm−1 associated with deprotonated carboxylate groups over the total >C = O intensities, calculated as the sum of the contributions of the 1570-cm−1 band and two bands (1700 and 1730 cm−1) of the protonated form of carboxylic groups. In this calculation, the extinction coefficients for the bands assigned to protonated and dissociated forms of the acidic groups are assumed to be equal [32,49].
Figure 4 shows that the ionization degree of PMAA increases with increasing pH of the buffer solution used to treat HBPCs. The elasticity as represented by the storage modulus and the magnitude of complex viscosity decrease monotonically with increasing ionization degree. Significant step changes in and are noted for the pH range of 4–5.5 suggesting that a trigger mechanism is activated in between the pH values 2–4 and 5.5. This behavior is consistent with the TEM, confocal microscopy and FTIR data of the HBPCs obtained at pH = 2 and pH = 5 as shown in Figs. 2 and 3.
B. Effects of cosolvent
The effects of exposure of the HBPCs to a polar aprotic cosolvent were investigated using DMSO. DMSO is a good hydrogen bonding acceptor, and should be able to weaken the hydrogen bonding between the block copolymer and the polyacid. This is indeed what was observed via the dynamic properties that are reported in Fig. 5. The and values in the 0.1–100 rad/s range decrease monotonically when the cosolvent concentration in the aqueous buffer solution is increased successively from 0% to 40% in steps of 10% each (overall an order of magnitude decrease).
What gives rise to the decreases in elasticity and viscosity of the HBPCs associated with exposure to the cosolvent, DMSO? Are the causes similar to those associated with exposure to buffer solutions with increasing pH?
Figure 6 shows that the effects of the cosolvent DMSO on PMAA/F127 complexes differ from the pH effects in that a reverse trend is observed for the change in the mass ratio of PMAA over F127 with increasing solvent concentration. There appears to be an increase of the PMAA/F127 ratio with increasing DMSO concentration, whereas a decrease of the PMAA/F127 ratio was observed for increasing pH. The FTIR spectra of the PMAA/F127 complex treated with pH = 2 aqueous solutions with increasing concentration of DMSO showed that the ratio of the band intensity of carbonyl groups in PMAA (1700–1730 cm−1 region) to ether groups in F127 (1104 cm−1 band) increased, indicating the decrease of the F127 content in the HBPC [Fig. 6(a)]. Use of an available calibration curve  revealed that the PMAA/F127 mass ratio increased from 1.5/1 to 4.5/1 when the DMSO concentration increased from 0% to ∼40% [Fig. 6(b)]. This suggests that F127 is preferentially removed from the PMAA/F127 complexes upon exposure to the buffers with increasing DMSO concentrations.
In spite of the large change in the PMAA/F127 composition, the decrease in the total mass of the HBPCs in DMSO/water solutions was only moderate [Fig. 6(b)], suggesting possible inclusion of the cosolvent DMSO, within PMAA/F127 complexes. Indeed, from FTIR spectrum of the dried DMSO treated complexes, a DMSO peak at 1020 cm−1, associated with >S = O stretching vibrations was observed. This suggests that DMSO has partially replaced the F127 in the hydrogen-bonded PMAA/F127 complexes. This mechanism is consistent with the TEM and confocal images showing the formation of nanosized pores resulting from the removal of F127 micelles from the material, and increased transparency of the complexes that are treated with DMSO (Fig. 7).
The effects of the cosolvent DMSO treatment on the elasticity and viscous behavior are shown in Fig. 8 as a function of the DMSO/F127 ratio at various solvent concentrations in the buffer solutions. It appears that the ratio of the DMSO to F127 is indeed a critical factor in giving rise to the deterioration of the linear viscoelastic properties, i.e. the storage modulus and the magnitude of complex viscosity with increasing solvent concentration. However, the decreases of the dynamic properties with increasing DMSO/F127 peak ratio associated with increasing solvent concentration, are more gradual in comparison to the catastrophic step change in dynamic properties observed when the HBPCs were exposed to increasing pH (compare the slopes in Figs. 4 and 8).
The mechanisms of the structural changes within the HBPCs observed with increasing solvent concentration or the pH of the buffer solutions, which lead to the deterioration of the dynamic properties, are schematically summarized in Fig. 9. Overall, with increasing pH, the ratio of the PMAA/F127 decreases and the amount of total mass retained diminishes, significantly leading to the break-down of the hydrogen-bonded network. On the other hand, with increasing solvent concentration, there is an increase of the PMAA/F127 ratio, generated by the replacement of the F127 with DMSO with the total weight only weakly affected by the increase of the solvent concentration. Figure 10 shows the tan δ values () at ω = 0.1 rad/s as a function of the PMAA/F127 ratio. The tan δ values increase from about 0.45 to 1.6 as the PMAA/F127 ratio increases from 0.5 to 4.5. Thus, as the PMAA to F127 weight ratio increases, the HBPCs become relatively less elastic and more viscous, primarily on the basis of the loss of F127 upon exposure to the solvent as schematically described in Fig. 9.
C. Extrudability of HBPCs at pH = 2
The HBPCs obtained at various cosolvent concentrations and pH were subjected to extrusion experiments using a capillary rheometer. It was observed that PMAA/F127 complex at low pH could be shaped via extrusion. Figure 11 shows a typical flow curve of the PMAA/F127 complex at pH 2 from capillary rheometry. The images of the extrudates emerging from the capillary are included as insets. It is significant that the PMAA/F127 complexes could be extruded through capillary dies with a relatively high length over the diameter ratios of 40–60 and relatively small capillary diameters of 800–1500 μm for a wide range of shear rates. As shown in Fig. 11, the extruded samples had sufficient elasticity to hold their shape upon exit from the capillary die. The demonstrated abilities of the HBPC to be extruded through dies and to hold their shapes upon exit suggest that the HBPCs have the potential to be processed using standard polymer processing operations, for example, extrusion through complex shaped dies.
The shapes of the extrudates shown in Fig. 11 indicate that flow instabilities are onset when the wall shear stress reaches about 65 kPa to give rise to significant distortions of the extrudate shapes. Such surface/bulk and gross distortions are commonly observed during the extrusion of high molecular weight polymer melts (designated as melt fracture, shark skin, gross surface or bulk irregularities) . One important contributor to the development of the flow instabilities and resulting surface or bulk irregularities of extruded strands of polymer melts and polymeric suspensions is the time-dependent loss of the contiguity of the flow boundary condition at the wall [50,51]. Thus, the wall slip behavior of such HBPCs needs to be carefully analyzed to tailor conditions or formulation modifications for their improved extrudability. One possible mechanism that can be exploited is the incorporation of particles into the HBPCs to generate a contiguous apparent slip condition at the wall, as was shown to be very effective in suppressing the flow instabilities associated with silicone polymers extruded from the capillary dies [51,52].
In the wall shear rate range of 1–30 s−1, at which the extrudates were relatively smooth and free from significant surface and bulk distortions, the extrudate swell ratios (the diameter of the extrudate immediately upon emerging from the capillary over the diameter of the capillary) of the HBPCs were determined. The swell ratios were in the 1.6–1.8 range. The swell ratios of fluids without elasticity depend on the Reynolds number, Re, and vary between 0.87 for Re ≥ 100 and 1.13 for Re ≤ 2 . Thus, the swell ratios of 1.6–1.8 are manifestations of the elasticity of the HBPCs.
D. The K-BKZ constitutive equation and the rheological behavior of HBPC at pH = 2
The K-BKZ equation  can be used for the determination of the shear viscosity, as well as other material functions of the HBPCs. Here is the Finger tensor, is the memory function (representing the fading memory of the fluid), which is given as function of the first , and second , invariants of the Finger strain tensor ( for simple shear flow) and the elapsed time s. Following Wagner's postulate  the memory function can be expressed as a product of two functions of time and strain (time and strain separability), i.e., where is the temperature-independent damping function, which tends to unity for small deformations, and the linear viscoelastic memory function is given as . The parameters of the damping function can be determined from the relaxation modulus data obtained with step strain experiments and the parameters of the linear viscoelastic memory function, i.e., the relaxation times , and relaxation strengths can be determined from dynamic properties characterized via small-amplitude oscillatory shearing.
E. Dynamic properties of HBPC at pH = 2
Linear viscoelastic properties versus temperature in the 5–80 °C range (at ω = 0.1 rad/s) are shown in Fig. 12. Significant changes in the dynamic properties of the HBPC with temperature could have been expected since the structure of F127 changes drastically with temperature, showing temperature-induced micellization that correlates with the lower critical solution temperature (LCST) of the PPO block [56,57]. However, the dynamic properties of the HBPC decrease only very gradually with increasing temperature up to 80 °C and no trigger mechanism is suggested within the 5–80 °C range. It is known that the LCST behavior of the PPO blocks of the PMAA/F127 colloidal complexes is not observed even at relatively low PMAA contents due to the interaction of the PMAA chains with the PPO core of the F127 . Also consistent with this, significant effects of temperature were not observed in the 4–40 °C range when pyrene was incorporated into PMAA/F127 complexes . These findings suggest that PMAA/F127 interaction can largely stabilize the hydrophobic component within a wide temperature range, thus explaining the lack of a drastic change in dynamic properties with temperature (Fig. 12).
The frequency-dependent dynamic properties of the hydrogen-bonded complex of Pluronic F127 block copolymer and the polyacid at pH = 2 are shown in Fig. 13. The data are presented using 95% confidence intervals determined according to Student's t-distribution. The use of a wide range of frequencies 0.001–100 rad/s, in oscillatory shear allows the characterization of the linear viscoelastic response of the HBPC's over a wide range of characteristic times to provide a detailed fingerprint of the linear viscoelastic response. Figure 13 shows that the temperature dependence of the dynamic properties could be accounted via shifts in the relaxation times using temperature-dependent shift factors aT, to a master curve drawn at 293 K. The resulting plots of G′ and G″ versus aTω are independent of temperature, indicating that the time-temperature superposition of the HBPCs is observed over 20–60 °C (thermorheological simplicity). The variation of temperature basically corresponds to a horizontal shift in the time scale, i.e. all relaxation times change with temperature proportional to the temperature dependent shift factor aT, i.e. . The shift factors aT are 0.243 at 313 K and 0.065 at 333 K, using a reference temperature T0, of 293 K. Assuming an Arrhenius relationship between the shift factors and absolute temperature T, i.e. , the Ea/R of the HBPC is determined to be 6530 K−1.
Figure 13 further shows that there are two cross-over points at 10−3 and 102 rad/s. In between the two cross-over points the storage modulus , values are greater than the loss modulus , values with the difference diminishing, i.e. the moduli approach each other toward the cross-over points. A plateau modulus is not apparent in the frequency range covered. The high values of both and values indicate that the complexation of the triblock copolymer F127 with PMMA and the associated hydrogen bonding gives rise to HBPCs that are highly elastic and viscous at pH = 2.
The dynamic data of the PMAA/F127 complex at pH = 2, shown in Fig. 13, were analyzed to obtain the discrete relaxation spectrum, i.e. relaxation strength , versus relaxation time values. Generally, a pattern search method (least squares fit), which minimizes the objective function F, defined is used
where N is the number of data points, and are the experimentally determined moduli at each ω, and and denote the best fit values, where the storage modulus , and the loss modulus of the generalized Maxwell model are
The determination of the relaxation spectrum, i.e. and from dynamic properties is recognized as an ill-posed problem [58–60]. Considering the ill-posedness of this problem the dynamic data were fitted according to the procedures developed by Winter and coworkers into a computer-aided method “IRIS” [61,62]. This algorithm involves the minimization of the objective function given in Eq. (1) using the following procedure:
Placing a large number of Maxwell modes that are initially evenly distributed over the frequency range of the data.
Including an additional frequency decade on both sides.
Nonlinear fitting while changing the spacings between the relaxation times .
The code is optimized to obtain the best fit of the data with the minimum number of modes, i.e. to converge to a “parsimonious spectrum” .
The best fit of the storage and loss moduli and the magnitude of the complex viscosity using the IRIS algorithm are shown in Fig. 13. The ten values of and that provide the best fit of the “parsimonious spectrum” are provided in the inset. The relaxation strengths , represent the contribution to rigidity associated with relaxation times which lie in the interval ln λ and ln λ + d ln λ. The relaxation time window of the HBPC is very broad with an unusually large maximum relaxation time that is over 104 s and a minimum relaxation time of 0.002 s. The longest relaxation time dominates the dynamic properties at the low frequencies and the relaxation of shear stress following steady shearing or a step strain at long times.
One manifestation of the long relaxation times of the HBPCs is the unusually slow relaxation of the normal force that is applied during sample loading. For example, with the 8 mm cone and plate geometry (cone angle of 5.7° and minimum gap between the apex of the cone and the plate of 50 μm) a typical compressive normal force of 15 N that was applied during sample loading would take over 1800 s to relax to less than 3 N under quiescent conditions. This type of slow relaxation is reminiscent, for example, of concentrated suspensions of polymer melts filled with rigid solids, which form a particle to particle network that imparts solidlike behavior to slow down and/or even prevent complete relaxation from compressive stresses.
F. Step strain flow
The time dependencies of the relaxation modulus (the ratio of the time dependent shear stress over the strain introduced) of the HBPC at pH = 2 collected upon the introduction of a step strain is shown in Fig. 14. Figure 14 contains data from both parallel disks (corrected for the radial nonuniformity of the shear rate as described in Appendix B) and cone and plate data. The range of strains (strain at the rim for parallel disks) over which the relaxation moduli are independent of the imposed strain represents the linear range. The strain γ, independent region of 0.1% to 20% constitutes the linear viscoelastic region. Using the generalized Maxwell model the discrete relaxation spectrum can be related to the shear relaxation modulus values , in the linear viscoelastic region
Figure 14 shows the comparisons of the values obtained with Eq. (3) and the values obtained from the step-strain experiments. There is general agreement between the experimental relaxation modulus values and those determined with the generalized Maxwell model using Eq. (3). The agreement holds for elapsed times as long as 300 s following the step strain (the experiments were stopped at 1 h following the introduction of the step strain).The very long relaxation times of the HBPC manifest themselves in the very slow relaxation of the modulus both in the linear and nonlinear region For example, it takes over an hour to reach 4000 Pa.
G. Damping function
The damping function describes the destructive effect of the deformation of structure, i.e., for example, the destructive effect on the entanglement density of polymer melts. The damping function is given by the vertical shift required to superimpose the curves of relaxation modulus at various strains on the reference curve representing the linear viscoelastic region. Thus, the ratio of the relaxation moduli determined in the nonlinear region over the linear viscoelastic relaxation modulus provides the damping function h(γ), which can be fitted with a single or double exponential function of γ  as
The results of the application of this procedure are shown in Fig. 14. A single exponential is sufficient to represent the damping function and the best fit of Eq. (4) gives f = 1 and n1 = 1.2. There is some degree of uncertainty in this analysis since the straight line marker information collected during the step strain experiments has revealed that the relaxation moduli have been affected by the wall slip. Such wall slip effects have also been observed during the step strain flow of polymer melts . The damping function of the HBPC was determined to be independent of the elapsed time following the introduction of the step strain. This supports the validity of the assumption of time and strain separability of the memory function for the HBPCs ( Appendix B).
H. Shear viscosity
Figure 15 shows the shear viscosity , versus the shear rate data of the HBPC collected with cone and plate, parallel disks, squeeze, and capillary flows. The details of the characterization are provided in Appendix B. At the low shear rates there is considerable scatter in the data. Such scatter prevents the assessment of the prediction of the generalized Maxwell fluid for the zero shear viscosity , of the HBPC, i.e., = . The role played by hydrogen bonding is evident from the very high shear viscosity values observed in the low shear rate range, i.e., O(106) considering that the HBPC is a blend of two polymers with moderate molecular weights (Mn of F127 is 12.5 kDa and Mw of PMAA is 150 kDa). The HBPC at pH = 2 is highly shear thinning, with the shear viscosity monotonically decreasing in a power law fashion with increasing shear rate, represented by a consistency index of 26,734 and a power law index n of 0.36 (correlation coefficient of 0.995).
The shear viscosity values , of the HBPC as a function of shear rate , were determined from the K-BKZ equation 
The comparisons between the experimental shear viscosity values and those that were predicted from the K-BKZ equation for f = 1 and n1 = 1.2 (parameters obtained from step strain data of Fig. 14) are shown in Fig. 15. The agreement is acceptable. This suggests that the use of the K-BKZ equation and the procedures used for the determination of the parameters of K-BKZ are adequate for the prediction of the shear viscosity of HBPCs over a broad range of shear rates.
I. Self-healing properties of the HBPCs
Self-healing ability of polyelectrolyte complexes is an important functional property. This is because the noncovalent bonding interactions of interpolymer complexes can give rise to intrinsic healing characteristics that do not require additional chemical or physical triggers . Due to their reformable labile bonds, PMAA/F127 complexes can be expected to have self-healing properties . For the assessment of their self-healing, disk-shaped HBPC samples (1.5 mm) were prepared and then split horizontally into two halves. Immediately upon introducing the cut, the two halves were placed on top of each other in between the two parallel disks of the rheometer and subjected to a normal force of 1.5 N. Subsequently, the dynamic properties were collected as a function of time.
Figure 16(a) shows the time dependence of the storage modulus (ω = 1 rad/s) of the PMAA/F127 at pH 2 and pH 5. At the beginning of the test, the (ω = 1 rad/s) values are significantly lower than those of the pristine specimen. This is primarily due to the relatively low shear stress values resulting from the occurrence of a slip plane between the two cut half-disks. However, as time elapses the effects of hydrogen bonding are felt, and the (ω = 1 rad/s) values approach those of the pristine sample, indicating that the self-healing process is indeed taking place. The storage modulus of HBPCs at pH = 2 could fully recover from the cut. On the other hand, when the pH was increased to 5 the cut HBPC sample never managed to self-heal to regain the original pristine state. This finding reflects the diminishing of the hydrogen bonding between F127 and PMAA with increasing pH, consistent with the mechanisms elucidated earlier.
The self-healing nature of the HBPCs and the effects that the pH plays are demonstrated further in Fig. 16(b). This figure shows the images of rectangular specimens of PMAA/F127, which were pre-exposed to pH 2 or 5, cut into two pieces and then held together using a clamp for 5 min. Different colors are used for the two halves to illustrate what happens at the interface during subsequent uniaxial stretching. The complexes at pH 2 could be stretched in the axial direction∼5.5-fold without severing of the interface, while the complexes at pH 5 broke down along the cut at a threefold elongation [Fig. 16(b)]. This result is consistent with the oscillatory shear measurements [Fig. 16(a)], and further confirms that the self-healing behavior of PMAA/F127 complexes is based on the pH-controllable hydrogen bonding interactions between PMAA and F127.
HBPCs, which form upon the association of macromolecules via multiple intermolecular hydrogen bonding interactions, are versatile materials for myriad applications, especially in the biomedical area. Here, hydrogen-bonded assemblies were fabricated from the complexation of a triblock copolymer Pluronic F127, with PMAA, and the structure and the rheological behavior of the hydrogen-bonded PMAA/F127 complexes were characterized. To our knowledge, this is the first comprehensive investigation of the rheological behavior of HBPCs and how they relate to various structural parameters affected by the pH, cosolvent, and temperature.
The nanostructure and the rheological behavior of the HBPCs could be readily manipulated via exposure of the complexes to different pH and solvent concentration levels. Upon exposure to high pH buffers, the ionization of the polyacid was enhanced, and the integrities of the PMAA/F127 complexes were reduced due to the smaller number of intermolecular hydrogen bonds and the loss of higher amounts of PMAA during the dissociation of the complexes, leading to increased porosity of the HBPC. The effects of cosolvent DMSO on the structure development of PMAA/F127 complexes differed from the pH effects in that a reverse trend was observed for the change in the mass ratio of PMAA to F127 with increasing solvent concentration. There appears to be an increase of the PMAA/F127 ratio with increasing DMSO concentration, whereas a decrease of the PMAA/F127 ratio was observed for increasing pH. The F127 content in the HBPC also decreased as the F127 was preferentially removed from the PMAA/F127 complexes upon exposure to the buffers with increasing DMSO concentrations. In spite of the large change in the PMAA/F127 composition, the decrease in the total mass of the HBPCs in DMSO/water solutions was only moderate, suggesting the inclusion of the cosolvent DMSO within the PMAA/F127 complexes. This mechanism is consistent with the observation of nanosized pores resulting from the removal of F127 micelles from the complexes that are treated with DMSO. Although the structuring mechanisms were different, both increasing pH and increasing cosolvent concentration gave rise to the decreases of elasticity and viscosity of the HBPCs. On the other hand, the effects of temperature (5–80 °C) on dynamic properties were only mild.
At a relatively low pH level, the HBPCs exhibited relatively high elasticity and shear viscosity, and long relaxation times as induced by the agglomeration of hydrogen-bonded complexes, i.e. nanoclusters, that are connected with the hydrogen bonding interactions, while exhibiting an open network structure. However, the formation of the nanoclusters did not prevent the extrusion of the HBPCs at low pH to be shaped into cylindrical strands. The ability of the HBPCs to be shapeable is encouraging for the application of the HBPCs in various industrial applications that are based on shaping via conventional polymer processing operations including extrusion flows. However, the extrudability of the HBPCs is handicapped by the development of flow instabilities at relatively high wall shear stress values that give rise to gross distortions of the extrudates. The gross distortions of the extrudate shapes would present bottle necks to the extrudability of HBPCs and need to be addressed, especially in conjunction with the tailoring of the wall slip behavior of the HBPCs via changes in geometry, materials of construction or formulations. Finally, the self-healing behavior of the PMAA/F127 polyelectrolyte system was demonstrated at low pH values. Such self-healing develops on the basis of the pH-controllable hydrogen bonding interactions between PMAA and F127 and further expands the application potential of these materials.
The authors thank Dr. Joseph Carnali of Unilever R&D for his comments and suggestions. The authors are grateful to Professor H. Henning Winter of University of Massachusetts, Amherst, MA, for making his IRIS source code available. This investigation was made possible by funding in part by the NSF under Award Nos. DMR-0906474 and DMR-1610725, and partly by the Highly Filled Materials Institute at Stevens Institute of Technology. The authors thank the Laboratory for Multiscale Imaging at Stevens for access to the electron microscopy facilities.
APPENDIX A: PREPARATION OF FLUORESCENTLY LABELLED PMAA AND PH/COSOLVENT STABILITY STUDIES
1. Preparation of fluorescently modified PMAA (PMAA*)
Labeling of PMAA with Alexa-488 to obtain PMAA* was performed using a procedure similar to that previously reported [67,68]. Briefly, solutions of 5 μl of 10 mg/ml PMAA (5.77 × 10−7 mol), 20 μl of 50 mg/ml EDC (5.22 × 10−6 mol), and 20 μl of 60 mg/ml of sulfo-NHS (5.53 × 10−6 mol) were prepared in 0.1 M phosphate buffer at pH 5, mixed and continuously stirred for 1 h. Then, 25 μl of 10 mg/ml Alexa-488 in 0.1 M phosphate buffer at pH 5 buffer was added to the mixture. The reaction mixture was stirred overnight and then diluted to 2 ml with 0.1 M phosphate buffer at pH 7. The solution was dialyzed against 0.01 M phosphate buffer at pH 7 also containing 0.1 M NaCl for 2 days, followed by dialysis against Milli-Q water for another 2 days. The molecular weight cutoff for the dialysis membrane was 2 kDa. The concentration of PMAA* was around 25 μg/ml, and the PMAA* solution was stored at 4 °C. This procedure resulted in one fluorescent label per 300 monomer units.
2. Exposure of polyelectrolyte complexes to aqueous buffer solutions at differing pH
For pH stability measurements, samples of precipitated PMAA/F127 complexes (∼10 mg) were removed from pH 2 solutions, dried for at least 3 h in the oven at 125 °C and weighed. The precipitates were then sequentially exposed to 50 ml of 10 mM phosphate buffer solutions to reach a higher pH in successive steps, with a pH increment of one between each step. The sample was allowed to equilibrate for 12 h at each pH followed by drying and weighing. The mass of HBPCs retained at each pH was calculated as w1/w0·100%, where w1 is the dry weight of HBPC precipitates equilibrated in solutions at pH > 2, and w0 is the original dry weight of the complex precipitated at pH 2.
3. Exposure of polyelectrolyte complexes to the cosolvent DMSO at various concentration ratios
The preparation method of the PMAA/F127 complexes is shown schematically in Fig. 17(a). Samples of precipitated HBPCs (∼10 mg) were removed from the pH 2 aqueous solution. The precipitates were then sequentially exposed to 50 ml of different DMSO, and pH 2 aqueous solutions, from 10 v/v% to 40 v/v% of the cosolvent DMSO. At each cosolvent concentration, the sample was allowed to equilibrate for 12 h, dried and weighed. The samples were dried in a vacuum oven to remove the DMSO residue in the DMSO-treated complexes. The conditions were set at ∼0.3 bar and 159 °C (which is higher than the boiling temperature of free DMSO, 153 °C) for 3 h. The mass of the complexes retained at each DMSO mixture solution was calculated as w1′/w0′·100%, where w1′ is the dry weight of HBPC precipitates equilibrated in mixture solutions, and w0′ is the original dry weight of the complex precipitated from DMSO-free aqueous solution at pH 2. The water concentration and solvent concentration of the HBPCs at various pH and cosolvent concentration were calculated as (w0′-w1′)/w0′·100% and are shown in Figs. 17(b) and 17(c), respectively. The water concentration approximately doubled with increasing pH from 2 to 7 in the absence of a cosolvent [Fig. 17(b)]. On the other hand, the solvent concentration changed only slightly with exposure of the samples to different DMSO concentrations [Fig. 17(c)].
APPENDIX B: RHEOLOGICAL CHARACTERIZATION AND STRUCTURAL ANALYSIS
1. Oscillatory shearing, steady torsional flow, and step strain
An Advanced Rheometric Expansion System (ARES) rheometer available from TA Instruments of New Castle, DE, was used in conjunction with a force rebalance transducer 2 K-FRTN1 and stainless steel parallel disks, and cone and disk fixtures with 8–25 mm diameter for small-amplitude oscillatory shearing, steady torsional flow, and step strain experiments. The actuator of the ARES is a dc servomotor with a shaft supported by an air bearing with an angular displacement range of 0.05–500 mrad and is capable of achieving a resolution of 0.005 mrad. The torque accuracy of the transducer is ±2 g cm. The samples were characterized under hydrated conditions for all experiments using rotational rheometry. The specimen was immersed in buffer solution (which was the same as the buffer solution used to treat the HBPC) kept at ambient temperature during rotational rheometry to prevent drying. The chamber holding the buffer solution consisted of two concentric cylindrical dishes, one of which was sealed and attached to the lower fixture, which was connected to the torque and normal force transducers and the second was attached to the upper fixture of the rheometer, which was coupled to the motor.
During oscillatory shearing, the shear strain , varies sinusoidally with time t, at a frequency of ω, i.e., where is the strain amplitude. The shear stress response of the fluid to the imposed oscillatory deformation consists of two contributions associated with the energy stored as elastic energy and energy dissipated as heat, i.e., The storage modulus and the loss modulus , also define the magnitude of complex viscosity , and In the linear viscoelastic region, all dynamic properties are independent of the strain amplitude In order to ensure that the hydrogen-bonded complexes are stable, the oscillatory shear data were collected first as a function of time at constant and . The time scans suggested that the dynamic properties were steady (and thus the HBPCs were stable) for durations that were longer than the time span of the strain and frequency sweeps (supplementary material) . The ranges for linear viscoelastic regions were determined at each pH and solvent concentration and were determined to lie within the 0.4%–2.5% range.
For parallel disks, the shear stress at the edge was corrected (assuming that the shear viscosity and the shear rate are continuous functions of the radial distance r) as where the shear rate at the rim , i.e., H is the gap in between the two plates, R is the radius of the plates, and is the rotational speed of the top plate in rad/s. The procedure involves the collection of the steady state torque values as a function of the shear rate at the rim, from which the slope is obtained and used for the determination of the shear stress at the edge. The straight line marker method  was employed, while the samples were being sheared.
Stress relaxation following a step strain, i.e., a sudden shearing displacement [71–73] was carried out using both parallel disks and cone and plate fixtures under ambient temperature conditions. In these experiments, the sample was sheared for a short duration of time (15–25 ms) followed by the determination of the time dependent torque . During the step-strain experiments for parallel disks the shear strain at the edge of the specimen , were 0.5% and 1%, while the strain range imposed during step strain with cone and plate was in the 0.5%–200% range. For the parallel disks the relaxation modulus was obtained as where . This correction is necessary to accommodate the nonhomogeneous strain imposition with the parallel plate geometry . The relaxation during the rise time (<25 ms) was assumed to be negligible. In the limit of linear viscoelasticity, the linear shear stress relaxation modulus G(t), is independent of the imposed shear strain.
The damping function values , from cone and plate or from parallel disks were obtained by the vertical shift of the or onto the linear viscoelastic modulus G(t). Especially in the nonlinear region, the true shear strain imposed on polymer melts can deviate from the targeted strain due to wall slip . Figure 14 shows that the curves of nonlinear relaxation modulus as a function of time for different strain levels are parallel for all times, as required by the time strain separability. The damping function values determined at various elapsed times upon the introduction of the step strain are shown in Fig. 18. All of the data can be superimposed to be represented by = exp(−1.2γ), regardless of the time following step strain, indicating that the strain time separability that is required for the K-BKZ constitutive equation, is indeed valid.
2. Compressive squeeze flow
The ARES rheometer was also employed in conjunction with 8-mm parallel disk fixtures for squeeze flow experiments. The squeeze flow involves the compression of the fluid that is partially or completely filling the space between two parallel and rigid circular disks, one or both of which are moving in the axial direction at constant relative velocity, while the time-dependent force is being measured, or under constant normal force while the time-dependent relative velocity of the plate is measured . Useful approximate solutions to this unsteady state problem can be obtained by assuming that the speed of travel of the disk is sufficiently low so that the time derivatives can be neglected, i.e., the “quasi-steady-state assumption.” During the squeeze flow experiments the top plate was moved vertically down at velocities of 0.005, 0.01, 0.02, and 0.04 mm/s and each condition was repeated at least three times. Figure 19 shows the normal force values versus gap between the two disks during compressive squeeze flow. The data could be analyzed using the lubrication and the “quasi-steady-state” assumption  with the no-slip at the wall condition to generate the shear viscosity versus shear rate that are included in Fig. 15.
3. Capillary flow
An Instron floor tester was employed in conjunction with a capillary rheometer to collect the shear viscosity data and to study the development of extrudate shapes of the polyelectrolyte complexes upon exit from the capillary. Three capillaries with diameter and length over diameter ratios of 0.8 mm and 60, 0.8 mm and 40, and 1.5 mm and 60 were used. Changes in the length over the diameter ratio at constant diameter allows the correction of the wall shear stress (Bagley correction), i.e., , where and are the total pressure drop values for the two lengths over diameter ratios of the two capillaries with a constant diameter D, i.e., and . The correction procedure for the wall shear rate involved the Rabinowitsch correction, i.e., where Q is the flow rate, R is the radius of the capillary, and is the Bagley corrected wall shear stress.
The change in diameter at constant length/diameter ratio allows an assessment of the wall slip effects. Flow curves were obtained using two capillaries with the same length/diameter ratio of 60 but with different diameters, i.e., D = 0.8 and 1.5 mm. For fluids that exhibit wall slip, the increase of the surface to volume ratio of the capillary die (4/D) should give rise to smaller wall shear stress values. However, the confidence intervals of the data (not shown) were too broad (reflecting significant scatter in the data) to allow the wall slip velocities to be determined and thus no wall slip corrections were attempted.
During the capillary flow experiments the polyelectrolyte sample was sandwiched in between the capillary die and the plunger with a thin cushion of Milli-Q water at the top to prevent the dehydration of the hydrogen-bonded complex during extrusion. The hydrogen-bonded complex was extruded at different crosshead velocities in the apparent shear rate range of 5–1100 s−1 at ambient temperature. The flow of the extrudate emerging from the capillary was monitored with a computer interfaced VEHO VMS-004 USB microscopic camera for obtaining a visual record. Each run was repeated at least three times.
4. Assessment of self-healing
The self-healing properties of the PMAA/F127 polyelectrolyte complexes were investigated by the preparation of disk-shaped polyelectrolyte samples (1.5 mm) that were cut, i.e. split horizontally into two halves using a sharp blade. Immediately upon introducing the cut, the two halves were placed on top of each other in between the two parallel plate fixtures of the rheometer and subjected to a normal force of 1.5 N. The cut and reassembled samples were exposed to oscillatory shearing at constant frequency and strain amplitude for 1600 s. The oscillatory shear behavior of the samples with cuts was compared with the oscillatory shear behavior of pristine samples.
A Bruker Tensor-27 spectrometer equipped with deuterated triglycine sulfate detector and OPUS 6.5 software were used for FTIR analysis. The spectra were collected with a 4 cm−1 resolution and averaged over 64 scans. Polymer complexes were analyzed using the KBr pellet method. Prior to FTIR measurements the precipitated complexes (∼1 mg) were separated from the mixture solution by centrifugation at 4000 rpm for 10 min, repeatedly rinsed with water at pH 2 for 1 h to remove unbound polymers, and dried in the oven at 125 °C for at least 3 h. For treatment with different pH buffer and mixture solvents, PMAA/F127 complexes were exposed to various pH and solvent solutions for 12 h and repeatedly rinsed with the specific buffers or solvent for 1 h after the treatment to remove the unbound polymers in the matrix. The complexes treated with pH buffers were then dried in the oven at 125 °C. The solvent treated complexes were dried in vacuum oven at ∼0.3 bar, 159 °C for at least 3 h.
For calibration curves, we used a similar procedure to that reported previously . Briefly, 0.5% polymer solutions were mixed at desired ratios, and after adjusting the acidity to pH 2, ∼60 μl of these solutions were deposited on a silicon wafer and dried. For assuring homogenous deposition of the polymer on the silicon wafers, all solutions were prepared at the mixing ratios at which no precipitation was observed. For FTIR measurements, the infrared-transparent silicon wafers were cut into 1.50 × 1.50 cm2 size with a Fletcher steel wheel glass cutter, exposed to UV for 2 h and treated with concentrated sulfuric acid to clean the wafer surface. Origin Pro 8.0 software was used to perform curve fitting and quantify the intensities of peaks characteristic of polymer components. Prior to the curve-fitting, the selected spectral regions were baseline corrected. The centers of all characteristic spectroscopic bands were fixed during curve fitting, and the shape of the peaks was assumed to be Gaussian.
TEM images were taken using an FEI CM20 FEG S/TEM. The TEM grids were treated by grow discharge prior to sample preparation. For images of the PMAA/F127 precipitate complexes, the PMAA/F127 precipitates were deposited on TEM grids. In 2 min after deposition, the droplets were removed with the filter paper, and 5 μl droplets of water (Milli-Q) were used to rinse the grid three times, followed by the staining of the samples with 1% aqueous solution of uranyl acetate. Water was used again for the final rinsing. To image the PMAA/F127 precipitate complexes at different pH environments or at different mixture solutions, the PMAA/F127 precipitate complexes were first deposited on the grids from pH 2 solution, followed by rinsing the samples for three times by water and then by a specific buffer or DMSO/water mixture used for further testing. Then, ∼10 μl of buffer at a specific pH or DMSO/acidic water solutions with a specific DMSO concentration were added and left in contact with the samples for 1 h, followed by the removal of the droplet with filter paper. The pH or solvent treatment was repeated in triplicate. The samples were stained with 1% uranyl acetate, followed by rinsing with water. Finally, the samples were dried and analyzed by TEM operated at 200 kV.
7. Confocal microscopy
A laser scanning microscope (CLSM 5 PASCAL, available from Zeiss, Germany) was used to capture fluorescence images of the PMAA*/F127 complexes at different pH or at different solvent (DMSO) concentrations using a C-Apochromat 60×/1.4 oil immersion objective. The PMAA*/F127 complexes were prepared as mentioned above, and ∼0.5 mg samples were cut and put in the chambered cover glass cells, and treated with an aqueous buffer or DMSO mixture solution. The equilibration time prior to imaging was 1 h. For imaging of the PMAA*/F127 complexes, the fluorophores were excited by a laser at λ = 488 nm, and emission was collected after filtering with a BP 500–560 pass filter.