Rheological Properties of Hybrid Hydrogels of Weakly Charged Polyelectrolytes Crosslinked by Aluminoxane Particles

The rheological behavior of hybrid hydrogels of weakly charged polyelectrolytes with aluminoxane particles (APs) formed by noncovalent interactions has been studied. This interaction observed for the polyelectro lyte Praestol-2500 is the most pronounced and is due to strong electrostatic noncovalent bonds between positively charged APs and anionic groups of the copolymer. By the methods of capillary, rotational, and vibrational rheometry, it has been ascertained that two processes compete: the compacting of coils of macromolecu les and their crosslinking through APs. The latter process dominates at relatively high concentrations of reagents, and depends on ratios between polymer units and APs and the presence of a low-molecular-mass indifferent electrolyte (NaCl). Formed hybrid hydrogels relate to physical gels with the unstable nature of the network o f physical bonds, and under the action of shear stress demonstrate “Weissenberg effect.” The method of dynamic mechanical analysis with the use of a micro-Fourier rheometer has shown that the ratio storage modulus – loss modulus depends on the amount of AP sol and its ratio to the quantity of copolymer in the init ial mixture. A scheme for spatial structure hybrid hydrogels has been suggested.


Introduction
At present, the creation of composite materials is characterized by the use of nanodisperse materials of both inorganic and organic nature. Such co mposites are often referred to as hybrid nano materials. [1] This term is often related to purely inorganic nanocrystals and semiconductors, [2], [3] organic nanocomposites, [4], [5] and mixed disperse systems. In the latter case, it is assumed that the composite includes metal or metal o xide (hydro xide) part icles as the disperse phase, whereas a polymer or its solution plays the role of the continuous phase. [6][7][8][9][10] Poly meric organo-inorganic co mposites belong to the promising class of hybrid materials due to a unique combination o f magnetic, catalytic, nonlinear optical, and sensoric properties of inorganic nanoparticles with a set of properties of the poly meric mat rix and its ability to stabilize inorganic clusters dispersed in it.
There are a lot of methods for obtaining nano-objects and their co mposites. [11][12][13][14] The interact ion of linear organ ic macro mo lecu les with aqueous d isp ers ions o f charg ed nanoparticles (hydrosols) may be regarded as a possible approach to the production of organo-inorganic nanocomposites.
This method looks attractive because (i) it makes possible the controllable arrangement of nanoparticles in a poly meric matrix, that is, v ia its reaction centers and (ii) the so-called polymer-collo id complexes (PCCs) (for brev ity sake, named polycomplexes) that are formed in this case are generated spontaneously due to noncovalent interactions. [15][16][17] The formation of polyco mplexes may proceed during the sol-gel synthesis of nanoparticles in the presence of polymers [18][19][20] or through the simplest method-via the blending of a sol with a poly mer solution. [15], [21][22][23] Exactly this method was used to prepare polycomplexes of some types of water-soluble poly mers with alu mino xane particles (APs) in the sols of superbase polyaluminu m hydro xychloride (PAHC). [24][25][26] These comp lexes represent the colloidal dispersion of APs formed during the hydrolysis of some salts of alu minu m as a result of the polycondensation of alu minu m aqua hydroxo co mplexes and are distinguished by high aggregate stability at a wide range of concentrations and temperatures. [27] On the basis of s mall-angle X-ray scattering studies, APs may be related to physical fractals having an internal self-similar structure with a fractal dimensionality d f = 1.0 and a radius of gyration r g = 1.6 nm. [28] Various kinds of noncovalent interactions are typical for APs. As a consequence, they may form polycomplexes both with nonionogenic polyacrylamide (PAA) [24], [26] and with its cation-active [29] and anion-active [30] copoly mers. Ho wever, soluble polycomplexes are obtained only at definite ratios of APs to functional groups of copolymers. Otherwise, insoluble polycomplexes are formed if unlikely charged reagents are used or polycomplexes are not formed at all because of large forces of repulsion of likely charged reagents. Polycomp lexes of PAHC sols with polyacrylamide show promise for practice as regulators of the stability of disperse systems, for examp le, in the processes of purificat ion of natural water and sewages, [31][32][33] in enhanced oil recovery techniques [34], [35] and as environmentally friendly binding agents for disperse materials. [36] In all the above-listed cases, hybrid polycomplexes are used in the form of aqueous suspensions or gels, that is, fluid systems. At the same t ime, no data are available on the rheological behavior of these new systems. For most real liquids, irreversible deformations, which appear during flow, are characterized by the complicated dependence of different factors, and their rheological behavior is often in the intermediate region between the liquid and solid. This feature is especially pronounced for high-mo lecular-mass polymers, aqueous solutions of which possess viscoelastic properties. The pattern of the flow of polymer solutions often determines the possibility of their processing and application. Therefore, the rheological study of such systems is of great importance for practice. Moreover, in addition to its main d irect purpose-determination of the rheological characteristic of flu id systems-rheology may serve as a structural method that relates rheological parameters and structural changes in a deformed system. [37] The goal of this work was to study the rheological behavior of aqueous solutions and hydrogels of polymer-collo id co mplexes of APs with weakly charged polyelectrolytes. As far as particles in a polycomplex occur in the chemically bound via noncovalent bonds state rather than in the inert form, they naturally affect the conformat ional state of polymer macro molecules. Therefore, to compare the rheological properties of a poly mer and its polycomplex, aqueous solutions of in itial poly mers were also investigated. As it is known, for polymer solutions, the regions of diluted and semidiluted solutions exist outside the crossover region, where the elastic properties of polymer liquids begin to manifest themselves. Therefore, capillary and rotational viscometry and the method of dynamic mechanical analysis with the use of a micro-Fourier rheometer were applied as investigation procedures.

Initial Materials
A dispersion of APs was prepared fro m an alu minu m alloy in the form of an aqueous sol containing 13.5 wt% Al 3+ and with the atomic ratio Cl -/Al 3+ = 0.45. The technique of preparation and the characteristics of the sol as well as the dimensional and fractal characteristics of APs were described in [27], [28].
As weakly charged polyelectro lytes, commercial samples with characteristics listed in Table 1 were emp loyed; they were used without any additional purification.
An aqueous solution of polyacrylamide was prepared via the free-rad ical poly merization of acrylamide (99.9%; Alfa Aesar, USA) in an aqueous solution (3 wt% acrylamide) in the presence of potassium persulfate (97%; Alfa Aesar, USA) at a temperature of 60°C and was used without additional purification.
Sodiu m chloride of special purity grade (99.99%; Alfa Aesar, USA) was used. In all experiments, twice-distilled water was used. Polycomp lexes were prepared by mixing aqueous solutions of polyelectrolytes of different concentrations with preset quantities of the AP sol. After shaking in a shaker, aqueous dispersions (gels) were allowed to stand at room temperature for a day.

Rheological Investigations
Viscomet ric measurements were performed by means of a Brookfield DV-II+Pro (USA) rotary viscometer equipped with a UL (Ver. Ro 4 s/s) adapter and a thermostated cell. Experimental data were processed with the use of a DVLOADER authorized program.
The yield stress was determined on a YR-1 special-purpose rheometer equipped with a set of V-71-73 vane spindles. The measurement data were processed by means of a YR-1-4A Y authorized program.
Viscoelastic properties were investigated on an MFR-2000 micro-Fourier rheometer (GBS, Australia). Measurements were performed in the frequency interval 0-100 Hz with a step of 1 Hz at a temperature of 25°C. All variable parameters and calculations of measurable characteristics were enclosed in an MFR-2100 Ver. 1.1b4 authorized program.

Results and Discussion
Poly mer-colloid co mplexes of APs with water-soluble polymers are thermodynamically stable compounds with a variable co mposition in the case of soluble polycomplexes [26] or with a characteristic co mposition when polycomp lexes are insoluble. [38] As was shown previously, polycomplexes may be soluble either if nonionogenic polyelectrolytes [25] or weakly charged polyelectrolytes [30] are used. In both cases, polycomplexes are transparent homogeneous disperse systems with specific physicochemical features peculiar to every co mponent. One of them is the aggregative stability of each of the dispersion phases. The specific feature of the given system is that the sol of PAHC is a known regulator of the stability of dispersion systems, whereas a water-soluble poly mer is often used as a flocculant in the separation of dispersion systems. The rheological behavior of each of the reagents may change in the presence of other reagents. Moreover, both reagents are polyelectrolytes; hence, they are influenced by the ionic strength of the solution. The superposition of such specific features on the properties of interacting reagents may cause inadequate dependences. Therefore, both interacting disperse systems-AP sols and aqueous solutions of polyelectrolytes-as well as polycomplexes, the products of their interaction, were investigated separately.

Investigation of Rheological Characteristics of the
Sol of Al uminoxane Particles Figure 1 presents the experimental data on the kinematic viscosity of the AP d ispersion measured at various concentrations of the disperse phase (Al 3+ ), and demonstrates the effect of a lo w-mo lecular-mass indifferent electrolyte (NaCl) on the aggregative stability of the sol. The curve for the kinematic v iscosity of the sol is composed of two regions: region I, where there is the linear dependence of viscosity on the concentration of the disperse phase corresponding to the free-disperse state of the system, and region II, where there is the exponential dependence conforming to the transition of the colloid system to the bound-dispersion state-gel. However, the flow of dispersion in the annular gap of the rotary viscometer is typical for Newtonian liqu ids; that is, viscosity is independent of the shear rate within the whole concentration range, and a change in shear stress follows a linear pattern ( Figure 2).
The PAHC gel (the sol in a concentrated state containing 13.5 wt% Al 3+ ) features a peculiar behavior in the presence of NaCl. Upon the addition of NaCl in the form of a concentrated aqueous solution, the aggregative stability of the dispersion is preserved ( Figure 1b); however, this operation leads to an adequate decrease in the dynamic viscosity of the disperse system. On the whole, the flow of this system remains similar to the flo w of a Newtonian flu id ( Figure 3). However, when NaCl is added in the dry state, the fluctuation format ion of part icles, nuclei o f the new phase, occurs, and the coagulation structure appears to be accompanied by the transition of the whole disperse system into a solid-like state without evolution of the dispersion med iu m-water. This case was realized through the preparation of the solid PAHC. [39], [40]

Rheological Properties of Aqueous Solutions of Weakly Charged Pol yelectrolytes and Their Complexes with Aluminoxane Particles
The behavior of polyelectrolytes in aqueous solutions is determined by the conformational state of macro molecules and their concentrations. In this study, we selected three kinds of water-soluble poly mers: nonionogenic polyacrylamide, weakly anionic Praestol-2500, and weakly cationic Praestol-611 BC. So me of their characteristics are given in [29], [34]. It should be noted that the characteristics of commercial samp les are tentative. Thus, Praestol-2500 relates to nonionogenic polymers. Ho wever, as follows fro m potentiometric analysis, 1.2 mol% COOH groups are contained in Praestol-2500. Hence, this compound may be related to weakly anionic poly mers that form polycomp lexes similarly to weakly charged copolymers of acrylamide with acrylic acid. [30] This is also the reason why polyacrylamide prepared under laboratory conditions via the free radical polymerization of react ive acrylamide was used as a nonionogenic polymer. In this case, its molecular mass was significantly smaller than those of commercial Praestol-2500 and Praestol-611 BC. As evidenced by potentiometric analysis, this polymer was free of COOH groups.
Soluble poly mer-colloid co mp lexes of APs with water-soluble poly mers are thermodynamically stable compounds with variab le co mpositions. Their behavior in aqueous solutions should evidently differ fro m the behavior of corresponding linear poly mers. In the case of strongly diluted solutions, the intramolecular interaction of macro molecules with APs acco mpanied by the compaction of macro mo lecules may occur. As is known, under thermodynamically favorable condit ions, with an increase in the polymer concentration, a network of topological entanglements appears between separate chains of macro molecules. [41] The concentration of crossover C* is a characteristic value of this state (Table 1). The rheological behavior o f aqueous solutions of the polymers under study should be determined by concentration intervals. As was shown in ( [29], [30]), in the region of diluted aqueous solutions (0.005-0.05 g/dl), there is the linear dependence of specific viscosity on the polymer concentration. In this case, the polyelectrolyte effect is dismissed due to the presence of NaCl in solution. However, the peculiarity of this system is that during the fo rmation of polycomplexes, the sol of PAHC is added to the aqueous solution of the polyelectrolyte. This sol is a d ispersion of APs carrying a positive surface charge and surrounded by Clcounterions; that is, the sol of PAHC is likewise an electrolyte. The calculat ion of the ionic strength of PAHC solutions is impossible because the charge and number of ions governing the potential on the surface of APs as well as the distribution of Clcounterions between the dense and diffuse portions of the electric double layer are unknown. However, with consideration for high aggregative and sedimentation stability of PAHC sols, [27] it may be suggested that the charge of a colloid part icle is rather high. The above data show that the effects of both salts are almost the same and are acco mpanied by the co mpaction of macro molecular coils. In the case of NaCl, co mpaction is caused by the shielding of charged functional groups in the polymer by counterions of the low-mo lecular-mass salt. [42] The degree of such a shielding is determined by the nature of counterions and the charge of the functional group of the polymer. As is seen from Figure 5, for nonionogenic PAA, the presence of NaCl in solution exerts almost no effect on the value of specific viscosity. To a s mall extent, this phenomenon is observed for the solution of lo w-an ionic Praestol-2500 and sharply manifests itself for Praestol-611 BC polycationite.
This phenomenon is probably related to a marked increase in the concentration of Clions in solution of the polymer having counterions of the same type as Praestol-611 BC, which contains dissociating functional N + (CH 3 ) 3 Clgroups. As for the influence of the AP sol on a decrease in the specific v iscosity of the Praestol-611 BC solution, t wo causes may be suggested. The first cause is that the ionic strength of the solution changes due to the dissociation of the high-basicity aluminu m salt accompanied by the evolution of Clions into the solution. The second cause is related to the intramolecular interaction of APs with poly mer macro molecules, which is acco mpanied by the co mpaction of macro molecular coils. As can be seen from Figure 5, a decay in the specific v iscosity of the solution takes place until a certain amount of introduced NaCl is achieved and further decrease in viscosity upon introduction of the AP sol into the solution of the polymer should be indicative of the formation of the polyco mplex, as was shown for the d iluted solutions of these polymers. [26], [29] Another rheological behavior should be observed for semiconcentrated solutions of polymers, where poly mer coils begin to overlap. [44] In the transition state, which correlates with the so-called crossover concentration C*, the intermolecular interaction of APs with two or a greater amount of macro mo lecules may occur. However, at the macroscopic level, the related structuring of a po ly mer solution man ifests itself at poly mer concentrations significantly higher than C*. For disperse systems similar to the system under consideration (aqueous solution of polymer-sol of inorganic particles), the deviation of the concentration dependence of viscosity fro m the linear pattern (the Einstein law) provides evidence for this phenomenon. [43], [44] In fact, the capillary v iscometry study of mixed solutions of polymer mixtures with APs showed that the deviation of the concentration dependence of viscosity on the concentration of the solution from the linear pattern begins at a polymer concentration almost twice higher than С* ( Figure 6). The main goal of this study was to compare the rheological behavior of polymers and their polycomplexes; therefore, it was necessary to ensure equal conditions for rheometry measurements and to use the same measuring system. In this work, a Searle rheometer equipped with a UL-1 adapter with coaxial cylinders was used. This adapter with a thermostated jacket was rig idly fastened to the body of the viscometer, thereby providing the reproduction of equal experimental parameters (depth of mergence of spindle, eccentricity, and gap in cylinders) and minimizing the impact of the so-called apparatus effects on the results of measurements. [37]  As follows fro m these data, the pattern of curves is indicative of the v iscoelastic properties of polymer fluids. Note that with an increase in the amount of APs in the polycomplexes, the contribution of elastic properties, especially in the case of Pr-2500, noticeably grows. This suggests the occurrence of structuring processes in the polymer solution upon introduction of the AP sol.
Similar experiments were conducted with Pr-611. Taking into account its dependence on NaCl, the experiments were performed in aqueous and aqueous-salt solutions. The quantitative results of these rheometric measurements are shown in Figure 9 in the form of colu mnar diagrams.
The above rheometric data show that the addition of both NaCl and AP sol to the aqueous solution of Pr-611 leads to a strong drop in the viscosity of the solution and in the shear stress (Figure 9a). This behavior of aqueous solutions of Pr-611 is observed for a wide range of polymer concentrations from 0.3 g/dl to 1.2 g/dl. Obviously, the reason behind this phenomenon is the compaction of macro molecular coils with an increase in the concentration of Сlcounterions in solution. Upon addition of the AP sol, the solutions of Pr-611 in 1% NaCl behave in a different way (Figure 9b): the viscosity and shear stress increase up to the equimolar rat io of reagents. During the flo w, the elastic p roperties of the poly mer-colloid system become more and more pronounced. This is indicative of the formation of a network of interchain bonds due to the crosslinking of macro molecules by gel particles. With an increase in the concentration of the poly mer in solution, in the flow of the poly mer flu id in the annular gap of the rheometer cell, normal shear stresses arise in the fluid, and as a result, the Weissenberg effect appears.
The difference in the behavior of aqueous and water-salt solutions of weakly cationic Pr-611 is apparently associated with the above-mentioned effect of Clcounterions. In an aqueous solution, the dissociation of functional groups of the polymer leads to the appearance of a positive charge on a macro molecular chain that hinders its interaction with the positively charged APs. In a saline solution, the dissociation of cationic groups is suppressed; as a result, favorable conditions for appearance of other noncovalent interactions between polymer macro molecu les and APs are created. However, the volu me fraction of macro molecu lar co ils should be sufficiently high and gels are formed at a Pr-611 concentration of 0.6 g/dl o r above.
A quite different behavior is observed in the case of solutions of lo w-anionic Pr-2500. As is known, among noncovalent interactions, electrostatic interactions are the strongest and longest range. [17], [45] In this case, these interactions turn out to be do minant, and as was noted in [30], an increase in the content of anionic groups in the polymer chain brings about the formation of insoluble stoichio metric polycomplexes. In this case, the interaction of sol part icles with Pr-2500 macro molecules is so pronounced that even at a poly mer concentration of 0.1 g/dl and a min imu m AP:Pr-2500 unit ratio of 0.1:1 (mo l/ mol), a transparent gel appears in the polymer-collo id solution, whose rheological characteristics cannot be measured by rotational rheometry because of the Weissenberg effect ( Figure 10). Gels, which appear in this case, relate to physical gels. In contrast to the chemically crosslinked gels, they are distinguished by the unstable nature of the network of physical bonds that brings about an uncertainty in the description of their properties. For such gels, determination of the gel point or of the value m c presents a problem. [46] However, for a co mparative evaluation of the strength of the physical network in such gels, the yield stress or shear stress, at which the destruction of physical bonds occurs and the material beco mes fluid as a liquid, may be used. The tests were conducted on a Yield Rheo meter-1 special-purpose instrument (Brookfield) without preliminary shear. The shear rate was varied for different systems within the interval fro m 1.5 to 4 rp m. Various vane spindles (V-71-73) were applied in the experiments. Figure 11 demonstrates typical flow curves for the gels of polyco mplexes of A Ps with (a) Pr-2500 and (b) Pr-611. The gels based on PAA featured a very small strength; hence, we failed to register this parameter These data are in agreement with the rheometric results of rotational viscometry measurements; that is, the gels based on Pr-2500 significantly surpass AP gels with Pr-611 with respect to strength. The yield stress, as expected, depends on the concentration of the poly mer in solution and on the amount of the AP sol, that is, on the density of the network of intermolecular crosslinks (Tab le 2). As is seen fro m these data, the gels based on Pr-2500 are considerably stronger and more rigid than Pr-611-based gels. If for the former gels, deformat ion up to the yield stress is small (2-6 rad), then deformat ion for the Pr-611-based gels it is significantly h igher (450 rad). Another specific feature of the Pr-2500 gels with APs is that they are sensitive to the composition of the polycomplex. Figure 12 shows that an increase in the content of APs evidently leads to a gain in the density of the network of interjunction bonds accompanied by strengthening of the gel and detachment of its whole mass fro m cell walls. Moreover, the appearing Weissenberg effect ( Figure 10) makes it impossible to achieve the shear stress corresponding to the yield stress ( Figure 12, curves 3 and 4). In the case of similar rheological systems, the method of dynamic mechanical analysis with the use of a micro-Fourier rheometer may be useful. For a fluid mediu m containing a polymer solution and colloid particles, both viscous and elastic reactions to the shear load are typical. The value of phase angle (α) between the shear stress and strain for viscoelastic liquids should vary fro m π/2 (the v iscous med iu m) to 0 (the elastic mediu m). For the gels under consideration, the viscoelastic deformat ion is evidently determined by two parameters: poly mer concentration and ratio between crosslinking agents (AP) and polymer. As follows fro m these data, the viscoelastic characteristics of solutions grow with an increase in the strain rate throughout the concentration range fro m 0.3 to 2.0 g/dl. In this case, the absolute value of G* for polycomp lexes is always significantly h igher than that for the corresponding initial copoly mer. The structuring is acco mpanied by an increase in the elastic co mponent of shear modulus (G`) ( Figure 14) and exerts virtually no effect on the loss modulus G`` (Figure 15).
Structuring due to the crosslinking of poly meric chains of APs is also confirmed by an increase in the storage modulus G' with a rise in the AP:poly mer unit. In this case, the viscosity component remains invariable ( Figure 16).  The influence of the amount of the AP sol in the initial mixtu re on the value of mechanical loss tangent is the specific feature of the system (Figure 17).
For the polyco mplex based on low-basicity Pr-2500, the crosslinking of the poly mer with APs begins at low ratios of reagents.
As was noted above (Table 2), crosslinking becomes more pronounced with an increase in this ratio. In this case, the curve exhibits a break in the range 0.5-1.0 mo l of Al 3+ per mo le of the polymer. A somewhat different behavior is observed for the gels based on a weakly cat ionic Pr-611. The dependence of tg(α) on the ratio of reagents shows a complicated pattern (Figure 8). At small amounts of AP, the elasticity of the gels declines; however, at ratios above 1:1, the elastic reaction increases abruptly to 4:1, and then its monotonic growth persists. This specific feature of cat ionic polyelectrolyte was also noted during the rotational viscometry experiments (Figure 9). This phenomenon is associated with the co mpetition o f processes in the compaction of Pr-611 macro mo lecules at low concentrations of AP as well as with the predo minance of crosslinking processes at higher concentrations of the polymer and a high amount of AP. To provide effective contact of APs with polymer macro molecules, a considerable volu me fraction of the polymer in the water-salt solution and a sufficient amount of the crosslinking agent (AP) are evidently required.

Conclusions
Alumino xane nanosized particles form stable bonds with polymer chains due to noncovalent interactions that lead to the format ion of an extended three-dimensional network rather than form another stable phase in a mixture with aqueous solutions of polyelectrolytes. Alu mino xane nanosized particles in the sol PAHC carry out a part of polyelectrolytes in the initial mixture with acrylamide copolymers and cause the compacting of coils of macro molecules. At that time, noncovalent interactions of APs with units of macro molecu les result in their crosslinking. A domination that or another process depends on the type of ionic groups and the presence of a low-mo lecular-mass indifferent electrolyte (NaCl). As a result, "soft" nanocomposite materials appear in the form of optically transparent gels, in which organic and inorganic components interact at the molecular level. Such organo-inorganic hydrogels lack their o wn shape, and their yield stress is determined by the nature of the three-dimensional network that appears through the interactions of positively charged alu mino xane clusters with the functional groups of polymers. Structurization takes p lace under the conditions of a single-phase state of the disperse system stabilized by stable hydrogen bonds in an aqueous solution.
Formed hybrid hydrogels possess viscoelastic characteristics and under the action of shear stress show the "Weissenberg effect." The ratio storage modulus -loss modulus depends on the amount of the AP sol and its ratio to the quantity of the copolymer in the init ial mixture. Inorganic alu mino xane particles under consideration are structurally similar to silica particles formed during the sol-gel synthesis fro m tetramethoxysilane; however, they differ in the sign of the surface charge, which is negative fo r silica part icles and positive for alu mino xane particles. a) b) Figure 19. Scattering particles in sol: a) silica (rd = 4-6 nm, df = 2.5) [47]; b) aluminoxane particles (rd = 2.2 nm and df = 1.0) [28] With due account for this similarity and results of [47], a similar scheme for the spatial structure of hybrid hydrogels may be suggested In such a scheme, alu mino xane particles play the role of network junctions that bind polyelectrolyte macro molecules into a co mmon spatial network. It is clear that the density of such a network is determined by the amount of particles, and its strength depends on the nature of noncovalent bonds of particles with poly mer chain units, which are the most pronounced for colu mn interactions typical for weakly anionic Pr-2500.