Article pubs.acs.org/Biomac
Evidence for the Coexistence of Interpenetrating Permanent and Transient Networks of Hydroxypropyl Methyl Cellulose Allahbash Shahin, Taco Nicolai,* Lazhar Benyahia, Jean-Francois Tassin, and Christophe Chassenieux LUNAM, Université du Maine, IMMM UMR CNRS 6283, PCI, 72085 Le Mans cedex 9, France ABSTRACT: Dynamic mechanical properties of aqueous solutions of hydroxypropyl methyl cellulose (HPMC) were investigated using oscillatory shear measurements. The structure was investigated with light scattering. A systematic investigation of the frequency dependence of the shear moduli showed that HPMC forms two distinct interpenetrating networks. A transient network is formed above about 0.3 wt % by reversible crosslinking of the chains. The elastic modulus of this network is independent of the temperature, but increases linearly with the concentration. An independent permanent network is formed involving a small fraction of the polymers and has an elastic modulus that increases with increasing temperature. Its elastic modulus is history dependent and evolves slowly with time. The transient network collapses at a critical temperature where micro phase separation occurs, but the permanent network is not influenced by this phenomenon. Light scattering showed that the pore size of the transient network is less than 40 nm, while probe diffusion measurements showed that the pore size of the permanent network is larger than 1 μm.
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INTRODUCTION Hydroxypropyl methyl cellulose is a polysaccharide obtained by modification of cellulose and is widely used as a thickener or gelling agent of aqueous solutions in industrial applications. Aqueous HPMC solutions are known to gel when heated at temperatures above 50 °C depending on the degree of substitution of the hydroxyl groups.1−7 The gels melt upon cooling, but at significantly lower temperature than the one at which they were formed. Numerous authors1−7 have reported a curious phenomenon when the storage (G′) and loss (G″) oscillatory shear moduli of HPMC at higher frequencies are measured as a function of temperature during heating, which is illustrated for G′ in Figure.1. With increasing temperature, G′ and G″ initially decrease progressively, but then drop sharply at a critical temperature (Tc). After reaching a minimum, the shear moduli increase again with increasing temperature. When the temperature is increased to a fixed value above Tc, G′ increases steeply in the first few minutes, followed by a much slower increase.5 The value of G′ at a given temperature increases with increasing polymer concentration.3−5 Tc depends on the degree of substitution of HPMC, but not on the polymer concentration,1,6 and was found to increase weakly with increasing heating rate.1 Several authors suggested that Tc is very close to the temperature at which HPMC starts to form a gel.1,2,6 However, Haque et al.3 showed that G′ starts to increase at temperatures much lower than Tc when a low oscillation frequency is used, which suggests that HPMC can gel at temperatures significantly below Tc. The different temperature dependence of G′ at low and high frequencies is illustrated in Figure 1 and will be discussed in detail. © 2013 American Chemical Society
Figure 1. Temperature dependence of the shear modulus at two frequencies during a heating ramp at 0.1 °C/min for a HPMC solution at 2 wt %.
At low temperatures, HPMC solutions were found to be shear thinning.3 Silva et al.6 observed that during a heating ramp the viscosity increased sharply above Tc at low shear rate but that it decreased at high shear rates. They attributed the sharp decrease to shear-induced destruction of the gel that is formed above Tc. It was shown that at Tc the transmittance of HPMC solutions decreases sharply.2,6,8 Upon cooling, the samples become transparent again but at somewhat lower temperatures. Bodvik et al.1 found for dilute HPMC solutions a sharp increase of the Received: October 20, 2013 Revised: November 27, 2013 Published: December 8, 2013 311
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Isothermal frequency sweeps were performed from ω = 0.1 to 100 rad/s with a strain fixed at 1% for 0.5 and 1 wt % solutions and 2% at higher concentrations. These strains were well within the linear response regime. The temperature was varied from 5 to 80 °C. Temperature ramps were performed with a heating rate of 0.1 and 1 °C/min at ω = 0.01 and 10 rad/s, respectively. Some experiments were repeated with a cone and plate geometry to confirm the validity of the observations. In order to avoid drying, a small amount of low viscosity mineral oil was added at the periphery of the geometry. The viscosity (η) of the transient networks at low temperatures was determined by measuring the viscosity as a function of the shear rate and extrapolation to zero shear rate. Light Scattering. Light scattering measurements were done using a commercial apparatus (ALV-CGS3, ALV-laser) operating with a vertically polarized laser with wavelength λ = 632 nm. The measurements were done at 20 °C over a wide range of scattering wave vectors (q = 4πn sin(θ/2)/λ, with θ the angle of observation and n the refractive index of the solvent). In dilute solutions, the scattered light intensity is related to the weight average molar mass (Mw), the concentration (C), and the q-dependent structure factor S(q) of the solute:
scattered light intensity and the hydrodynamic radius at the critical temperature, indicating the onset of aggregation. With optical microscopy a heterogeneous structure was observed to appear at Tc on length scales of several micrometers, indicating microphase separation.2 Kita et al.9 studied the initial stages of the phase separation using light scattering measurements and concluded that coarsening was stopped by gelation. Electron microscopy showed that long fibrillar aggregates were formed at higher temperatures.1 The aggregation and microphase separation were found to be accompanied by an endothermal process that some authors have suggested to be due to dehydration of the hydrophobic substituents.3,8 Several techniques showed that changes occur in HPMC solutions during heating already below Tc. Fluorescence measurements indicate the formation of hydrophobic domains at temperatures below Tc.3,6,10 Haque et al.3 concluded from optical rotation measurements that a cooperative conformational transition occurs when the temperature is increased starting at low temperatures and which is practically complete at Tc. NMR measurements showed that HPMC is not present in the form of fully disordered coils below Tc.3 The mobility of the polymer segments increased with increasing temperature until Tc beyond which it dropped. The changes observed with these different techniques during heating were fully reversed during cooling, but as for the rheology with significant hysteresis. It has recently been suggested that it is the microphase separation that induces gelation of HPMC a few degrees above Tc.2 The proposed mechanism of gelation is that above Tc the solubility of the chains is reduced leading to phase separation into polymer-rich and polymer-poor phases. The polymers in the polymer-rich phase connect through hydrophobic interactions and inhibit macroscopic phase separation. However, this mechanism appears to be in stark contradiction with the observation mentioned above that G′ increases at temperatures much below Tc. The objective of the present investigation is to explain the origin of the sharp dip in the shear moduli at Tc and to clarify the relationship between gel formation and microphase separation for HPMC solutions. The existence of two interpenetrated networks will be demonstrated. We will show that the dip is caused by the combined effects of the collapse of a transient network at Tc and the progressive strengthening of a permanent network with increasing temperature that starts forming at temperatures well below T c . A systematic investigation using oscillatory shear measurements and static and dynamic light scattering allowed us to characterize the structure and the dynamic mechanical properties of the transient and the permanent networks separately.
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Ir = KCM w S(q)
(1)
with K an optical constant: K=
2 2 4π 2n2 ⎛⎜ ∂n ⎟⎞ ⎛⎜ ns ⎞⎟ 1 4 λ Na ⎝ ∂C ⎠ ⎝ n ⎠ R s
(2)
where Na is the Avogadro’s number, ∂n/∂C is the refractive index increment, Rs is the Rayleigh ratio of toluene, and ns is the refractive index of toluene. We have determined the refractive index increment as ∂n/∂C = 0.14 mL·g−1 and used for the Rayleigh ratio Rs = 1.35 × 10−5 cm−1. The z-average radius of gyration (Rg) radius of gyration can be derived from the initial q-dependence of the structures factor:
⎛ 1 + (qR )2 ⎞−1 g ⎟ S(q) = ⎜⎜ ⎟ 3 ⎝ ⎠
(3)
At higher concentrations, where interactions are no longer negligible one measures an apparent molar mass (Ma) or radius of gyration (Rg). With dynamic light scattering (DLS) measurements, the normalized intensity autocorrelation functions g2(t) is measured, which is related to the electric field autocorrelation function g1(t):g2(t) = 1 + g21(t).11 g1(t) was analyzed in terms of a relaxation time (τ) distribution (A(τ)) using the REPES routine.12 g1(t ) =
∫ A(log τ)exp(−t /τ)d log τ
(4)
2
In all solutions we observed a fast q -dependent relaxation mode, which was caused by cooperative diffusion of the solute. The cooperative diffusion coefficient was calculated from the average relaxation rate as Dc = ⟨τ−1⟩/q2. In dilute solutions Dc is related to the z-average hydrodynamic radius of the solute: Rh =
EXPERIMENTAL SECTION
kT 6πηDc
(5)
At higher concentrations one measures an apparent hydrodynamic radius. In addition to the cooperative diffusion, we observed a slow relaxation mode due to a small weight fraction of large spurious scatterers. At lower concentrations the spurious scatterers could be removed by filtration, but at higher concentrations the solutions became very viscous rendering filtration impossible. Therefore it was not possible to characterize HPMC solutions with light scattering for C > 2 wt %.
Materials. The hydroxypropyl methyl cellulose sample used in this study (Methocel E4M Premium) was procured from Dow Chemical. The methoxyl content is 29% and the hydroxypropyl content is 8.5%, corresponding to a degree of substitution of 1.9 and molar substitution of 0.23. The HPMC solutions were prepared by dispersing the polymer in deionized water and stirring for 12 h. The solutions were stored in the refrigerator at 4° for a minimum of 48 h to allow complete hydration of the polymers. Methods. Oscillatory Shear Measurements. Oscillatory shear measurements were done with a stress controlled rheometer (ARG2, TA Instruments) fitted with a parallel plate geometry (40 mm diameter, gap 0.8 mm). The dynamic storage (G′) and loss (G″) moduli were monitored as a function of frequency and temperature.
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RESULTS AND DISCUSSION We have investigated the frequency dependence of the shear moduli as a function of the temperature during heating and 312
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frequencies increased with increasing temperature and above 60 °C it dominated the viscoelastic relaxation. The viscoelastic relaxation observed at different temperatures could be superimposed using only horizontal shift factors, see Figure 3. The horizontal shift factors (aT) used for the frequency−temperature superposition are shown in Figure 4.
cooling at different HPMC concentrations. An example is shown for C = 2 wt % in Figure 2. At low temperatures the
Figure 4. Shift factors used to obtain the master curves shown in Figure 3. The shift factors obtained for other HPMC concentrations are also included in the figure. The dashed line represents the temperature dependence of the viscosity of water. The solid line is a guide to the eye.
The master curves show more clearly how the relative contributions of the viscoelastic response at high frequencies and the elastic response at low frequencies vary with temperature. The fact that the viscoelastic response superimposes well at all temperatures using only horizontal shifts shows that the elastic response of the transient network is independent of the temperature, but that its terminal relaxation time becomes shorter with increasing temperatures. The superposition also shows how the elastic response of the permanent network dominates the response of the transient network over an increasing frequency range with increasing temperature. The frequency−temperature superposition was not reliable at temperatures above 58 °C, because the viscoelastic relaxation moved beyond the accessible frequency window. Similar results were observed at other concentrations, with the relative contribution of the viscoelastic relaxation becoming greater at higher HPMC concentrations. Since no vertical shift factors were needed, aT in Figure 4 represents not only the
Figure 2. Frequency dependence of the loss (triangles) and storage (circles) shear moduli for a HPMC solution at 2 wt % at different temperatures. The temperature was increased in discrete steps and the measurements were done after equilibrating about 20 min at each temperature.
system behaved as a visco-elastic liquid, but for T > 40 °C a plateau appeared at low frequencies in both G′ and G″, while the viscoelastic relaxation shifted to higher frequencies with increasing temperature. The storage modulus at low
Figure 3. Frequency dependence of the storage (left) and loss (right) moduli obtained at different temperatures for a HPMC solution at 2 wt % after temperature-frequency superposition of the high frequency data. The temperature was increased in discrete steps and measurements were done after equilibrating about 20 min at each temperature. The reference temperature was 20 °C. 313
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Figure 5. Frequency dependence of the storage and loss shear moduli for a HPMC solution at 4 wt % at different temperatures close to the critical temperature. The temperature was increased in discrete steps and the measurements were done after equilibrating about 20 min at each temperature.
variation of the relaxation time but also of the viscosity. Up to 56 °C, aT decreased relatively weakly with temperature, although more strongly than the temperature dependence of water viscosity indicated by the dashed line, but at higher temperatures it dropped sharply. The strong effect at T > 56 °C was studied in more detail at 4 wt %, where the relative contribution of the viscoelastic relaxation was more important, see Figure 5. With increasing temperature above 56 °C, the viscoelastic relaxation shifted rapidly to higher frequencies causing a sharp drop of aT, see Figure 4. As found for the 2 wt % sample, the frequency independent elastic modulus increased with increasing temperature and dominated the viscoelastic response at increasingly higher frequencies. Using these results, we can easily explain the curious temperature dependence of G′ and G″ at higher frequencies. At higher frequencies and polymer concentrations, the visco-elastic response dominates up to a few degrees above Tc, which causes the progressive decrease of G′ and G″ with increasing temperature up to Tc (less than 1 order of magnitude between 5 and 55 °C) and the sharp dip at Tc (more than 1 order of magnitude between 56 and 62 °C). However, as the viscoelastic contribution decreases rapidly for T > Tc, the elastic response starts to dominate also at high frequencies and causes the increase of the moduli at higher temperatures. It is clear that the sharp dip can only be observed if the viscoelastic response is significant at Tc. Since the relative contribution of the viscoelastic response is stronger for G″ than for G′, the dip is better observed for G″.1−6 In fact, when G′ is probed at very low frequencies one observes only a progressive increase with increasing temperature, see Figure 1. In conclusion, we have demonstrated that HPMC forms two distinct interpenetrating networks: a transient one which dominates the viscoelastic behavior at high frequencies and a permanent one which is reflected in the elastic plateau observed at low frequencies. In the following we will investigate in more detail the structure and the dynamic mechanical properties of each network. Dynamic Mechanical Properties of the Transient and Permanent Networks. Transient Network. The transient network is best observed at low temperatures. Figure 6 shows the viscosity as a function of the concentration at 5 °C. It rises sharply above 0.3%, indicating the formation of a transient network. The viscoelastic behavior of the transient network is shown for different concentrations in Figure 7a. Increasing the
Figure 6. Concentration dependence of the low shear viscosity of HPMC solutions at 5 °C.
polymer concentration led to an increase of both the relaxation time and the storage modulus at high frequencies. The results obtained at different concentrations could be superimposed using both vertical and horizontal shift factors, see Figure 7b, implying that the morphology of the transient network does not vary with the concentration in range covered here. The master curve shows more clearly the viscoelastic behavior of the transient network over a broad frequency range. The concentration dependence of the relaxation time (τ) defined as τ = ω−1 at G′ = G″ and the elastic modulus (Gel) defined as Gel = G′ at τ·ω = 10 are shown in Figure 8. These definitions are rather arbitrary as the relaxation is very broad, but that does not influence the dependence of τ and Gel on C and T since the shape of the relaxation is independent of C and T. Gel increased approximately linearly with the concentration, while τ increased much more rapidly: τ ∝ C2.5. The concentration dependence of the viscosity is a combination of that of Gel and τ because η ∝ G′·τ. It follows that η ∝ C3.5, which is consistent with our direct measurements of the viscosity, see Figure 6. It is clear that the same concentration dependence of the viscosity can be obtained with different concentration dependences of Gel and τ. Therefore, the latter are better suited to discriminate between different possible origins of the viscoelastic properties. One possible origin of the visco-elastic behavior is entanglements of HMPC chains in the random coil conformation. The concentration dependence for entangled polymer solutions in good solvents has been investigated extensively in the past:13 Gel ∝ C2.2 and τ ∝ C1.6. Slightly different exponents are found in theta solvents, but it is clear 314
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Figure 7. (a) Frequency dependence of the loss (closed symbols) and storage (open symbols) shear moduli for HPMC solutions at different concentrations at 5 °C: 8, 4, 2, 1, and 0.5 g/L from top to bottom. (b) Master curves obtained by temperature-frequency superposition of the results shown in (a).
can be determined by measuring G′ at sufficiently low frequencies so that it is no longer influenced by the transient network. Figure 1 shows that the elastic modulus of the permanent network increased gradually with increasing temperature above 40 °C. A similar result was already reported by Haque et al.3 for a different type of HPMC. It is difficult to obtain trustworthy values below 40 °C, because the network is very weak and breaks at low stress. We observed that the modulus increased with increasing polymer concentration as was already reported in the literature,3,4 but the values were not very reproducible and depended on the temperature history contrary to those of the transient network. The dependence on the history is perhaps most clearly expressed by the hysteresis between heating and subsequent cooling, but it was manifest also when the heating rate was varied or when the system was heated in steps with different durations. In addition, when the temperature was fixed after a rapid increase from 5 °C, G′ continued to increase with time for a period of at least one day, which is illustrated for the case of 50 °C in Figure 9. The nonreproducibility and the dependence on the temperature history imply that the permanent network is not at thermodynamic equilibrium. Structure of the Transient and Permanent Networks. Transient Network. The structure of the transient network was investigated by light scattering up to 2 wt %. Figure 10 shows the concentration dependence of the apparent molar mass (Ma) and radius of gyration of the polymers (Rg). In dilute solutions Ma and Rg correspond to the weight average molar mass and
Figure 8. Concentration dependence of the elastic modulus (circles) and the relaxation time (squares) for HPMC solutions at 5 °C. The solid lines represent linear least-squares fits.
that whatever the solvent quality the observed concentration dependences of G′ and τ are incompatible with that of entangled polymer solutions. A linear increase of Gel can be explained if the HPMC chains have a fixed number of binding sites that can form transient cross-links with other chains. Assuming rubber elasticity, we can estimate the average molar mass between binding sites as Mc = CRT/Gel, which gives roughly 8 × 104 g/mol. Here we considered that all polymers contained the same amount of binding sites. Comparison with the weight average molar mass determined by light scattering, see below, shows that there are on average about four binding sites per chain. The relaxation time increased more strongly than expected for entangled polymer chains. It is clearly not solely determined by the average lifetime of a single bond in which case it would be independent of the concentration. We suggest that relaxation of the chains involves diffusion of the segments while continuously breaking and reforming transient bonds. The probability of reforming a bond during relaxation of the chains increases with the concentration and hence slows it down. A scaling theory for the relaxation of polymers containing a limited number of sites that can form transient cross-links was developed by Rubinstein and Semenov.14 It predicts a linear increase of G′ with the concentration and a power law increase of the terminal relaxation time (τ ∝ C3) close to that observed here for HPMC. Permanent Network. The temperature and concentration dependence of the elastic modulus of the permanent network
Figure 9. Evolution of the storage shear modulus at ω = 0.01 rad/s with waiting time after rapidly heating a HPMC solution at C = 1 wt % from 5 to 50 °C. 315
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Figure 10. Concentration dependence of the apparent molar mass (a) and radius of gyration (b) for HPMC solutions at 20 °C. The concentration dependence of the apparent hydrodynamic radius is compared to Rg in (b).
the z-average radius of gyration: Mw = 4 × 105 g/mol and Rg = 70 nm. Using these values we may estimate the overlap concentration as (C* = 3Mw/Na4πR3g) = 0.05 wt %. With dynamic light scattering a fast diffusional relaxation mode was observed due to cooperative diffusion of the polymers from which the apparent hydrodynamic radius (Rha) was derived as explained in the Materials and Methods sections. The values of Rha were systematically smaller than Rg, see Figure 10, which can in part be explained by the fact that they represent different averages. In dilute solutions we find Rha = 40 nm. Using this value in the calculation of C* gives C* = 0.25 wt %. With increasing concentration Ma, Rg, and Rha decrease as expected for a solution of linear polymers with repulsive excluded volume interactions. In the semidilute regime, that is, for C > C*, Rg and Rha represent the static and dynamic correlation lengths of the system, respectively. The correlation length of the transient network that is formed above about 0.3 wt % is smaller than 40 nm. The temperature dependence of Ma, Rg, and Rha was determined at three concentrations. At 0.5 and 1.0 wt %, Ma increased weakly at lower temperatures followed by a sharp upturn when the critical temperature of 56 °C was approached, see Figure 11. At 56 °C, the scattering intensity increased dramatically, but the solutions were still transparent. At this temperature we found I ∝ q−4 over the whole q-range, implying that a few very large homogeneous particles were formed. This
was confirmed by the appearance of a slow relaxation mode in autocorrelation functions caused by the diffusion of these particles. At 57 °C, the system became highly turbid, which rendered standard light scattering experiments no longer possible. Notice that 57 °C is the temperature where the viscosity of the transient network starts to decrease sharply, see Figures 4 and 5. At C = 0.1 wt %, Ma remained almost independent of the temperature until at 57 °C again large dense particles were formed. This solution became turbid at 58 °C. The sharp increase of the intensity at a critical temperature was earlier reported for dilute HPMC solutions by Bodvik et al.1 The variations of Rg and Rha with temperature corresponded to that of Ma. The initial increase of Ma with increasing temperature at the two higher concentrations can be explained by a reduction of the average repulsive interactions between the polymers. We speculate that with increasing temperature attractive hydrophobic interactions increasingly counteract the repulsive excluded volume interactions. This effect becomes strong close to 57 °C and leads to the formation of large relatively dense HPMC domains at higher temperatures. The amount of these domains is still very small at 57 °C, but rapidly increases with increasing temperature. They can be seen by optical microscopy and their formation has been attributed to micro phase separation.2 We note that the intensity was stable and reproducible up to 57 °C. We may conclude that increasing the temperature reduces the effective solvent quality until it leads to microphase separation at 57 °C that is inhibited to develop into macroscopic phase separation by the presence of the permanent network. Permanent Network. Unexpectedly, we did not find any effect of the formation of the permanent network using static or dynamic light scattering. At all temperatures investigated by light scattering the system was ergodic and the autocorrelation functions fully relaxed. The relaxation time remained q2dependent and was characterized by a single translation diffusion mode with a corresponding Rha that remained proportional to Rg. The implication is that the light scattered by the permanent network was negligible compared to that scattered by the transient network. To obtain further information on the structure of the permanent network we measured the diffusion of spherical probe particles in the system with DLS. Remarkably, we found that particles with a diameter as large as 1 μm diffused freely in the solutions at all temperatures where measurements could be
Figure 11. Temperature dependence of the apparent molar mass at three HPMC concentrations. 316
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done (up to 56 °C). Knowing the size of the particles, the effective viscosity felt by the particles could be determined using eq 5 and was found to be close to that of the transient network, see Figure 12. There is a small systematic difference
Figure 13. Schematic drawing of the interpenetrating network formed by aqueous solutions of HPMC for T < Tc: cross-linked flexible chains (blue) form a transient network with small pores and permanently cross-linked rigid fibrils form a permanent network with large pores.
Figure 12. Comparison of the viscosity of the transient network formed by 1 wt % HPMC at different temperatures deduced from particle tracking or from oscillatory shear experiments. The filled circle was obtained after heating 30 min at 80 °C and subsequent cooling to 50 °C.
temperature especially close to a critical temperature (56 °C) where microphase separation occurs. Above the critical temperature, phase separation leads to the collapse of the transient network. A permanent network is formed that is very weak at low temperatures, but the stiffness increases with increasing temperature. The elastic modulus of this network increases slowly with time after elevation of the temperature and is history dependent. Spherical particles with radii as large as 1 μm diffuse freely through the permanent network, but feel the friction of the transient network. The pores of the permanent network are thus larger than 1 μm and are interpenetrated by the transient network. Possibly the permanent network is formed by connected long fibrillar aggregates involving a small fraction of HPMC chains. The structure of the permanent network is not influenced by phase separation but its presence inhibits coarsening.
that we attribute to the different methods that were used. Interestingly, the effective viscosity was smaller at 50 °C when the solution was cooled after heating at 80 °C than when heated from 5 °C, while the elastic modulus of the permanent network was much higher. A possible explanation is that a larger fraction of the HPMC chains was involved in the permanent network at 50 °C after cooling so that the concentration of HPMC chains forming the transient network was lower, resulting in a lower viscosity of the transient network. The implication of this finding is that the pores of the permanent network are significantly larger than 1 μm. Bodvik et al.1 observed in transmission electron microscopy long fibrillar aggregates of HPMC. We speculate that a permanent network with large pores is formed by permanent cross-linking of fibrils. The fraction of polymers involved in the formation of the fibrils is small at least below Tc and the large majority forms the transient network that fills the pores of the permanent network, see Figure 13. The structure of the permanent network is not modified by the phase separation above 56 °C that drives the collapse of the transient network .
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work has been funded by the Agence Nationale de la Recherche in the framework ANR-11-BSV5-0022.
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CONCLUSION HPMC chains contain a limited amount of sites that allow them to bind to each other via transient cross-links. This leads to the formation of a transient network for C > 0.3 wt % with a modulus that increases linearly with the concentration. The terminal relaxation time of this network increases as C2.5, which we suggest is due to repeated breaking and formation of transient bonds during relaxation of the chains. The correlation length of the transient network is less than 40 nm and decreases with increasing concentration. The elastic modulus of the transient network does not depend on the temperature, but the relaxation time decreases weakly with increasing temperature leading to a slightly stronger relative decrease of the viscosity than that of water. The correlation length of the network increases with increasing
REFERENCES
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(5) Sarkar, N. Kinetics of thermal gelation of methylcellulose and hydroxypropylmethylcellulose in aqueous solutions. Carbohydr. Polym. 1995, 26 (3), 195−203. (6) Silva, S. r. M. C.; Pinto, F. t. V.; Antunes, F. E.; Miguel, M. G.; Sousa, J. o. J. S.; Pais, A. A. C. C. Aggregation and gelation in hydroxypropylmethyl cellulose aqueous solutions. J. Colloid Interface Sci. 2008, 327 (2), 333−340. (7) Yoo, Y. J.; Um, I. C. Examination of thermo-gelation behavior of HPMC and HEMC aqueous solutions using rheology. Korea Aust. Rheol. J. 2013, 25 (2), 67−75. (8) Sarkar, N.; Walker, L. Hydrationdehydration properties of methylcellulose and hydroxypropylmethylcellulose. Carbohydr. Polym. 1995, 27 (3), 177−185. (9) Kita, R.; Kaku, T.; Kubota, K.; Dobashi, T. Pinning of phase separation of aqueous solution of hydroxypropylmethylcellulose by gelation. Phys. Lett. A 1999, 259, 302−307. (10) Kita, R.; Kaku, T.; Ohashi, H.; Kurosu, T.; Iida, M.; Yagihara, S.; Dobashi, T. Thermally induced coupling of phase separation and gelation in an aqueous solution of hydroxypropylmethylcellulose (HPMC). Phys. A 2003, 319, 56−64. (11) Berne, B.; Percora, R. Dynamic Light Scattering; Wiley: New York, 1976. (12) Brown, W. Dynamic Light Scattering: The Method and Some Applications; Clarendon Press: Oxford, 1993. (13) Rubinstein, M.; Colby, R. Polymer Physics (Chemistry); Oxford University Press: U.S.A., 2003. (14) Rubinstein, M.; Semenov, A. N. Thermoreversible gelation in solutions of associating polymers. 2. Linear dynamics. Macromolecules 1998, 31 (4), 1386−1397.
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Evidence for the Coexistence of Interpenetrating Permanent and Transient Networks of Hydroxypropyl Methyl Cellulose Allahbash Shahin, Taco Nicolai,* Lazhar Benyahia, Jean-Francois Tassin, and Christophe Chassenieux LUNAM, Université du Maine, IMMM UMR CNRS 6283, PCI, 72085 Le Mans cedex 9, France ABSTRACT: Dynamic mechanical properties of aqueous solutions of hydroxypropyl methyl cellulose (HPMC) were investigated using oscillatory shear measurements. The structure was investigated with light scattering. A systematic investigation of the frequency dependence of the shear moduli showed that HPMC forms two distinct interpenetrating networks. A transient network is formed above about 0.3 wt % by reversible crosslinking of the chains. The elastic modulus of this network is independent of the temperature, but increases linearly with the concentration. An independent permanent network is formed involving a small fraction of the polymers and has an elastic modulus that increases with increasing temperature. Its elastic modulus is history dependent and evolves slowly with time. The transient network collapses at a critical temperature where micro phase separation occurs, but the permanent network is not influenced by this phenomenon. Light scattering showed that the pore size of the transient network is less than 40 nm, while probe diffusion measurements showed that the pore size of the permanent network is larger than 1 μm.
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INTRODUCTION Hydroxypropyl methyl cellulose is a polysaccharide obtained by modification of cellulose and is widely used as a thickener or gelling agent of aqueous solutions in industrial applications. Aqueous HPMC solutions are known to gel when heated at temperatures above 50 °C depending on the degree of substitution of the hydroxyl groups.1−7 The gels melt upon cooling, but at significantly lower temperature than the one at which they were formed. Numerous authors1−7 have reported a curious phenomenon when the storage (G′) and loss (G″) oscillatory shear moduli of HPMC at higher frequencies are measured as a function of temperature during heating, which is illustrated for G′ in Figure.1. With increasing temperature, G′ and G″ initially decrease progressively, but then drop sharply at a critical temperature (Tc). After reaching a minimum, the shear moduli increase again with increasing temperature. When the temperature is increased to a fixed value above Tc, G′ increases steeply in the first few minutes, followed by a much slower increase.5 The value of G′ at a given temperature increases with increasing polymer concentration.3−5 Tc depends on the degree of substitution of HPMC, but not on the polymer concentration,1,6 and was found to increase weakly with increasing heating rate.1 Several authors suggested that Tc is very close to the temperature at which HPMC starts to form a gel.1,2,6 However, Haque et al.3 showed that G′ starts to increase at temperatures much lower than Tc when a low oscillation frequency is used, which suggests that HPMC can gel at temperatures significantly below Tc. The different temperature dependence of G′ at low and high frequencies is illustrated in Figure 1 and will be discussed in detail. © 2013 American Chemical Society
Figure 1. Temperature dependence of the shear modulus at two frequencies during a heating ramp at 0.1 °C/min for a HPMC solution at 2 wt %.
At low temperatures, HPMC solutions were found to be shear thinning.3 Silva et al.6 observed that during a heating ramp the viscosity increased sharply above Tc at low shear rate but that it decreased at high shear rates. They attributed the sharp decrease to shear-induced destruction of the gel that is formed above Tc. It was shown that at Tc the transmittance of HPMC solutions decreases sharply.2,6,8 Upon cooling, the samples become transparent again but at somewhat lower temperatures. Bodvik et al.1 found for dilute HPMC solutions a sharp increase of the Received: October 20, 2013 Revised: November 27, 2013 Published: December 8, 2013 311
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Isothermal frequency sweeps were performed from ω = 0.1 to 100 rad/s with a strain fixed at 1% for 0.5 and 1 wt % solutions and 2% at higher concentrations. These strains were well within the linear response regime. The temperature was varied from 5 to 80 °C. Temperature ramps were performed with a heating rate of 0.1 and 1 °C/min at ω = 0.01 and 10 rad/s, respectively. Some experiments were repeated with a cone and plate geometry to confirm the validity of the observations. In order to avoid drying, a small amount of low viscosity mineral oil was added at the periphery of the geometry. The viscosity (η) of the transient networks at low temperatures was determined by measuring the viscosity as a function of the shear rate and extrapolation to zero shear rate. Light Scattering. Light scattering measurements were done using a commercial apparatus (ALV-CGS3, ALV-laser) operating with a vertically polarized laser with wavelength λ = 632 nm. The measurements were done at 20 °C over a wide range of scattering wave vectors (q = 4πn sin(θ/2)/λ, with θ the angle of observation and n the refractive index of the solvent). In dilute solutions, the scattered light intensity is related to the weight average molar mass (Mw), the concentration (C), and the q-dependent structure factor S(q) of the solute:
scattered light intensity and the hydrodynamic radius at the critical temperature, indicating the onset of aggregation. With optical microscopy a heterogeneous structure was observed to appear at Tc on length scales of several micrometers, indicating microphase separation.2 Kita et al.9 studied the initial stages of the phase separation using light scattering measurements and concluded that coarsening was stopped by gelation. Electron microscopy showed that long fibrillar aggregates were formed at higher temperatures.1 The aggregation and microphase separation were found to be accompanied by an endothermal process that some authors have suggested to be due to dehydration of the hydrophobic substituents.3,8 Several techniques showed that changes occur in HPMC solutions during heating already below Tc. Fluorescence measurements indicate the formation of hydrophobic domains at temperatures below Tc.3,6,10 Haque et al.3 concluded from optical rotation measurements that a cooperative conformational transition occurs when the temperature is increased starting at low temperatures and which is practically complete at Tc. NMR measurements showed that HPMC is not present in the form of fully disordered coils below Tc.3 The mobility of the polymer segments increased with increasing temperature until Tc beyond which it dropped. The changes observed with these different techniques during heating were fully reversed during cooling, but as for the rheology with significant hysteresis. It has recently been suggested that it is the microphase separation that induces gelation of HPMC a few degrees above Tc.2 The proposed mechanism of gelation is that above Tc the solubility of the chains is reduced leading to phase separation into polymer-rich and polymer-poor phases. The polymers in the polymer-rich phase connect through hydrophobic interactions and inhibit macroscopic phase separation. However, this mechanism appears to be in stark contradiction with the observation mentioned above that G′ increases at temperatures much below Tc. The objective of the present investigation is to explain the origin of the sharp dip in the shear moduli at Tc and to clarify the relationship between gel formation and microphase separation for HPMC solutions. The existence of two interpenetrated networks will be demonstrated. We will show that the dip is caused by the combined effects of the collapse of a transient network at Tc and the progressive strengthening of a permanent network with increasing temperature that starts forming at temperatures well below T c . A systematic investigation using oscillatory shear measurements and static and dynamic light scattering allowed us to characterize the structure and the dynamic mechanical properties of the transient and the permanent networks separately.
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Ir = KCM w S(q)
(1)
with K an optical constant: K=
2 2 4π 2n2 ⎛⎜ ∂n ⎟⎞ ⎛⎜ ns ⎞⎟ 1 4 λ Na ⎝ ∂C ⎠ ⎝ n ⎠ R s
(2)
where Na is the Avogadro’s number, ∂n/∂C is the refractive index increment, Rs is the Rayleigh ratio of toluene, and ns is the refractive index of toluene. We have determined the refractive index increment as ∂n/∂C = 0.14 mL·g−1 and used for the Rayleigh ratio Rs = 1.35 × 10−5 cm−1. The z-average radius of gyration (Rg) radius of gyration can be derived from the initial q-dependence of the structures factor:
⎛ 1 + (qR )2 ⎞−1 g ⎟ S(q) = ⎜⎜ ⎟ 3 ⎝ ⎠
(3)
At higher concentrations, where interactions are no longer negligible one measures an apparent molar mass (Ma) or radius of gyration (Rg). With dynamic light scattering (DLS) measurements, the normalized intensity autocorrelation functions g2(t) is measured, which is related to the electric field autocorrelation function g1(t):g2(t) = 1 + g21(t).11 g1(t) was analyzed in terms of a relaxation time (τ) distribution (A(τ)) using the REPES routine.12 g1(t ) =
∫ A(log τ)exp(−t /τ)d log τ
(4)
2
In all solutions we observed a fast q -dependent relaxation mode, which was caused by cooperative diffusion of the solute. The cooperative diffusion coefficient was calculated from the average relaxation rate as Dc = ⟨τ−1⟩/q2. In dilute solutions Dc is related to the z-average hydrodynamic radius of the solute: Rh =
EXPERIMENTAL SECTION
kT 6πηDc
(5)
At higher concentrations one measures an apparent hydrodynamic radius. In addition to the cooperative diffusion, we observed a slow relaxation mode due to a small weight fraction of large spurious scatterers. At lower concentrations the spurious scatterers could be removed by filtration, but at higher concentrations the solutions became very viscous rendering filtration impossible. Therefore it was not possible to characterize HPMC solutions with light scattering for C > 2 wt %.
Materials. The hydroxypropyl methyl cellulose sample used in this study (Methocel E4M Premium) was procured from Dow Chemical. The methoxyl content is 29% and the hydroxypropyl content is 8.5%, corresponding to a degree of substitution of 1.9 and molar substitution of 0.23. The HPMC solutions were prepared by dispersing the polymer in deionized water and stirring for 12 h. The solutions were stored in the refrigerator at 4° for a minimum of 48 h to allow complete hydration of the polymers. Methods. Oscillatory Shear Measurements. Oscillatory shear measurements were done with a stress controlled rheometer (ARG2, TA Instruments) fitted with a parallel plate geometry (40 mm diameter, gap 0.8 mm). The dynamic storage (G′) and loss (G″) moduli were monitored as a function of frequency and temperature.
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RESULTS AND DISCUSSION We have investigated the frequency dependence of the shear moduli as a function of the temperature during heating and 312
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frequencies increased with increasing temperature and above 60 °C it dominated the viscoelastic relaxation. The viscoelastic relaxation observed at different temperatures could be superimposed using only horizontal shift factors, see Figure 3. The horizontal shift factors (aT) used for the frequency−temperature superposition are shown in Figure 4.
cooling at different HPMC concentrations. An example is shown for C = 2 wt % in Figure 2. At low temperatures the
Figure 4. Shift factors used to obtain the master curves shown in Figure 3. The shift factors obtained for other HPMC concentrations are also included in the figure. The dashed line represents the temperature dependence of the viscosity of water. The solid line is a guide to the eye.
The master curves show more clearly how the relative contributions of the viscoelastic response at high frequencies and the elastic response at low frequencies vary with temperature. The fact that the viscoelastic response superimposes well at all temperatures using only horizontal shifts shows that the elastic response of the transient network is independent of the temperature, but that its terminal relaxation time becomes shorter with increasing temperatures. The superposition also shows how the elastic response of the permanent network dominates the response of the transient network over an increasing frequency range with increasing temperature. The frequency−temperature superposition was not reliable at temperatures above 58 °C, because the viscoelastic relaxation moved beyond the accessible frequency window. Similar results were observed at other concentrations, with the relative contribution of the viscoelastic relaxation becoming greater at higher HPMC concentrations. Since no vertical shift factors were needed, aT in Figure 4 represents not only the
Figure 2. Frequency dependence of the loss (triangles) and storage (circles) shear moduli for a HPMC solution at 2 wt % at different temperatures. The temperature was increased in discrete steps and the measurements were done after equilibrating about 20 min at each temperature.
system behaved as a visco-elastic liquid, but for T > 40 °C a plateau appeared at low frequencies in both G′ and G″, while the viscoelastic relaxation shifted to higher frequencies with increasing temperature. The storage modulus at low
Figure 3. Frequency dependence of the storage (left) and loss (right) moduli obtained at different temperatures for a HPMC solution at 2 wt % after temperature-frequency superposition of the high frequency data. The temperature was increased in discrete steps and measurements were done after equilibrating about 20 min at each temperature. The reference temperature was 20 °C. 313
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Figure 5. Frequency dependence of the storage and loss shear moduli for a HPMC solution at 4 wt % at different temperatures close to the critical temperature. The temperature was increased in discrete steps and the measurements were done after equilibrating about 20 min at each temperature.
variation of the relaxation time but also of the viscosity. Up to 56 °C, aT decreased relatively weakly with temperature, although more strongly than the temperature dependence of water viscosity indicated by the dashed line, but at higher temperatures it dropped sharply. The strong effect at T > 56 °C was studied in more detail at 4 wt %, where the relative contribution of the viscoelastic relaxation was more important, see Figure 5. With increasing temperature above 56 °C, the viscoelastic relaxation shifted rapidly to higher frequencies causing a sharp drop of aT, see Figure 4. As found for the 2 wt % sample, the frequency independent elastic modulus increased with increasing temperature and dominated the viscoelastic response at increasingly higher frequencies. Using these results, we can easily explain the curious temperature dependence of G′ and G″ at higher frequencies. At higher frequencies and polymer concentrations, the visco-elastic response dominates up to a few degrees above Tc, which causes the progressive decrease of G′ and G″ with increasing temperature up to Tc (less than 1 order of magnitude between 5 and 55 °C) and the sharp dip at Tc (more than 1 order of magnitude between 56 and 62 °C). However, as the viscoelastic contribution decreases rapidly for T > Tc, the elastic response starts to dominate also at high frequencies and causes the increase of the moduli at higher temperatures. It is clear that the sharp dip can only be observed if the viscoelastic response is significant at Tc. Since the relative contribution of the viscoelastic response is stronger for G″ than for G′, the dip is better observed for G″.1−6 In fact, when G′ is probed at very low frequencies one observes only a progressive increase with increasing temperature, see Figure 1. In conclusion, we have demonstrated that HPMC forms two distinct interpenetrating networks: a transient one which dominates the viscoelastic behavior at high frequencies and a permanent one which is reflected in the elastic plateau observed at low frequencies. In the following we will investigate in more detail the structure and the dynamic mechanical properties of each network. Dynamic Mechanical Properties of the Transient and Permanent Networks. Transient Network. The transient network is best observed at low temperatures. Figure 6 shows the viscosity as a function of the concentration at 5 °C. It rises sharply above 0.3%, indicating the formation of a transient network. The viscoelastic behavior of the transient network is shown for different concentrations in Figure 7a. Increasing the
Figure 6. Concentration dependence of the low shear viscosity of HPMC solutions at 5 °C.
polymer concentration led to an increase of both the relaxation time and the storage modulus at high frequencies. The results obtained at different concentrations could be superimposed using both vertical and horizontal shift factors, see Figure 7b, implying that the morphology of the transient network does not vary with the concentration in range covered here. The master curve shows more clearly the viscoelastic behavior of the transient network over a broad frequency range. The concentration dependence of the relaxation time (τ) defined as τ = ω−1 at G′ = G″ and the elastic modulus (Gel) defined as Gel = G′ at τ·ω = 10 are shown in Figure 8. These definitions are rather arbitrary as the relaxation is very broad, but that does not influence the dependence of τ and Gel on C and T since the shape of the relaxation is independent of C and T. Gel increased approximately linearly with the concentration, while τ increased much more rapidly: τ ∝ C2.5. The concentration dependence of the viscosity is a combination of that of Gel and τ because η ∝ G′·τ. It follows that η ∝ C3.5, which is consistent with our direct measurements of the viscosity, see Figure 6. It is clear that the same concentration dependence of the viscosity can be obtained with different concentration dependences of Gel and τ. Therefore, the latter are better suited to discriminate between different possible origins of the viscoelastic properties. One possible origin of the visco-elastic behavior is entanglements of HMPC chains in the random coil conformation. The concentration dependence for entangled polymer solutions in good solvents has been investigated extensively in the past:13 Gel ∝ C2.2 and τ ∝ C1.6. Slightly different exponents are found in theta solvents, but it is clear 314
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Figure 7. (a) Frequency dependence of the loss (closed symbols) and storage (open symbols) shear moduli for HPMC solutions at different concentrations at 5 °C: 8, 4, 2, 1, and 0.5 g/L from top to bottom. (b) Master curves obtained by temperature-frequency superposition of the results shown in (a).
can be determined by measuring G′ at sufficiently low frequencies so that it is no longer influenced by the transient network. Figure 1 shows that the elastic modulus of the permanent network increased gradually with increasing temperature above 40 °C. A similar result was already reported by Haque et al.3 for a different type of HPMC. It is difficult to obtain trustworthy values below 40 °C, because the network is very weak and breaks at low stress. We observed that the modulus increased with increasing polymer concentration as was already reported in the literature,3,4 but the values were not very reproducible and depended on the temperature history contrary to those of the transient network. The dependence on the history is perhaps most clearly expressed by the hysteresis between heating and subsequent cooling, but it was manifest also when the heating rate was varied or when the system was heated in steps with different durations. In addition, when the temperature was fixed after a rapid increase from 5 °C, G′ continued to increase with time for a period of at least one day, which is illustrated for the case of 50 °C in Figure 9. The nonreproducibility and the dependence on the temperature history imply that the permanent network is not at thermodynamic equilibrium. Structure of the Transient and Permanent Networks. Transient Network. The structure of the transient network was investigated by light scattering up to 2 wt %. Figure 10 shows the concentration dependence of the apparent molar mass (Ma) and radius of gyration of the polymers (Rg). In dilute solutions Ma and Rg correspond to the weight average molar mass and
Figure 8. Concentration dependence of the elastic modulus (circles) and the relaxation time (squares) for HPMC solutions at 5 °C. The solid lines represent linear least-squares fits.
that whatever the solvent quality the observed concentration dependences of G′ and τ are incompatible with that of entangled polymer solutions. A linear increase of Gel can be explained if the HPMC chains have a fixed number of binding sites that can form transient cross-links with other chains. Assuming rubber elasticity, we can estimate the average molar mass between binding sites as Mc = CRT/Gel, which gives roughly 8 × 104 g/mol. Here we considered that all polymers contained the same amount of binding sites. Comparison with the weight average molar mass determined by light scattering, see below, shows that there are on average about four binding sites per chain. The relaxation time increased more strongly than expected for entangled polymer chains. It is clearly not solely determined by the average lifetime of a single bond in which case it would be independent of the concentration. We suggest that relaxation of the chains involves diffusion of the segments while continuously breaking and reforming transient bonds. The probability of reforming a bond during relaxation of the chains increases with the concentration and hence slows it down. A scaling theory for the relaxation of polymers containing a limited number of sites that can form transient cross-links was developed by Rubinstein and Semenov.14 It predicts a linear increase of G′ with the concentration and a power law increase of the terminal relaxation time (τ ∝ C3) close to that observed here for HPMC. Permanent Network. The temperature and concentration dependence of the elastic modulus of the permanent network
Figure 9. Evolution of the storage shear modulus at ω = 0.01 rad/s with waiting time after rapidly heating a HPMC solution at C = 1 wt % from 5 to 50 °C. 315
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Figure 10. Concentration dependence of the apparent molar mass (a) and radius of gyration (b) for HPMC solutions at 20 °C. The concentration dependence of the apparent hydrodynamic radius is compared to Rg in (b).
the z-average radius of gyration: Mw = 4 × 105 g/mol and Rg = 70 nm. Using these values we may estimate the overlap concentration as (C* = 3Mw/Na4πR3g) = 0.05 wt %. With dynamic light scattering a fast diffusional relaxation mode was observed due to cooperative diffusion of the polymers from which the apparent hydrodynamic radius (Rha) was derived as explained in the Materials and Methods sections. The values of Rha were systematically smaller than Rg, see Figure 10, which can in part be explained by the fact that they represent different averages. In dilute solutions we find Rha = 40 nm. Using this value in the calculation of C* gives C* = 0.25 wt %. With increasing concentration Ma, Rg, and Rha decrease as expected for a solution of linear polymers with repulsive excluded volume interactions. In the semidilute regime, that is, for C > C*, Rg and Rha represent the static and dynamic correlation lengths of the system, respectively. The correlation length of the transient network that is formed above about 0.3 wt % is smaller than 40 nm. The temperature dependence of Ma, Rg, and Rha was determined at three concentrations. At 0.5 and 1.0 wt %, Ma increased weakly at lower temperatures followed by a sharp upturn when the critical temperature of 56 °C was approached, see Figure 11. At 56 °C, the scattering intensity increased dramatically, but the solutions were still transparent. At this temperature we found I ∝ q−4 over the whole q-range, implying that a few very large homogeneous particles were formed. This
was confirmed by the appearance of a slow relaxation mode in autocorrelation functions caused by the diffusion of these particles. At 57 °C, the system became highly turbid, which rendered standard light scattering experiments no longer possible. Notice that 57 °C is the temperature where the viscosity of the transient network starts to decrease sharply, see Figures 4 and 5. At C = 0.1 wt %, Ma remained almost independent of the temperature until at 57 °C again large dense particles were formed. This solution became turbid at 58 °C. The sharp increase of the intensity at a critical temperature was earlier reported for dilute HPMC solutions by Bodvik et al.1 The variations of Rg and Rha with temperature corresponded to that of Ma. The initial increase of Ma with increasing temperature at the two higher concentrations can be explained by a reduction of the average repulsive interactions between the polymers. We speculate that with increasing temperature attractive hydrophobic interactions increasingly counteract the repulsive excluded volume interactions. This effect becomes strong close to 57 °C and leads to the formation of large relatively dense HPMC domains at higher temperatures. The amount of these domains is still very small at 57 °C, but rapidly increases with increasing temperature. They can be seen by optical microscopy and their formation has been attributed to micro phase separation.2 We note that the intensity was stable and reproducible up to 57 °C. We may conclude that increasing the temperature reduces the effective solvent quality until it leads to microphase separation at 57 °C that is inhibited to develop into macroscopic phase separation by the presence of the permanent network. Permanent Network. Unexpectedly, we did not find any effect of the formation of the permanent network using static or dynamic light scattering. At all temperatures investigated by light scattering the system was ergodic and the autocorrelation functions fully relaxed. The relaxation time remained q2dependent and was characterized by a single translation diffusion mode with a corresponding Rha that remained proportional to Rg. The implication is that the light scattered by the permanent network was negligible compared to that scattered by the transient network. To obtain further information on the structure of the permanent network we measured the diffusion of spherical probe particles in the system with DLS. Remarkably, we found that particles with a diameter as large as 1 μm diffused freely in the solutions at all temperatures where measurements could be
Figure 11. Temperature dependence of the apparent molar mass at three HPMC concentrations. 316
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done (up to 56 °C). Knowing the size of the particles, the effective viscosity felt by the particles could be determined using eq 5 and was found to be close to that of the transient network, see Figure 12. There is a small systematic difference
Figure 13. Schematic drawing of the interpenetrating network formed by aqueous solutions of HPMC for T < Tc: cross-linked flexible chains (blue) form a transient network with small pores and permanently cross-linked rigid fibrils form a permanent network with large pores.
Figure 12. Comparison of the viscosity of the transient network formed by 1 wt % HPMC at different temperatures deduced from particle tracking or from oscillatory shear experiments. The filled circle was obtained after heating 30 min at 80 °C and subsequent cooling to 50 °C.
temperature especially close to a critical temperature (56 °C) where microphase separation occurs. Above the critical temperature, phase separation leads to the collapse of the transient network. A permanent network is formed that is very weak at low temperatures, but the stiffness increases with increasing temperature. The elastic modulus of this network increases slowly with time after elevation of the temperature and is history dependent. Spherical particles with radii as large as 1 μm diffuse freely through the permanent network, but feel the friction of the transient network. The pores of the permanent network are thus larger than 1 μm and are interpenetrated by the transient network. Possibly the permanent network is formed by connected long fibrillar aggregates involving a small fraction of HPMC chains. The structure of the permanent network is not influenced by phase separation but its presence inhibits coarsening.
that we attribute to the different methods that were used. Interestingly, the effective viscosity was smaller at 50 °C when the solution was cooled after heating at 80 °C than when heated from 5 °C, while the elastic modulus of the permanent network was much higher. A possible explanation is that a larger fraction of the HPMC chains was involved in the permanent network at 50 °C after cooling so that the concentration of HPMC chains forming the transient network was lower, resulting in a lower viscosity of the transient network. The implication of this finding is that the pores of the permanent network are significantly larger than 1 μm. Bodvik et al.1 observed in transmission electron microscopy long fibrillar aggregates of HPMC. We speculate that a permanent network with large pores is formed by permanent cross-linking of fibrils. The fraction of polymers involved in the formation of the fibrils is small at least below Tc and the large majority forms the transient network that fills the pores of the permanent network, see Figure 13. The structure of the permanent network is not modified by the phase separation above 56 °C that drives the collapse of the transient network .
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work has been funded by the Agence Nationale de la Recherche in the framework ANR-11-BSV5-0022.
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CONCLUSION HPMC chains contain a limited amount of sites that allow them to bind to each other via transient cross-links. This leads to the formation of a transient network for C > 0.3 wt % with a modulus that increases linearly with the concentration. The terminal relaxation time of this network increases as C2.5, which we suggest is due to repeated breaking and formation of transient bonds during relaxation of the chains. The correlation length of the transient network is less than 40 nm and decreases with increasing concentration. The elastic modulus of the transient network does not depend on the temperature, but the relaxation time decreases weakly with increasing temperature leading to a slightly stronger relative decrease of the viscosity than that of water. The correlation length of the network increases with increasing
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