Thermodynamics of Aqueous Methylcellulose Solutions

Article pubs.acs.org/Macromolecules

Thermodynamics of Aqueous Methylcellulose Solutions John W. McAllister,† Peter W. Schmidt,‡ Kevin D. Dorfman,‡ Timothy P. Lodge,*,†,‡ and Frank S. Bates*,‡ †

Department of Chemistry and ‡Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States S Supporting Information *

ABSTRACT: The weight-average molecular weight Mw, z-average radius of gyration Rg, and second virial coefficient A2 have been determined between 15 and 52 °C for dilute aqueous solutions of methylcellulose (MC) with three different molecular weights and constant degree of substitution (DS) of 1.8 using static light scattering. These measurements, conducted within 1 h of heating the homogeneous solutions from 5 °C, reveal that the theta temperature for MC in water is Tθ = 48 ± 2 °C, with A2 < 0 for T > Tθ, indicative of lower critical solution temperature (LCST) behavior. However, after annealing a solution for 2 days at 40 °C evidence of high molecular weight aggregates appears through massive increases in the apparent Mw and Rg, a process that continues to evolve for at least 12 days. Cryogenic transmission electron microscopy images obtained from a solution aged for 3 weeks at 40 °C reveal the presence of micron size fibrils with a diameter of 16 ± 4 nm, structurally analogous to the fibrils that form upon gelation of aqueous MC solutions at higher concentrations and elevated temperatures. Growth of fibrils from a solution characterized by a positive A2 indicates that semiflexible MC dissolved in water is metastable at T < Tθ, even though the solvent quality is apparently good. The minimum temperature required for MC solutions to aggregate is estimated to be 30 °C, based on the rate-independent gel-to-solution transition determined by small-amplitude oscillatory shear measurements conducted while cooling 0.5 and 5.0 wt % solutions. These results cannot be explained based solely on separation into two isotropic phases upon heating using classical Flory−Huggins solution theory. We speculate that the underlying equilibrium phase behavior of aqueous MC solutions involves a nematic order parameter.

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thermodynamic properties that govern these semiflexible30,31 macromolecules in water as a function of temperature. MC is a partially derivatized cellulose, in which some of the hydroxy groups at the 2-, 3-, and 6-positions of the anhydroglucose (AGU) repeat units have been heterogeneously substituted with methoxy groups (Figure 1). When the average degree of substitution (DS, with units of [mol MeO] [mol AGU]−1) is between about 1.6 and 2.1, CEs are usually watersoluble at low temperature. Gelation at elevated temperatures is accompanied by an increase in optical turbidity, and many have attributed this behavior to liquid−liquid phase separation.14,20−29,32−34 Some have further suggested that the gel structure is a result of viscoelastic phase separation.21,22,26,27,32 Kato et al.35 reported the theta temperature (Tθ) for MC solutions with DS = 1.2 to be 47 °C using osmotic pressure measurements, and since many MC solutions undergo a sol− gel transition above the reported Tθ, the notion that gelation is linked to phase separation seems plausible. A few reports have attempted to map the behavior of MC in water onto a temperature−composition phase diagram14,21,36 with varying degrees of success, yet we are not aware of experimental

INTRODUCTION Water-soluble polymers exhibit a wide range of aqueous solution properties. Poly(ethylene oxide),1−4 poly(N-acrylamides),5−8 poly(vinyl alcohols),9,10 and poly(ethylene oxide− poly(propylene oxide) block polymers11,12 have well-reported and experimentally accessible lower critical solution temperatures (LCSTs), which may occur in conjunction with a sol−gel transition.13,14 Many aqueous solutions of modified polysaccharides (especially cellulose ethers, CEs) have a reported LCST as well, although these systems are often less well characterized than synthetic polymers, despite academic and industrial interest in these materials for many pharmaceutical, cosmetic, and food applications.15−17 Methylcellulose (MC) is among the simplest substituted derivatives of cellulose, with a structure depicted in Figure 1. Aqueous MC solutions gel upon heating, and this behavior has been investigated for decades.18,19 Gelation has been associated with LCST phase behavior by analogy with the aforementioned synthetic polymers.14,20−27 However, our recent studies on the structure and properties of aqueous MC solutions14,28,29 show that the fibrillar morphology and associated viscoelastic response of these solutions are fundamentally different than those characteristic of other polymeric hydrogels. The work presented here addresses the phase behavior of homogeneous dilute solutions of MC, providing further insight into the © XXXX American Chemical Society

Received: July 12, 2015 Revised: September 8, 2015

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DOI: 10.1021/acs.macromol.5b01544 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Structure of MC, with all possible substitution patterns of an anhydroglucose repeat unit. Commercially available MC is prepared via heterogeneous substitution, and a material with a DS = 1.8 will contain all of these repeat units.

evidence that conclusively establishes coexistence (binodal) and stability (spinodal) curves for this system, the hallmarks of equilibrium liquid−liquid two-phase behavior. Recently, we reported that the morphology of aqueous MC gels is dominated by networks of nanostructured fibrils, a result established using a combination of cryogenic transmission electron microscopy (cryo-TEM) and small-angle neutron scattering (SANS).28,29 Electron micrographs of MC films vitrified to cryogenic temperatures from 65 °C show fibrils with a uniform diameter of 15 ± 2 nm for a range of molecular weights and concentrations. Small-angle neutron scattering (SANS) data obtained from macroscopic solutions with the same molecular weights and over a wider range of concentrations than is accessible by cryo-TEM at conditions above the gelation temperature yield a fibril diameter of 14 ± 1 nm based on fitting to a flexible cylinder model. This fascinating structure can lead to a host of new materials but

necessitates development of characterization techniques designed specifically for this morphology.37−41 This report focuses on the dilute solution behavior (i.e., concentrations less than the overlap concentration c*) of the same three MC materials investigated previously. Static light scattering (SLS) measurements obtained between 15 and 52 °C, after heating from 5 °C, reveal Tθ = 48 ± 2 °C and A2 < 0 for T > Tθ, consistent with LCST behavior. However, when aged for more than a day at 40 °C, the initially homogeneous solution develops fibrillar aggregates, essentially identical in structure to those reported earlier in the gel state, evidenced both by large increases in the apparent molecular weight and radius of gyration as determined by static light scattering (SLS) and through cryo-TEM imaging. This discovery sheds new light on the thermodynamic properties of the homogeneous solution state that exists at low temperatures, and makes a fundamental B


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Figure 2. Rheological temperature cycles of MC solutions of different concentration (a) and M (b) at a heating and cooling rate of 1 °C min−1, 5% strain, and 1 rad s−1. T(G′ = G″) on cooling is denoted by a yellow star, which is an estimation of the temperature at which MC gels revert to an entangled solution. additional 10 min, and then allowed to fully hydrate at 5 °C for at least 12 h. Prior to measurement, samples were degassed and filtered with a 0.2 μm syringe filter. Small-amplitude oscillatory shear measurements of aqueous MC solutions were carried out on a TA Instruments AR-G2 rheometer fitted with concentric cylinders (stator i.d. 15 mm, 1 mm gap, immersed height 42 mm) and a Peltier temperature control unit. To inhibit solvent evaporation, a thin layer of silicon oil (Aldrich, density 0.963 g/mL, boiling point >140 °C) was floated over the top of the solution. The storage (G′) and loss (G″) moduli were measured as functions of temperature at a heating or cooling rate of 1 °C/min in strain-control mode with a strain amplitude of 5% and a frequency of 1 rad/s. Light scattering measurements were performed using a Brookhaven BI-200SM light scattering instrument with a 637 nm laser operating at 10 mW and an avalanche photodiode detector with a 1 mm pinhole. Scattering intensity was monitored between angles of 15° and 150° corresponding to a q range of 3.5 × 10−4 to 2.5 × 10−3 Å−1. The Rayleigh ratio (Rθ) of the sample was calibrated using an ultrapure (≥99.9%) toluene standard, with R(90°) = 8.50 × 10−6 cm−1 at 25 °C.50 Measured solution concentrations were between 0.2 and 0.6 mg mL−1, below the chain overlap concentrations (c*) reported previously.14 For each temperature, fresh aliquots of MC solutions were removed from the refrigerator at 5 °C and annealed at the desired test temperature for 1 h prior to the measurement. Cryo-TEM images were obtained from a filtered (0.45 μm syringe filter) 0.2 wt % MC300 solution after annealing at 40 °C for 3 weeks. Small droplets (ca. 10 μL) of the solution were deposited onto 200 mesh carbon-coated lacey Formvar TEM grids (NetMesh, Ted Pella) inside an FEI Vitrobot device with the blotting environment set to 40 °C and 100% relative humidity. The samples were blotted for 1 s with an offset of −1 mm and allowed to equilibrate for 1 s and then plunged into liquid ethane at its freezing point of −183 °C. Vitrified grids were stored in liquid nitrogen before being transferred to a Gatan-626 single tilt cryo-transfer holder and held at −196 °C during imaging in an FEI Technai G2 Spirit BioTWIN operating at a 120 kV accelerating voltage. TEM micrographs were recorded with a FEI Eagle CCD camera. Images were collected at a magnification range between 16000× and 25000× with the objective lens underfocused by approximately −20 μm.

connection with the formation of fibrils during gelation upon heating at higher concentrations. Nucleation and growth of fibrils under conditions where A2 > 0, i.e., from a solution of MC in a good solvent, is counter to traditional liquid−liquid phase separation into two isotropic phases. (It should be noted that for certain flexible polymer/ solvent systems the concentration dependence of the interaction parameter χ can lead to phase separation at higher concentrations at temperatures for which the dilute solution A2 > 0.42,43 Also, other systems undergo aggregation or even gelation under similar conditions, such as atactic polystyrene in CS2.44−46 However, in these cases any possible role for welldefined fibrils remains to be established, as far as we are aware.) We speculate that these results indicate that the underlying phase behavior of MC in water must account for the large persistence length of the MC polymer (ca. 8 nm) and the associated tendency for such semiflexible chains to form a nematic state at high concentrations (c ≫ c*) and phase separate into an isotropic phase and a nematic phase at elevated temperatures, as illustrated by mean-field calculations.47−49 We further conjecture that kinetic limitations to the development of a macroscopic nematic phase following heating of homogeneous low concentration (c < 20c*) solutions leads to the formation of the fibrillar structure over the range of temperatures Tsol ≤ T, where Tsol ≈ 30 °C is the gel−sol transition temperature that occurs upon cooling.

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EXPERIMENTAL SECTION

Three methylcellulose materials (trade name METHOCEL) were generously supplied by The Dow Chemical Company, where DS = 1.8. These samples are designated as MC150 (Đ = 3.6), MC300 (Đ = 5.4), and MC530 (Đ = 4.1), with the number denoting the approximate Mw in kg mol−1 consistent with our previous reports,14,28,29 and characterized by 2 wt % solution viscosities at 20 °C of 0.36, 4.3, and 31.5 Pa s, respectively. The indicated dispersities were determined by size exclusion chromatography.14 Aqueous MC solutions were prepared by the method described previously,14 with the following changes to ensure microorganism-free samples. MC was dried in a vacuum oven at 100 mTorr for 12 h at 60 °C, then added to half the required amount of ultrapure water (less than 10 ppb organic and ion content and at least 18 MΩ cm resistivity), and heated to 70 °C. The mixture was stirred for 10 min followed by addition of the remaining ultrapure water at 25 °C, stirred in an ice bath for an

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RESULTS AND ANALYSIS This section is organized as follows: characterization of the gel−sol transition by dynamic mechanical spectroscopy, solution thermodynamics by SLS, and MC aggregation and fibril formation by SLS and cryo-TEM. C


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Macromolecules Gel−Sol Transition. As we reported previously,14 the gelation temperature (Tgel) of MC depends on heating rate, whereas the point at which the gel “melts” back to a viscid solution, referred to as the gel−sol transition temperature (Tsol), is independent of the rate of cooling. These viscoelastic transitions are readily characterized using linear dynamic mechanical spectroscopy (DMS) measurements as shown in Figure 2. Tsol is denoted by yellow stars and estimated by the crossover temperature, T(G′ = G″), for concentrations from 5.0 to 50 mg mL−1 and three molecular weights of MC. As shown in Figure 3, Tsol displays slight concentration dependence and

concentration dependence of the zero-q absolute scattering intensity Rθ. Positive values of A2 indicate a good solvent, in which solvent−polymer interactions are preferred over polymer−polymer interactions. The opposite scenario occurs when A2 is negative: a poor solvent, in which polymer−polymer interactions are favored. The condition A2 = 0 defines the special case, the theta temperature, where polymer−water and polymer−polymer interactions compensate. For many polymer solutions it is helpful to apply corrections to the Zimm analysis as proposed by Berry,55,56 which empirically minimizes contributions of the third virial coefficient by relating it to the second virial coefficient using the parameter α3 = {3A3Mw/(A2Mw)2 − 1}/2 and assuming this value to be small. Since most polymers of modest M have 248 measurable A3, this correction is often appropriate. The Berrymodified Zimm equations (often called Berry equations) are given by eqs 1 and 2 ⎧ ⎫ ⎛ Kc ⎞1/2 R g 2q2 ⎪ 1 ⎪ ⎬ ⎨ + + lim⎜ ⎟ = 1 ... ⎪ c → 0⎝ R θ ⎠ 6 M w1/2 ⎪ ⎭ ⎩

(1)

⎛ Kc ⎞1/2 1 lim ⎜ ⎟ = {1 + A 2 M w c + α3(A 2 M w c)2 + ...} θ → 0⎝ R θ ⎠ M w1/2 (2)

Figure 3. An estimation of the gel−sol transition temperature Tsol obtained from T(G′ = G″) on cooling with 1 °C min−1 cooling rate, 5% strain, and 1 rad s−1. These values are within a degree of the frequency-independent gel point definition, G′(ω) ∼ G″(ω) ∼ ωb. The average value of Tsol is about 30 °C and shows very little molecular weight dependence.

2 2

2

λ0−4NA−1

where K = 4π n (∂n/∂c) is the optical constant; n, ∂n/∂c, λ0, and NA are the solution index of refraction, differential refractive index increment, wavelength of incident light in vacuum, and Avogadro constant, respectively. The differential refractive index increment for MC in water was measured on a Wyatt differential refractometer (OptiLab rEX) and found to be ∂n/∂c = 0.136 ± 0.001 and 0.137 ± 0.002 cm3 g−1 at 25 and 50 °C, respectively, in good agreement with previously reported values.23 Representative Berry-modified Zimm plots for solutions of aqueous MC300 at 40, 47, and 55 °C are shown in Figures 4a, 4b, and 4c, respectively. These results demonstrate that MC exists as independent semiflexible coils in solution for a period of at least 1 h after heating from 5 °C. The slopes of the lines fit to extrapolations to zero angle (black triangles and eq 2) indicates a positive A2 at 40 °C, the theta condition A2 = 0 near 47 °C, and a negative A2 at 55 °C. Results of multiple Berrymodified Zimm plots for three molecular weights and multiple temperatures between 15 and 55 °C are shown in Figure 5. Molecular weights in this temperature range were determined to be equivalent within experimental uncertainty (Figure 5a): Mw = (1.7 ± 0.2) × 105, (2.9 ± 0.4) × 105, and (5.3 ± 0.8) × 105 g mol−1 for MC150, MC300, and MC530, respectively (obtained from the intercept of the double extrapolation to zero concentration and zero angle, eqs 1 and 2). These values are consistent with prior analysis by size exclusion chromatography and intrinsic viscosity.14 Rg values, determined by fits to eq 1 between 15 and 55 °C, change little with temperature (Figure 5b), where Rg = 44.1 ± 0.7, 57.5 ± 1.4, and 70 ± 2 nm for MC150, MC300, and MC530, respectively. A2 is plotted as a function of inverse temperature for these three materials in Figure 6. From these data the “classical” theta temperature is Tθ = 48 ± 2 °C, consistent with osmotic pressure measurements for an MC solution with M = 5.1 × 104 g/mol.35 For T < 48 °C the values indicate that MC solutions exist as semiflexible coils in a good solvent. As the temperature increases above 48 °C, the magnitude of A2 < 0 suggests that

very little Mw dependence. Other reports17,22,34,36 have shown a correlation between changes in viscoelastic response and peaks in differential scanning calorimetry (DSC) curves on heating and cooling, which indicates that the gelation of MC involves a thermodynamic phase transition. That Tsol is independent of cooling rate lends credence to the notion that Tsol is a better representation of the equilibrium thermodynamic transition, compared to Tgel on heating, which is complicated by kinetics of formation of the gel network. As Tgel and Tsol are mechanically defined transitions between a mostly elastic gel and a mostly viscid liquid, the preferred definition is specified by the temperature at which G′(ω) ∼ G″(ω) ∼ ωb and display a frequency-independent convergence in tan(δ), as proposed by Winter and Chambon.51,52 At low frequencies (ω ≤ 1 rad/s), we find that the relaxation exponent b is near 0.5, and thus T(G′ = G″) is within about a degree of Tsol (see Figure S1), validating use of T(G′ = G″) for identifying Tsol at oscillation frequencies ω ≤ 1 rad/s. It is important to note that for any system that develops an elastic network the sol−gel transition should preferably be first characterized by a frequency-independent method, prior to estimations using T(G′ = G″).53 Solution Thermodynamics. Static light scattering (SLS) is often a preferred method to probe dilute polymer−solvent interactions. Using a Zimm analysis,54 the weight-average molecular weight, Mw, and z-average radius of gyration, Rg, can be determined from measurements of the Rayleigh ratio, Rθ, at numerous concentrations and scattering wavevectors. These measurements require the Guinier scattering regime for the sample to be within the q-range of the instrument (qRg ≤ 1). The second virial coefficient A2 can be determined by the D


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Figure 5. (a) Mw and (b) Rg as functions of temperature of MC150, MC300, and MC530. Mw and Rg change very little between 15 and 55 °C, which is indicative that these experiments capture single dissolved semiflexible coils in solution.

Figure 4. Berry-modified Zimm plots of aqueous MC300 with Mw = 2.9 × 105 at 40 °C (a), 47 °C (b), and 55 °C (c). Measured concentrations range from 0.20 to 0.60 mg mL−1.

water rapidly becomes an increasingly poorer solvent. It should be noted that at these concentrations (0.2−0.6 mg mL−1) MC solutions do not turn visibly turbid on the time scale of the measurement, in agreement with our previous turbidity measurements.14 An unusual feature of these results is the very strong temperature dependence of A2 above 48 °C, which could indicate an intramolecular conformational change in MC prior to the growth of fibril aggregates, which has been suggested by optical rotation measurements of MC solutions.57,58 However, a largely invariant Rg (Figure 5b) argues against this interpretation. The assumption made by eqs 1 and 2, that the third virial coefficient A3 can be empirically related to A2, was initially developed for polystyrene (a flexible chain) in organic solvents55 and has been widely accepted as a correction for most polymer solutions. We are not aware of a detailed study on the applicability of the Berry approximation to semiflexible polymers like MC. It is conceivable that the empirical relationship between A2 and A3 is different for semiflexible

Figure 6. Second virial coefficients (A2) for three molecular weights of MC calculated from Berry-modified Zimm plots as a function of inverse temperature. From these data, the theta temperature (Tθ) for MC is 48 ± 2 °C.

polymers in solution, in which case the A2 values obtained here for MC should be interpreted cautiously.59 However, comparative Zimm plots with and without the Berry approximation are provided in Figure S2. Values of A2 using a traditional Zimm plot and the Berry approximation are equivalent within the uncertainty of the measurement for MC. To confirm that A2 < 0 in Figure 6 is not an artifact of nucleation and growth of MC aggregates, a freshly prepared 0.3 mg mL−1 sample of MC300 was heated to 48 °C and scattering data were collected. Then the sample was rapidly quenched (ca. 10 s) to 15 °C, and scattering data were collected again. Figure 7 shows plots of the associated data at 48 and 15 °C in the Guinier format, which yield apparent values for Rg of 52 ± 1 E


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at about 2 × 10−3 Å−1 is a result of high-angle (>120°) backscattering from the micron-sized aggregates. After 12 days, quiescent dilute MC solutions of concentrations 0.2−0.6 mg mL−1 have visibly precipitated aggregates of polymer (Figure 8b). Less than 1% by mass of the original MC concentration (0.3 mg mL−1) remains dissolved in the solution after centrifuging. This result is quite remarkable, since A2 > 0 at 40 °C; hence, MC coils would be expected to remain in solution. Cryo-TEM experiments confirmed the presence of fibrils in a 2.0 mg mL−1 solution of MC300 annealed at 40 °C for 21 days without stirring, as shown in Figure 9. (The lowest concentration at which we could reliably image multiple fibrils within the field of view in the cryo-TEM instrument was 2.0 mg mL−1, c ≈ c*, which is somewhat higher than used in the SLS measurements.) Fibril diameters were determined to be 16 ± 4 nm using image analysis software, in agreement with the previous reports that dealt with more concentrated MC hydrogels.28,29 Solutions containing a dispersion of individual fibrils, such as the one that produced the images in Figure 9, were relatively clear to the unaided eye, suggesting that the aggregates evident in Figure 8b were promoted by stirring. The images in Figure 9, combined with the mass balance provided by centrifugation experiments, confirm that after annealing for long times below Tθ ≈ 48 °C, most of the MC exists in the form of fibrils.

Figure 7. Guinier plots of a 0.30 mg mL−1 MC300 solution heated to 48 °C (red points) and held long enough to collect the data (∼30 min) and the same sample cooled back to 15 °C (blue points). For the time scale of the measurement, MC solutions heated to Tθ for a short time remain as semiflexible coils in solution and do not aggregate.

and 55 ± 1 nm, respectively, consistent within experimental uncertainty with Figure 5b. This result confirms that the Zimm plots in Figures 4 and 5 were collected prior to any significant MC aggregation. MC Aggregation and Fibril Formation. An 0.3 mg mL−1 solution of freshly prepared MC300 was heated from 5 to 40 °C, held at that temperature for 1 h, and then probed by SLS. This temperature was chosen to be intermediate between the theta temperature and the gel dissolution temperature. Figure 8a displays the resulting Rθ vs q data (red points) modeled with

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DISCUSSION The following paragraphs describe phase separation in MC solutions based on an effective interaction parameter χeff extracted from the experimentally measured A2, fitting of Tsol to an equilibrium phase transition based upon semiflexible coils in solution, and concluding with a speculative explanation of MC fibrils in terms of the phase diagram for semiflexible coils. The transition of MC from a fibrillar gel to an entangled solution on cooling (Tsol, see Figure 2) has been widely reported to generate an exothermic maximum in DSC measurements between 30 and 35 °C.17,22,34,36 Conversely, the transition from solution to gel (Tgel) is associated with an endothermic minimum between 60 and 70 °C. Thus, Tsol and Tgel can be interpreted as reflecting hysteresis in a first-order phase transition. In this regard, gelation of MC is analogous to crystallization of fibrils upon heating, and gel dissolution is analogous to melting of fibrils back to semiflexible coils. We propose that Tsol is correlated with the equilibrium transition between dissolved MC coils and phase-separated fibrils, since dissolution of the locally structured material is less encumbered by kinetic factors than fibril formation from the isotropic state, analogous to the rapid melting of a crystal during heating as opposed to slow fusion upon cooling. From the results in Figures 8 and 9, MC solutions begin to aggregate into micron-sized fibrils at temperatures at least as low as 40 °C, notwithstanding A2 > 0. Flory−Huggins theory anticipates that solutions of flexible coils phase separate into a two-phase mixture containing a low concentration solution of (collapsed) globules and an isotropic concentrated mixture when χ > χc > χθ = 1/2, where the volume-fraction critical composition is defined by ϕc ≈ 1/√N for N ≫ 1 (where N is the degree of polymerization). For MC, aggregation occurs while water is still a “good” solvent (i.e., T < Tθ ≈ 48 °C) in fundamental conflict with this concept. Figure S3 shows the binodal and spinodal boundaries calculated using Flory− Huggins theory, which predicts phase separation into low and

Figure 8. (a) Light scattering from a 0.30 mg mL−1 solution of MC300 at 40 °C. At short times (up to a few hours) a Guinier function can approximate the apparent radius of gyration, and a Zimm plot analysis is appropriate. The increase in scattering indicates that MC slowly aggregates over time. The increase in scattering at q ≈ 0.002 Å−1 results from large-angle backscattering. (b) The same solution of MC300 which has annealed for 15 days at 40 °C. Polymer aggregates are clearly visible (the white spot at the bottom of the vial is a stir bar).

Guinier’s law, I(q) ∼ exp(−q2Rg2/3), which gives an apparent Rg = 49 ± 2 nm, i.e., within the range of the previous Rg obtained from the Berry plots (Figure 5b). The sample was then annealed at 40 °C for 12 days (with gentle stirring) while periodically obtaining SLS data. Representative results shown in Figure 8a reveal that the scattering intensity increases dramatically during this time (violet, green, and blue data points). After 2 days at 40 °C, MC has aggregated to the point that the light scattering data lie outside the Guinier regime, which corresponds to features greater than about 1 μm in size. This obviates use of a Zimm analysis since qRg > 1. Scattering intensity increases further with longer times, which we attribute to growth of larger aggregates of MC. The upturn in scattering F


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namics of polymers, and there are several approaches to dealing with its relationship to χeff. One method, employed with and without polar interactions, identifies an effective interaction parameter based on enthalpic and (excess) entropic components: χeff = χh + χs = AT−1 + B, where A and B are systemdependent constants. Hydrogen bonding effects can be incorporated into χh, as done by Matsuyama and Tanaka60 and Dormidontova61 in describing water−poly(ethylene oxide) (PEO) solutions. Since PEO has a simple structure, and predictable hydrogen bonding between solvent and repeat units, this idea works well. MC has a more complicated molecular structure (see Figure 1), including hydrogen bonding donor and acceptor sites that depend on the detailed pattern of methoxyl group substitution along the polymer chain. In addition, MC chains contain intrachain and interchain hydrogen bonding, which further complicates the solution behavior. The results shown in Figure 6 cannot be represented by a simple linear form of χeff(T). Therefore, we take the phenomenological approach of separating contributions to χeff that dominate at low (ca. T < 30 °C) and high (ca. T > 40 °C) temperatures, crudely associated with dispersion and hydrogen bonding interactions, respectively. This empirical technique provides a working relationship for use in estimating phase boundaries based on global models such as Flory−Huggins theory (flexible chains) and the Flory theory for stiff and semiflexible chains.47−49 In the context of Flory−Huggins theory, A2 is related to the interaction parameter χeff by A2 =

2 ⎛1 ⎞ Vp̅ ⎜ − χeff ⎟ 2 ⎝2 ⎠ M 0 Vs̅

(3)

where V̅ s is the solvent molar volume and V̅ p and M0 are the polymer repeat unit molar volume and molecular weight, respectively. For MC with DS = 1.8 and a density of 1.341 g cm−3,62 V̅ s = 18 cm3 mol−1, V̅ p = 139.5 cm3 mol−1, and M0 = 187.4 cm3 mol−1 resulting in χeff as shown in Figure 10. It is

Figure 9. Cryo-TEM micrographs of a thin film of 2.0 mg mL−1 solution of MC300 after annealing for 21 days at 40 °C. The black web is the lacey carbon support grid, and the thread-like structures are MC fibrils. Image analysis of the fibrils gives an average diameter of 16 ± 4 nm. Scale bar denotes 500 nm.

Figure 10. Values of χeff calculated from A2 using eq 3. The curve is a fit of χeff to eq 4. Phenomenologically, χeff has the form AT−1 + B for T < 30 °C and α exp[βT−1] for T > 40 °C.

high concentration isotropic phases, also in conflict with fibril formation. This motivated us to consider alternative explanations for fibril formation, rooted in the semiflexible rather than flexible nature of the MC chains in solution. Estimation of χeff in MC Solutions. Hydrogen bonding plays an important role in the aqueous solution thermody-

important to recognize that eq 3 is based on the osmotic pressure associated with Flory−Huggins lattice theory, which assumes that all lattice sites on the polymer chain are equivalent. Therefore, the measurement of A2, and our estimation of χeff, represent solution averages, rather than the interaction energy of individual lattice sites. The highly G


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Figure 11. (a) Mean-field coexistence curves for semiflexible coils with liquid crystalline elements for different axial ratios as predicted by Flory,47−49 predicting isotropic (I) and nematic (N) phases. (b) Experimentally measured Tsol (on cooling) from Figure 3 (stars) and Tgel (on heating) (circles) from Arvidson et al.14 evaluated using eq 4. The solid and line in (b) correspond to the binodal lines for semiflexible coils for axial ratios of xk = 28.

is in contrast with the results obtained with strictly flexible chains, where separation between dilute and concentrated phases is usually restricted to χ > χθ. We have plotted the gel− sol transition, Tsol, obtained during cooling and sol−gel transition, Tgel, which results from slow heating14 of aqueous MC in Figure 11b, where the measured transition temperatures have been converted to χeff using eq 4 (see Figure 10). The Kuhn length of MC30,31 with DS = 1.8 has been measured to be 16 ± 3 nm with a chain diameter on the order of 0.5 nm, yielding xk ≈ 35. Considering the crude assumptions associated with mapping aqueous MC solutions onto the meanfield isotropic−nematic theory, we do not expect quantitative agreement with experimentally measured transitions. Lateral intrachain hydrogen bonding along the cellulose backbone (especially between C2 and C6 groups on adjacent anhydroglucose units) likely contributes to chain stiffness, and at elevated temperature the breaking of hydrogen bonds may cause a decrease in Sk .60 We associate the gel−sol transition (cooling, Tsol) data with the equilibrium nematic−isotropic binodal curve on the low composition side of the two-phase region; the sol−gel transition (Tgel) obtained on heating reflects the metastable region between the equilibrium and stability limits. In principle, the stability limit for the isotropic phase is governed by Flory−Huggins theory; this molecular weight dependent behavior (illustrated in Figure S3), which leads to dilute and concentrated isotropic phases, applies to flexible coils rather than semiflexible ones. The stability limit of the nematic phase has been considered by Dorgan,63 and his approach may be applicable to extend to the isotropic phase. Nonetheless, the stability of isotropic solutions containing semiflexible polymers is an unresolved issue that lies beyond the scope of this article.64−66 Nematic Order and MC Fibrils. We have extensively characterized the fibrillar structure of MC gels by cryo-TEM, SANS, and nonlinear rheology.28,29,67 Clearly, this fibril morphology does not reflect the microscopically (molecular level) and macroscopically homogeneous state associated with the nematic phase predicted by the Flory theory. Unfortunately, we have not yet established the exact molecular structure of the

nonlinear form of the results plotted in Figure 10 obviates use of χeff = AT−1 + B. We have adopted a four-constant model given by eq 4 to fit the highly nonlinear results shown in Figure 10. ⎡ −β ⎤ A χeff ≈ α exp⎢ + +B ⎣ T ⎥⎦ T

(4)

The form of this equation includes an exponential term to account for hydrogen bonding and all other intermolecular interactions not included in χh and χs. As with other polymers characterized by an LCST, the fit of χeff to eq 4 yields A < 0 and B > 0 (the fitting parameters used to fit χeff to eq 4 can be found in Figure S2). While this method is an oversimplification of all the intermolecular interactions in an aqueous MC solution, the fit to eq 4 is good and can serve as a crude estimation for understanding the thermodynamics of MC in water. Liquid Crystallinity and Semiflexible Polymers. Flory has described the phase behavior of stiff rod-like chains that form nematic liquid crystals in solution47−49 based on a onedimensional orientational (nematic) order parameter. In the athermal limit (χ = 0) separation into isotropic (I) and nematic (N) phases is controlled by the ratio of the rod length (S ) to diameter (d) defined as the axial ratio, x = S /d. Finite repulsive rod−solvent interactions (χ > 0) broaden the two-phase window with increasing χ, as illustrated in Figure 11a for x = 20, 35, and 50. Flory suggested that such nematic−isotropic phase behavior can be extended to semiflexible polymers in solution by substituting the Kuhn length, Sk , for S , xk = Sk /d, where d represents the effective chain diameter. With this assumption, Figure 11a helps rationalize why phase separation can occur with semiflexible polymer solutions even when χ < 1/2. Increasing chain stiffness (Sk ) simultaneously shifts the isotropic solution (I) boundary of the two-phase window to lower polymer volume fraction (ϕ) and smaller values of χ, illustrated with Figure 11a. This brings the equilibrium limit for the single phase solution behavior at low concentrations below the theta condition associated with flexible coils (χθ = 1/2), driven by the requirement of equal component chemical potential between nematic and isotropic phases. This behavior H


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Macromolecules

40 °C leads to the slow nucleation of relatively few fibrils that subsequently grow to high aspect ratio over relatively long time. Heating to a higher temperature increases both the nucleation and growth rates. At higher concentrations (c > c*) the rates of nucleation and growth both increase, leading to many fibrils that can link together through the simultaneous incorporation of individual high molecular weight polymers into two fibrils, thereby forming a branch point. As the stability limit is approached during rapid heating the homogeneous solution will become unstable resulting in spontaneous gelation, with a rapid rise in modulus (see Figure 2). Upon cooling, dissolution of the fibrils occurs when the binodal curve is crossed. Of course, the actual location of the binodal, relative to the predicted location of the two-phase boundary based on the Flory theory, will be influenced by the nonequilibrium fibril morphology, including the detailed homogeneity of the cylindrical structure and the presence of defects such as branches.

fibrils, although we have shown that these objects are remarkably uniform in diameter and contain about 60% water.29 We believe the most plausible explanation involves a toroid-like, helical molecular configuration, similar to the structures simulated by Kong et al.68 for certain short semiflexible chains that undergo a coil-to-toroid transition in response to a reduction in temperature. These authors show that certain combinations of Kuhn length and intrachain attractive interactions shift the familiar coil−globular collapse transition that characterizes flexible polymers to one that produces hollow cylinders. We hypothesize that the MC fibrils consist of interlinked collapsed toroids (see Figure 12), formed

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CONCLUSIONS We propose that the gel−sol transition on cooling (Tsol) of aqueous MC solutions is associated with an equilibrium (binodal) phase transition. DMS measurements on three molecular weights of MC show that Tsol is independent of molecular weight and cooling rate, with a slight dependence on concentration. This contrasts with the sol−gel transition on heating (Tgel), which exhibits a strong dependence on heating rate and concentration but no dependence on molecular weight. SLS measurements conducted with dilute solutions (c < c*) of three molecular weights of MC gave Mw, Rg, and A2 over a range of temperatures between 15 and 55 °C. We find that Tθ ≈ 48 °C. Time-resolved SLS indicates that slow (ca. 2 days) aggregation occurs in dilute solutions at 40 °C when A2 > 0, which means that MC does not phase separate by an isotropic− isotropic transition predicted by Flory−Huggins theory. CryoTEM images obtained from MC solutions with c ≈ c* held at 40 °C for 21 days conclusively demonstrate that most of the polymer has formed high aspect ratio fibrils, with a diameter of 16 ± 3 nm, indicative of slow nucleation and growth. We postulate that the equilibrium solution behavior of semiflexible MC coils in water is governed by a nematic order parameter, represented by the 1956 lattice theory developed by Flory, which describes the coexistence of isotropic and nematic phases. We further propose that MC fibrils reflect a kinetically trapped state that represents a compromise between equilibrium macroscopic ordering and a state of local orientational order reflected in a toroidal molecular configuration, where the fibril diameter is governed by the persistence length of the MC chains. In the dilute limit a coil-to-collapsed toroid transition leads to isolated high aspect ratio fibrils.

Figure 12. Schematic representation of the structure of MC fibrils. The fibrils consist of collapsed cylindrical and/or toroidal chains (predicted by Kong et al.68) assembled axially into fibrils so as to achieve a degree of nematic ordering. The portion of the fibril in red approximates a single MC chain with N ≈ 800, corresponding to the MC150 sample.

by winding chains onto the end of an existing fibril, beginning with a primary single or multichain toroidal nucleus, through a secondary nucleation and growth process. Interestingly, there are numerous examples of related fibril growth with semiflexible biomolecules such as neurofilaments,69 self-assembled βhairpins,70 bile analogues,71 and fibrin protofibrils,72 although in these cases the process is often facilitated by a broken chiral symmetry along the molecular axis. Note that it appears unlikely that individual MC chains bundle into fibrils with the chain axes parallel to the fibril axis because this provides no mechanism for the fibril diameter to be so well-defined. We propose that the overarching isotropic−nematic phase diagram drives the aggregation of MC into fibrils. Because MC chains in solution are long (for this study, the degree of polymerization of MC150 is about 800) macroscopic phase separation is thwarted by slow nucleation compounded by limited chain diffusion. We speculate that the fibrillar structure of MC is a kinetically facile metastable structure in which the chains gain local orientational order, likely reinforced by favorable hydrophobic interactions between substituted methoxyl groups (and perhaps Maier−Saupe type interactions)73−75 at the Kuhn length scale by forming a compact toroidal morphology. Significantly, the diameter of the fibrils (ca. 15 nm) is essentially the Kuhn length of MC, Sk = 16 nm. These arguments help rationalize the results reported here and in previous publications dealing with MC gelation. Heating a dilute (c ≪ c*) solution of MC to the metastable condition at

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01544. Rheological signatures of gel melting on cooling, comparison of Zimm and Berry plots, temperaturedependent interaction parameter, phase diagram on the basis of Flory−Huggins theory (PDF) I


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Macromolecules

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (F.S.B.). *E-mail: [email protected] (T.P.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by a business unit (Dow Pharma and Food Solutions) of The Dow Chemical Company and in part by the National Science Foundation through the University of Minnesota MRSEC under Award DMR-1420013. Extensive discussions with Robert Sammler, Robert Schmitt, Meinolf Brackhagen, Tirtha Chatterjee, and Valeriy Ginzburg were very helpful. We acknowledge Dr. David Giles for assistance with rheological measurements. Parts of this work were carried out in the CSE Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program. We appreciate the helpful comments by a reviewer.

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