Grafting Density on Methylcellulose Fibril Formation

Oct 30, 2018 - Effect of Poly(ethylene glycol) Grafting Density on Methylcellulose. Fibril Formation. Svetlana Morozova,. ‡. Peter W. Schmidt,. †...
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Effect of Poly(ethylene glycol) Grafting Density on Methylcellulose Fibril Formation Svetlana Morozova,‡ Peter W. Schmidt,† Frank S. Bates,† and Timothy P. Lodge*,†,‡ †

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

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S Supporting Information *

ABSTRACT: We investigate the effect of short-chain poly(ethylene glycol) (PEG) graft density on the formation of methylcellulose (MC) fibrils at elevated temperatures. Thiol−ene click chemistry was used to systematically graft 800 and 2000 g/mol PEG onto the backbone of allylated MC, with a wide range of grafting densities from 0.7% to 33%. As determined from light scattering, grafting leads to an increase in the persistence length of this semiflexible copolymer, by as much as a factor of 10. Upon heating, SAXS and AFM studies show that fibril formation is suppressed at around 10% grafting density for shorter PEG grafts, corresponding to persistence lengths about ∼22 nm. For longer grafts fibril formation is suppressed at 7% grafting density, at around the same ∼22 nm persistence length. The radius of the fibrils increases with the square root of the persistence length of the chains, which is consistent with a theory for the radius of twisted chains. The ability to form networks at 80 °C is highly correlated to the ability to form fibrils, and accordingly the modulus systematically decreases with grafting density. When the fibril formation is suppressed, MC solutions no longer form solid networks. Therefore, grafting modulates the molecular architecture and gelation properties of MC and also provides new insight into the structure of MC fibrils.

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er,11,12,19 folded into ribbon-like sheets, or twisted into helical assemblies.10 The principal question is: why do finite structures form with a remarkably uniform diameter and with a length that has a dependence on the chain contour length?10 If MC were to simply undergo liquid−liquid phase separation, there is no obvious benefit (either thermodynamic or kinetic) to fibril formation. Of the various possibilities, the hypothesis that MC chains twist together into helical assemblies is gaining favor. It has been shown that stiff chains in poor solvents will arrange in this way because there is a competition between surface energy that favors bulk phase separation and the chain persistence length that results in an elastic penalty and limits the lateral size scale.20−22 Organization into fibrils is not unique to MC and is found in many biological systems. Collagen proteins,23,24 amyloid proteins,25,26 actin filaments,27 and cellulose crystals28 all twist together into finite diameter bundles. It has been shown that for assembling semiflexible chains or filaments the finite diameter of the resulting bundles is set by elastic stresses. As these polymers aggregate, surface energies favor bulk separation, but the size scale is limited by flexibility or how much each chain is willing to bend in the bundle.20−22 Ultimately, at the onset of aggregation the bundle radius is related to the persistence length of individual chains and their axial separation. On the basis of related numerical calculations,

INTRODUCTION Methylcellulose (MC) is a fundamentally interesting commercial material. It is derived from cellulose in a process that substitutes a fraction of the hydroxyl groups on each repeat unit with methoxy groups.1−3 This disrupts the inter- and intramolecular hydrogen bonding, such that MC is soluble in water at low temperatures. The process also adds hydrophobicity to the backbone, which leads to an intriguing phenomenon. With increased temperature MC assembles into fibrils that are micrometers in length and ∼15 nm in diameter.4−7 Fibril formation is concurrent with gelation of aqueous MC solutions.8 Interestingly, the diameter of the fibrils is effectively independent of the temperature of formation, MC concentration, and MC molecular weight but does change if MC is further substituted with hydroxypropyl groups.4,5,9,10 For shorter MC chains, in particular, the length of the fibrils has a strong correlation with the contour length of the assembling MC chains.10 The detailed mechanism of assembly is unknown, but the uniformity of the fibril diameter is hypothesized to be correlated to the inherent stiffness of MC chains, characterized by the persistence length (∼6−13 nm).11−18 A systematic increase in the persistence length, such as by grafting of side chains, could potentially lead to a deeper understanding of the assembly process. A complete picture of how MC organizes into fibrils has proven elusive. Since the recent discovery that MC assembles into fibrils, there have been different suggestions for the mechanism. The chains could be extended and stacked lengthwise,17 folded into toroidal loops that stack togeth© XXXX American Chemical Society

Received: September 3, 2018 Revised: October 30, 2018

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DOI: 10.1021/acs.macromol.8b01899 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Controlled thiol−ene grafting. During step one MC is dissolved in aqueous 1 M NaOH at room temperature with allyl bromide. Percent allylation is controlled by the molar ratio of MC monomers to allyl bromide. During the second step, allylated MC is dissolved in water with excess thiol-terminated PEG with a UV-active curing agent and exposed to UV light for 1 h.

it has been predicted that sufficiently long and flexible chains generally favor a twisted geometry.21 Recently we disclosed a method to systematically change the stiffness of MC chains by grafting small molecular weight poly(ethylene glycol) (PEG) chains randomly along the backbone.29 When the grafting density of PEG-800 is changed from 0.7% to 33%, the MC persistence length (lp) increased by as much as a factor of 4. This effect is expected to be even stronger for higher molecular weight grafts. The finding fits well in the context of recent research on chain dimensions as a function of grafting density and graft length.30−33 In the low grafting density, “loose-comb” regime, lp increases without affecting the overall conformation of the molecule. This result provides a systematic way to probe MC fibril structure as a function of MC chain stiffness and overall polymer−polymer interactions and solution. Here, lp of 150 and 300 kg/mol MC is modified by grafting PEG-800 and PEG-2000 over a range of grafting densities from 0.7% to 37% to investigate the effect of chain stiffness and PEG grafts on MC fibril formation. The resulting fibril structure and its consequences on gelation are characterized by AFM, SAXS, and rheology as a function of PEG grafting density and length. The fiber radius is correlated to the chain dimensions and lp. Beyond a certain percent grafting density, which corresponds to a lp ∼ 22 nm, fibril formation is no longer observed. At this grafting density, gelation is also suppressed. These findings present the first systematic investigation of how chain flexibility and interactions impact MC assembly and present a direct correlation between gel strength and fibril formation. Furthermore, the results support the twisted bundle hypothesis of MC fibrils.

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exposed to UV (295−360 nm) for 1 h. Unreacted compounds were then removed by dialysis using 4−6 kg/mol molecular weight cutoff dialysis tubing, and the resulting MC-g-PEG was recovered by freezedrying. Grafting densities were determined by subsequent 1H NMR spectroscopic analysis (Supporting Information). The grafting density, σ, is defined as the number of PEG branches per repeat unit of MC, as quantified by NMR and static light scattering (Supporting Information). AFM. To prepare AFM samples, 0.003 wt % MC and MC-g-PEG solutions were heated to 80 °C at ∼1 °C/min and kept at 80 °C for 15 min. On the same hot plate, freshly cleaved 10 mm mica disks (Ted Pella Highest Grade V1 AFM Mica Discs) were heated to 80 °C. 20 μL of the hot MC-g-PEG solution was then deposited on the mica slides using a micropipet, and the excess droplet was pipetted off. The mica slide was then left to dry at 80 °C for at least 20 min and then subsequently cooled slowly down to room temperature. AFM images were acquired on a Bruker Nanoscope V Multimode 8 scanning probe microscope (SPM). Peak force quantitative nanomechanical property mapping (QNM) was used to acquire height images with a Cantilever C on HQ:NSC35 series chip (MIRKOMASCH USA). This cantilever is 130 μm in length, 32.5 μm wide, and 1 μm thick, with a force constant of 0.6 N/m and a resonance frequency of 65 Hz. The typical radius of the n-type silicon tip is 8 nm with a full tip cone angle of 40°. The resulting images were analyzed using Gwyddion software. Light Scattering. The radius of gyration and persistence length of grafted MC were investigated with static light scattering (SLS). Results for PEG-800 grafted MC were reported previously.29 The results for PEG-2000 grafted MC are reported in the Supporting Information. To quantify the coil dimensions in solution as a function of grafting density, SLS measurements were taken on a Brookhaven BI-200SM instrument with a 5 mW laser for q = 2πn0/λ sin(θ/2) of (6.79−22.7) × 106 m−1 (θ = 30°−120°). Here, n0 is the water refractive index (1.333) and λ is the laser vacuum wavelength (637 nm). The samples were filtered through an 0.45 μm filter before analysis. The refractive index increment in water dn/dc = 0.136 mL/g for MC and 0.132 mL/g for PEG.19,35 For the grafted polymers, dn/ dc was calculated from the relative volume fractions of the backbone and graft. Zimm plots were constructed for each graft density, and radius of gyration Rg, weight-averaged molecular weight Mw, and second virial coefficient A2 were determined (Supporting Information). Small-Angle X-ray Scattering (SAXS). SAXS experiments were conducted at the DND-CAT, Sector 5-ID-D of the Advanced Photon Source at Argonne National Laboratory. Samples were prepared by loading 1 wt % solutions into 1.5 mm diameter quartz capillaries, which were subsequently sealed with epoxy and placed into a custom fabricated eight-capillary heating stage. Each set of eight samples was heated stepwise by 10 °C for 10 min to approximate a 1 °C/min temperature ramp. 2D scattering patterns were collected during 1 s exposures to 0.0729 nm wavelength X-rays on a Rayonix MX170-HS CCD detector at a sample-to-detector distance of 8.5 m. The detector readout was binned to 4 by 4 pixels to decrease the detector readout noise. The 2D SAXS data were integrated azimuthally, yielding 1D scattering patterns as intensity versus the scattering wave vector q. At

EXPERIMENTAL SECTION

Materials and Methods. Methylcellulose (Mw ≈ 150 kg/mol, Đ ≈ 3.6, degree of methyl substitution, DS = 1.8, and Mw ≈ 300 kg/mol, Đ ≈ 5.4, degree of methyl substitution, DS = 1.8) was graciously provided by the Dow Chemical Company. All other reagents (allyl bromide, IRGACURE D-2959, thiol-terminated poly(ethylene glycol) methyl ether (Mw = 800 and 2000 g/mol, Đ < 1.1) were purchased from Sigma-Aldrich and used without further purification. MC and MC-g-PEG solutions were prepared by directly dissolving freeze-dried polymer in water. (This procedure differs slightly from previous MC solution preparations since freeze-dried MC is no longer a powder.34) Chemical Modification. The detailed grafting procedure may be found in a previous publication.29 Briefly, the modification was performed in two steps as outlined in Figure 1. In the first step, MC was dissolved in 1 M NaOH with allyl bromide for 24 h at room temperature. The percent allylation was controlled by changing the monomer:allyl bromide molar ratio. After 24 h, the product was neutralized with 1 M HCl and precipitated with acetone. In the second step, allylated MC was dissolved in water with 3 times molar excess of thiol-terminated PEG and 5 mol % IRGACURE D-2959 and B

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Figure 2. High-magnification AFM images of ungrafted MC fibrils formed at 80 °C from (a) 150 kg/mol MC (MC150) and (b) 300 kg/mol MC (MC300) following drying. The typical height profiles along the long axis of fibrils show clear variations in height (±2−3 nm) on the order of ∼30 nm along the axis both for (c) 150 kg/mol MC and for (d) 300 kg/mol MC.

Figure 3. AFM height profile images of MC-g-PEG800 and MC-g-PEG2000 structures at 80 °C and 0.003 wt %. Fibrils persist until about σ ∼ 0.1 for PEG-800 and until about σ ∼ 0.07 for PEG-2000.

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the X-ray wavelength and detector distance used, the q range accessed was 2.35 × 10−3−0.137 Å−1. The scattering patterns were modeled using SASView (Small-Angle Scattering Analysis Software Package) developed at NIST. A powerlaw background was subtracted from each sample to account (approximately) for water and quartz scattering. A form factor for a semiflexible cylinder with a disperse radius was used to fit the scattering patterns at 80 °C.36,37 The scattering length density and scale terms (volume fraction of polymer, φ, multiplied by the fibril volume) were combined into a single fitting term, Ascale. Because of the lower limit of q (0.00235 Å−1), the fibril length and Kuhn length were fixed at 500 μm and 50 nm, respectively. The values were estimated from previous work regarding the length of MC fibrils.10 The radius dispersity was held at 0.30 based on a Schulz−Zimm distribution of radii to reduce the number of free parameters. Rheology. The storage (G′) and loss (G″) moduli were measured as a function of frequency, strain amplitude, and temperature using a TA Instruments AR-G2 rheometer. Because of a limited sample volume, a 20 mm cone and plate geometry with a 2° cone angle and 50 μm truncation gap was used. After sample application, solvent evaporation was mitigated by adding several drops of low-viscosity silicone oil (ν ≈ 5 cSt at 25 °C) to the perimeter. Samples were then heated from 5 to 80 °C at 2.5 °C/min, 5% strain, and 1 rad/s. Strain sweeps were conducted at room temperature and at 80 °C to ensure the sample was in the linear elastic regime. Frequency sweeps were taken from 0.1 to 100 rad/s for 20−50 °C at 10 deg intervals and for 50−80 °C at 5 deg intervals.

RESULTS PEG grafts modify the properties of MC in two fundamental ways. lp of MC-g-PEG increases systematically as a function of both grafting density σ and graft length, and the solution interactions (i.e., second virial coefficient) are modified (Figure S3f in the Supporting Information). The two effects in combination lead to a change in fibril structure as a function of increasing σ and at high σ suppress fibril formation altogether. AFM. Using AFM, we have examined the structure of MC-gPEG at 80 °C as a function of σ and graft length. Ungrafted MC assembles into micrometer long fibrils that are ∼12 nm in diameter. The structure of the fibrils in the AFM analysis does not change as a function of molecular weight over the range 150−300 kg/mol and is broadly consistent at 0.003 wt % with the structures formed at 0.2 wt % analyzed previously with SANS and cryogenic TEM.4 Along the long axis of the fibril there are clear modulations in the height profile, reminiscent of other twisted assemblies (Figure 2).38−40 This interpretation is limited to comparisons with other AFM images of known twisted morphologies, and other possibilities, including the previously proposed toroid model, may also be plausible.11−14 Both AFM images show evidence of branch points along the fibril, which could lead to a connected network at higher concentrations. At the lowest graft density and length MC-g-PEG (σ = 0.007, PEG-800) still assembles into fibrils (Figure 3), C

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Figure 4. High-magnification height profile images of MC-g-PEG800 and MC-g-PEG2000 structures at 0.003 wt %. (a) For σ = 0.04 PEG-800 the fibrils are ∼500 nm in length, showing the same twisted striations as ungrafted MC. (b) At σ = 0.1 800 g/mol grafting density, the fibrils are much thicker, and there is a population of aggregated structures. (c) σ = 0.04 MC-g-PEG2000 still assembles into fibrils ∼500 nm in length, and the height variations along the length of the fibril are washed out.

Figure 5. AFM image analysis. (a) Typical height profiles of ungrafted MC fibrils. (b) Height results as a function of graft density for 800 g/mol grafted MC (red) and 2000 g/mol grafted MC (blue). Circles represent average height of fibrils, while squares are average height values of aggregates. Height increases as a function of grafting density. (c) Average height from AFM analysis plotted as a function of the solution persistence length.

When σ = 0.007 for 800 g/mol grafts, h ≈ 12 nm. When σ = 0.04, h increases slightly to 14 nm, and when σ = 0.11, h ≈ 18 nm. For the longer 2000 g/mol grafts the increase in h is a steeper function of σ. When σ = 0.02, h increases to 15 nm, and when σ = 0.04, h increases to 17 nm. Fibril formation is suppressed after fibrils reach h ≈ 17−18 nm for both graft lengths. At this point, grafted MC assembles into isotropic aggregates. The height profiles of these structures have a high variability (Figure 5b squares) and increase as a function of grafting density. SAXS. The AFM images reflect the fibril structure in a dried state at extremely low concentrations (0.003 wt %). To compare this with the fibril structure in solution, SAXS scattering patterns of 1 wt % solutions at 80 °C were investigated as a function of PEG-800 grafting density (Figure 6a). After annealing at high temperatures, the characteristic “shoulder” near q ≈ 0.015 Å−1, which has been previously shown to reflect the fibril form factor,4,5 gradually shifts to lower q values and lower intensities with increasing σ. This observation is at least qualitatively consistent with the AFM analysis, in that the radius increases, while the volume fraction of fibrils formed at 80 °C decreases. For σ > 0.11, the shoulder is no longer observed. Instead, the scattering patterns for both σ = 0.22 and σ = 0.33 are monotonically decaying functions of q, which strongly supports the AFM observation that at higher σ fibril formation is suppressed and chains come together in larger aggregates. For σ < 0.11, SAXS patterns are fit to the flexible cylinder model developed by Pederson et al.36 and Chen et al.,37 which

qualitatively similar to those formed by ungrafted MC. With increasing σ the fibrils formed are systematically shorter and thicker until σ ∼ 0.1. At this grafting density, a transition occurs beyond which fibril formation is suppressed. Rather, MC-g-PEG assembles into what appears to be aggregated, approximately isotropic structures. The AFM data for MC with PEG-2000 grafts are qualitatively similar. At σ < 0.07, MC-gPEG forms fibrils. For σ ≈ 0.04 the fibrils are distinctly shorter and thicker than at σ = 0. Beyond σ ≈ 0.07, only isotropic aggregates are observed. Higher magnification AFM images of fibrils at the transition are presented in Figure 4. The first two images are for (a) σ = 0.04 and (b) σ = 0.1 for PEG-800 grafted MC. At σ = 0.04, the fibrils are ∼500 nm in length and still show the same height variations along the long axis as ungrafted MC fibrils. This result is consistent with the previous finding that the average contour length (∼500−600 nm in this case) controls the length of the fibril as MC chains twist together.10 At σ = 0.1 (b), there appear to be populations of both fibrils and aggregates. The fibrils are considerably thicker than the fibrils formed with σ = 0.04. Their length is also on the order of ∼500 nm. As seen in Figure 4c, σ = 0.04 PEG-2000 grafted MC shows the same structural characteristics, but the height variations along the length axis are not as distinct. Typical height (h) profiles of the fibrils are plotted in Figure 5a. Ungrafted MC forms fibrils that are 12 ± 3 nm in diameter (averaged over ∼20 profiles). The height, which is a measure of the dry diameter of the fibril, increases monotonically with σ for both 800 and 2000 g/mol grafts, as shown in Figure 5b. D

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MC chains are twisting together into a bundle, the radius is set by the flexibility of the chains and the average planar distance (d). The inner chains are the least twisted, while the outer chains are the most twisted. The evidence for this twist is found both in the long-axis striations along the fiber (Figure 2) and previously published circular dichroism results. Hynninen et al. have found that after the formation of fibrils MC solutions strongly absorbed preferentially right-handed light.41 Because of the elastic penalty, it is unfavorable for the chains to bend beyond the persistence length unless there is a strong binding force to compensate. The result is a gradient of twist as a function of radius within the fibril. On the basis of this intuition, it is expected that the r ∼ (lp d)1/2, where d is the typical spacing between chains. For the data in Figure 7b, d was calculated by assuming that each graft adds a sphere with an approximate radius of 0.6 nm to the mean spacing between chains. The consequent mean spacing is calculated from the sum of the weighted number fraction of repeat units with and without grafts. For example, for a chain with σ = 0.007, 6 repeat units have a radius of 0.95 nm and the other 796 have a radius of 0.35 nm. Assuming an even spacing between chains, the grafts at σ = 0.007 would increase the radius from 10.5 to 10.63 nm. For a chain with the highest grafting density (σ = 0.11), 88 repeat units would have a radius of 0.95 nm, and the average fibril radius increases to 12.4. The average distance between chains does not account for the entire radius increase. However, taking into account the persistence length, the radius is very closely correlated to the (lp d)1/2 values. The radii measured by AFM are about half those determined from SAXS. This is consistent with a previous observation that there is a significant volume fraction of solvent within the fibril. To estimate the fraction of water within a fibril, the crosssectional areas of fibrils were measured from AFM images and determined from SAXS analysis, and compared in Figure 7c. According to this simple estimate, water takes up ∼65% of the cross-sectional area, which is very consistent with previous estimates. For example, Lott et al.4 reported that the SANS intensity, which is related to the volume fraction of fibrils and the scattering length density difference, was accounted for by assuming 60% water by volume within the fibrils. From the analysis depicted in Figure 7c, the water-to-polymer ratio is constant as a function of grafting density, implying PEG grafts do not strongly contribute to this value. Rheology. The occurrence of fibrils has striking rheological consequences. It has been previously demonstrated that the sharp increase in the modulus of aqueous MC solutions as they

Figure 6. SAXS of MC-g-PEG800 for σ = 0−0.33 (a) at 80 °C and (b) fits as a function of σ for 1 wt % solutions. The form factor associated with fibril structure persists until about σ ∼ 0.11. In (b) the intensity profiles are shifted vertically for clarity.

previously gave consistent fitting results in both SAXS and SANS studies of MC fibrils.4,5 The details of the model are available in the previous publications and in the Supporting Information.4 The fits overlaid on the scattering patterns are shown in Figure 6b, and the fits describe the SAXS patterns quite well. After a general power law background subtraction, there are several fitting parameters involved: the fibril radius (and its distribution), the fibril length, persistence length, intensity scale factor, and contrast. The model is most sensitive to the radius, the results of which are plotted in Figure 7. The remaining parameters were kept constant, as described in the Materials and Methods section. The radius of the fibrils increases systematically as a function of σ (Figure 7a). The increase from 10 to 15 nm is consistent with the increase in dried fibril height observed with AFM. The radii are plotted as a function of (dlp)1/2 in Figure 7b.20 If the

Figure 7. Results of the SAXS fits for 1 wt % solutions of MC-g-PEG800 with increasing σ at 80 °C. (a) The fibril radius increases systematically as a function of σ. (b) The fibril radius as a function of (dlp)1/2. The red line indicates a fit to r = 0.9(dlp)1/2. (c) The percent polymer in a fibrillar cross section calculated from the ratio of the square dry and wet fibril radii. The value is constant as a function of grafting density. E

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order of 10 Pa for MC solutions with higher grafting densities for which fibril formation is suppressed (Figures 3 and 8a). Moreover, the temperature at which gelation occurs (Tgel) systematically increases at a constant heating ramp. For ungrafted MC Tgel = 62 °C, for σ = 0.007 Tgel = 63 °C, for σ = 0.02 Tgel = 65 °C, and for σ = 0.04 Tgel = 68 °C. Beyond σ = 0.1, fibril formation is completely suppressed, which is consistent with both AFM and SAXS analysis. At these grafting densities instead of a sharp increase in G′, there is a steady, reversible increase as a function of temperature, corresponding to the formation of aggregated structures. The elastic modulus dependence on temperature and σ is consistent for higher molecular weight PEG grafted MC solutions (Figure 8b). At lower σ, for which fibril formation is observed, there is a sharp increase in the modulus at around 60 °C, indicative of gelation. The longer grafts lead to a more substantial change in Tgel as a function of σ. This is consistent with the AFM analysis, for which a sharper change in structure is observed with increasing σ with respect to the shorter PEG grafts (Figures 3 and 4). When σ ≥ 0.07, fibril formation is suppressed (Figure 3), and gelation is no longer observed.

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DISCUSSION MC fibril formation is suppressed as a function of PEG grafting density, which has a direct impact on the rheological properties of MC solutions. When there is evidence of fibril formation from AFM or SAXS analysis, 2 wt % MC-g-PEG solutions still gel. Conversely, if fibril formation is suppressed, so is gelation. Without fibrils, there is no longer a percolated rigid structure to provide support, even though the chains still associate. This finding strongly confirms previous observations that the MC gel strength is primarily derived from the stiffness of the associated fibrils.8 The value of σ at which fibril formation is suppressed depends modestly on graft length and provides important insights into how chains are organized in the fibrils. The persistence length of the backbone increases as a function of both graft length and σ. The polymer chains extend due to the added steric hindrance, and the effect is more pronounced for longer grafts. At elevated temperatures, low σ MC-g-PEG still associates into fibrils. The fibril diameter increases as a function of σ, regardless of the molecular weight of the grafts. This result is clearer from the SAXS fitting results. As the dry fibril diameter reaches 18 nm, fibril formation is suppressed, and instead the chains associate into more isotropic aggregates. The σ at which fibril formation is suppressed depends on the molecular weight of the grafts but in both cases occurs when the solution persistence length of the polymers is ∼22 nm. There are at least three distinct possible explanations for the increase in fibril diameter with σ. One is that the overall polymer−polymer interactions are more attractive relative to the polymer−solvent interactions, thereby increasing the crosssectional aggregation number, while keeping the volume fraction of water constant (Figure 7c). Second, the grafts could interfere with the chain packing by increasing the effective diameter of the chains, thereby reducing the cohesive energy benefit of assembly. Third, it could be a result of increasing lp. If the chains are packed in a twisted bundle such that the pitch of the twist has a radial dependence and the axial chains are completely untwisted and the bounding chains at a maximum twist, the radius will be set by the elastic penalty of growing the bundle further. While contributions from all three are likely, in Figure 5c the AFM height is plotted as a function

Figure 8. Elastic modulus G′ as a function of temperature and σ using 40 mm 2° cone and plate geometry at 1 rad/s, 5% strain, and 2.5 °C/ min temperature ramp. (a) 2 wt % PEG-800 grafts. Upon heating, the sharp increase in modulus corresponding to fibril formation decreases in amplitude and shifts to higher temperatures with increasing σ. (b) 2 wt % PEG-2000 grafts.

gel upon heating is a result of fibril formation. As fibril formation is suppressed, it is expected that the increase in the high-temperature modulus will also be suppressed. A summary of the rheological results is plotted in Figure 8. The elastic modulus G′ is shown for 1 rad/s and 5% strain as a function of temperature and σ for 2 wt % samples. For the ungrafted MC control (black points in Figures 8a and 8b), the modulus increases slightly until 60 °C, at which point it increases sharply by 2 orders of magnitude. The initial increase is likely due to changing relaxation times and interactions as a function of temperature, since these solutions are well above the overlap concentration. The sharp increase near 60 °C has been previously related to the formation of fibrils as the solutions gel. The fibrillar network gives G′ = 1.3 kPa at 80 °C, despite having only 2 wt % polymer in solution. There are distinct trends in G′ as a function of graft density and length. In Figure 8a, data are overlaid for MC solutions grafted with PEG-800. Because the molecular weight of the polymer increases dramatically as a function of σ, at a constant mass concentration there are systematically fewer polymers. The persistence length of these polymers also systematically increases as a function of σ. It is not surprising that the initial G′ and its subsequent temperature dependence prior to fibril formation change as a function of graft density. Below 60 °C, the modulus is set by polymer relaxations, which are expected to change as a function of both polymer number concentration and persistence length. At ∼60 °C, the modulus sharply increases for σ = 0.007 (red filled points) from ∼10−3 to 740 Pa, for σ = 0.02 from ∼10 to 325 Pa, and for σ = 0.034 from ∼10 to 160 Pa and stays on the F

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ΔF(r ) 3 ij 2γ 4 yzz zz = − jjj 2 jk K3 z{ k bTπL

1/3

of the lp of the grafted chains (for measurements of persistence length, see the Supporting Information and the previous publication).25 The height profiles for both the PEG-800 and PEG-2000 grafted MC superpose when plotted against the persistence length. Within the uncertainty, and independent of the graft length, changing lp leads to the same change in the dry fibril width. Using SAXS, we have investigated the effects of increasing chain diameter and persistence length on the fibril radius (Figure 7b). The radius is nearly perfectly correlated to (dlp)1/2. At still higher grafting densities, lp and d increase further but fibril formation is suppressed. From this evidence is it likely that the fibril diameter is primarily controlled by MC chain thickness and lp, as opposed to the change in polymer− polymer interactions. We suspect that the tendency to twist is derived from molecular origins. The building blocks of MC are chiral. Locally, substituted and unsubstituted cellulose is planar due to the β-glycan linkage, with a slight tendency to twist. This leads to a general twist of cellulose in nanocrystals, which has been observed both experimentally and theoretically.42−44 We speculate that the methyl groups would perturb this molecular structure slightly, possibly adding more twist. Similar conclusions have been drawn from previous circular dichroism data that compares polysaccharide derivatives with both αglycan and β-glycan linkages.45−47 According to Grason22 and Grason and Bruinsma,20 the free energy of semiflexible chains that are associating into twisted bundles is set by an elastic penalty due to the twist, the attractive energy between the chains, and the surface energy of the exposed twisted bundle. If there is a preference to twist into columnar liquid crystalline hexagonally packed bundles,19 the elastic energy takes the form K ij Etwist(θ , R ) r 2 yz = 3 θ 4jjj1 + 2 zzz − 2γTθr k bTπL 4 k l {

1/2

K3 μ

( )

r 4/3 r2 l2

1/3

(1 + )

− r 2ρ0 Δϵ + 2r Σ (4)

where ρ0 is the number of chains per cross-sectional area, L is the contour length of the fibril, r is the radius, Σ is the surface energy of the fibril, and −ΔεL is net free energy per bundle. At the phase separation temperature, the bundle radius is expected to equal l, the length scale associated with the elastic penalty. Without the twist-dependent energy gain (γT = 0), the bundles would grow to infinite r, indicating bulk phase separation. The assembly of PEG grafted MC is likely a more complicated phenomenon, and future simulation and/or theoretical work is required to establish the exact dependence of the graft influence on both l and Σ. Despite this, eq 4 makes predictions that are consistent with experimental observations. For example, Σ, d, and lp are all expected to change as a function of σ. The change in Σ is possibly responsible for an increase in Tgel observed rheologically (Figure 8) and for the suppression of fibril formation. The changes in d and lp set r of the fibrils. The 1/2 power dependence of r as a function of lp is consistent with the SAXS results, although the AFM data are too noisy to clearly discern the persistence length dependence. In addition to the above thermodynamic analysis, the 1/2 power law dependence of r on lp is also approximately consistent with the stacked toroidal model previously suggested for the subfibril structure.13 In the toroid model, the radius is expected to increase with lp as a power of 2/5. In both cases, the lateral size scale is determined by the bending modulus of the semiflexible chains. The suppression of fibril formation is a result of the change in surface energies and the long persistence length of the grafted polymers. According to Bruss and Grason,21 the ability for chains to twist together decreases as a function of chain stiffness. On this basis, we schematically illustrate the transitions in Figure 9. As the persistence length increases with increasing grafting density, the interactions change slightly, but more importantly the chains can no longer twist together the same way. Initially this results in larger radius

(1)

where kbT is Boltzmann’s constant times absolute temperature, K3 is the splay elastic constant that describes the resistance to bending of individual chains, θ is the angle of the twist relative to the central axis, γT is the gradient of θ as a function of radial distance r, and l is the resistance to compressive distortions perpendicular to the long axis, also known as the bend penetration length. The quantity l is related to the shear modulus in the direction perpendicular to the long axis of the fibril (μ) and K3 as l ∝

Article

. According to Grason22 and

Grason and Bruinsma,20 l ∼ (lp d)1/2. By minimization of the energy with respect to θ for a fixed r ij 2γ yz θ0(r ) = jjj T zzz j K3 z k {

1/3

r1/3 1/3

r2 l2

(1 + )

(2)

with a preferred radially dependent energy of the twist: Etwist(θ0 , r ) 3 ji 2γ 4 zyz zz = − jjj k bTπL 2 jk K3 z{

1/3

r 4/3 r2 l2

1/3

(1 + )

(3)

Figure 9. Schematic representation of chain association as a function of σ. PEG grafts change the backbone stiffness of MC as well as solution interactions. At σ < 0.1, the chains still assemble into fibrils with a diameter set by changes in surface tension and chain stiffness. At larger grafting densities, the chains are too stiff to assemble into fibrils and come together in loose aggregates instead.

Equation 3 has a thermodynamically preferred dimension, set by l. During fibril formation, there is a competition between the twist energy, the bulk energy of formation, and the drive to minimize the surface of the bundle. The total free energy is G

DOI: 10.1021/acs.macromol.8b01899 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules structures, but by lp ≈ 22 nm, the chains become too stiff to twist together.

operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. The AFM images were collected at the Characterization Facility, University of Minnesota, which receives partial support from the NSF through the MRSEC program. We thank Douglas Hall, Dr. S. Piril Ertem, and Professor Peter Olmsted for helpful discussions.

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CONCLUSIONS Solutions of methylcellulose gel upon heating as the chains assemble into fibrils of remarkably uniform ∼15 nm diameter, independent of concentration, molecular weight, and temperature of formation. A precise accounting of how MC chains assemble into fibrils has proved elusive, but the results presented here support the recently proposed helical bundling of chains. AFM images suggest that the assemblies are twisted, as evidenced by the striations along the length of the fibril seen in AFM. The average diameter systematically increases as a function of PEG graft density. Short PEG grafts modify the persistence length by a factor of 4, while the long PEG grafts change the persistence length by up to a factor of 10. Consistent with established theories for bundling of semiflexible chains, the elastic penalty to twist MC chains into fibrils increases as a function of σ, which increases the radius. As the persistence length is increased to ∼22 nm, the elastic energy becomes too great, and fibril formation is suppressed. The occurrence of fibrils has profound consequences for the rheological properties of MC solutions. In line with previous understanding, fibrils are responsible for the magnitude of the modulus of MC gels at elevated temperatures. As fibril formation is suppressed with increasing σ, the solutions no longer gel. This work provides the first systematic investigation of how chain flexibility affects the assembly of MC and confirms directly that the modulus strength is derived from the strength of the fibrils.

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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.8b01899. Additional NMR spectra, light scattering and SAXS data (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Peter W. Schmidt: 0000-0001-6702-411X Frank S. Bates: 0000-0003-3977-1278 Timothy P. Lodge: 0000-0001-5916-8834 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported primarily by the National Science Foundation through the University of Minnesota MRSEC under Award DMR-1420013. We thank the Dow Chemical Company for generously providing the MC samples. The SAXS measurements were taken at the DuPont-NorthwesternDow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by Northwestern University, E.I. DuPont de Nemours & Co., and The Dow Chemical Company. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility H

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