Molecular Weight Dependence of Methylcellulose Fibrillar Networks

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Molecular Weight Dependence of Methylcellulose Fibrillar Networks Peter W. Schmidt,† Svetlana Morozova,‡ Paige M. Owens,† Roland Adden,§ Yongfu Li,∥ Frank S. Bates,*,† and Timothy P. Lodge*,†,‡

Macromolecules Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 09/25/18. For personal use only.

†

Department of Chemical Engineering & Materials Science and ‡Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States § Dow Pharma and Food Solutions, Bomlitz 05161, Germany ∥ Analytical Sciences, The Dow Chemical Company, Midland, Michigan 48667, United States S Supporting Information *

ABSTRACT: Gelation of aqueous methylcellulose (MC) solutions upon heating has been shown to result from the formation of a network of semiflexible fibrils, with diameters of 15 ± 2 nm. Here, we investigate the impact of MC molecular weight on the elasticity and structure of aqueous gels at concentrations between 0.1 and 3 wt %. Small-amplitude oscillatory shear measurements conducted at a fixed concentration reveal that the gel modulus increases monotonically by a factor of 5 for weight-average molecular weights (Mw) between 22 and 550 kg/mol. Small-angle X-ray scattering data, fit to a semiflexible cylinder model, demonstrate that the fibril radius, Kuhn length, and volume fraction are approximately constant throughout this molecular weight range. Small-angle light scattering shows that the fibrillar-rich and fibrillar-depleted domains within the gel are associated with an essentially invariant heterogeneity correlation length. Direct visualization by cryo-TEM reveals that lower molecular weight MC forms fibrils of lower average length. The distribution of fibril lengths measured by cryo-TEM and the distribution of the polymer chain contour lengths are similar, especially for shorter chains, and these features are correlated to network connectivity. We propose that the underlying fibril structure consists of bundles of polymer chains with a preferred orientation coincident with the fibril axis, while the fibril diameter is controlled by a circumferential helical pitch associated with the single chain Kuhn length and interactions between chains.

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INTRODUCTION Cellulose derivatives constitute a broad class of materials that are produced from native cellulose by substituting various chemical moieties for a fraction of the hydroxyl groups along the backbone of the chain. Chemical modification of cellulose was implemented as early as the 19th century in the case of nitrocellulose and during the first half of the 20th century for organic cellulose esters and ethers.1 Methylcellulose (MC), a partially methoxy-substituted cellulose ether, is employed in diverse applications ranging from food, cosmetic, and consumer products to industrial pastes.2 The degree of substitution of commercial grades of MC (typically 1.7−2 mol of OCH3 per mol of anhydroglucose unit) is tailored to produce a cellulose derivative that is soluble in water at low temperatures and that forms a turbid hydrogel at elevated temperatures.3 The thermogelation of MC is a valuable property for many applications and is of particular importance in food products due to its biocompatibility.4 Controlling the temperature where the aqueous mixture transitions from a solution to a gel, and the resulting gel modulus, are critical factors for these applications. The underlying mechanism of gelation in MC has been debated for decades. In general, most explanations postulate © XXXX American Chemical Society

that MC gels form by hydrophobic association of methoxy substituents that lose solubility upon heating. Until about 6 years ago, various microscopic mechanisms related to hydrophobic association in MC ranging from micelle formation5,6 and cross-links7,8 to trapped phase separation3,9−12 have been proposed to explain gelation. However, none of these models can account for the magnitude of the observed increase in modulus upon gelation.13 Recent reports have shown that the onset of gelation is concurrent with the formation of a network composed of ca. 15 nm diameter fibrils.14−16 Fibrils have been observed directly by cryogenic transmission electron microscopy (cryo-TEM) imaging and quantified through modeling of small-angle neutron and X-ray scattering (SANS and SAXS) profiles. While the discovery of fibrils has led to an improved understanding of the structure of MC gels, many aspects of these soft materials are yet to be understood in the context of a fibrillar network. Specifically, the modulus of MC gels has been demonstrated to increase with increasing molecular weight Received: June 18, 2018 Revised: September 7, 2018

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DOI: 10.1021/acs.macromol.8b01292 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules (M) over a range of M and concentration.17,18 This increase in modulus has been attributed to an enhancement in polymer chain entanglements, which act as additional cross-links, beyond those due to hydrophobic association. However, this explanation is not compatible with the evidence of a fibril network structure. Hence, the M dependence of the gel modulus in MC must be reconsidered within this framework. To understand the relationship between elasticity and structure, we measure the modulus of MC gels using smallamplitude oscillatory shear rheology. Fibril and fibrillar network structure is probed through small-angle X-ray scattering (SAXS), small-angle light scattering (SALS), and cryogenic transmission electron microscopy (cryo-TEM). The results demonstrate that the average length of the MC fibrils decreases with decreasing M, while the fibril radius remains constant.

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time and temperature varied to achieve the desired Mw. The partially depolymerized MC is neutralized with sodium bicarbonate. Physical Property Characterization. The M and dispersity of MC materials were characterized by size-exclusion chromatography (SEC) methods described previously.22 Briefly, SEC with multiangle laser light scattering and differential refractive index detectors were used to accurately determine the M distribution for disperse polymers over the wide range of M investigated. The intrinsic viscosity ([η]) of each sample was calculated using the differential solution viscosity relative to the viscosity of water. The critical overlap concentration (c*) for each sample was approximated by c* ≈ 1/[η]. A summary of these results can be found in Table 1. Solution Preparation Protocol. Each MC powder was dried in a vacuum oven at 60 °C overnight and stored in a desiccator. Deionized water used to make solutions was sourced from a Millipore water filtration system. Solutions were prepared by dispersing a specified mass of MC in half the final mass of water for 10 min at 70 °C, followed by the addition of room temperature water to afford the desired concentration. The samples were stirred for another 10 min then placed in an ice bath for 10 min. Solutions were stored in a freezer below 5 °C for a minimum of 12 h prior to use. Rheology. Rheological measurements were conducted on a TA Instruments AR-G2 with the concentric cylinder conical DIN geometry (rotor o.d. 14 mm, rotor height 42 mm, cup i.d. 15 mm, gap height 5 mm). Before loading, samples were degassed to prevent the formation of bubbles. Low-viscosity silicone oil (ν ≈ 5 cSt at 25 °C) was floated on top of the sample to prevent evaporation during measurements. Samples were heated from 5 to 80 °C at 1 °C/min at 1% strain and 1 rad/s. Strain sweeps were conducted at room temperature and at 80 °C to ensure that the sample was in the linear viscoelastic regime. 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. Solutions were loaded into 1.5 mm diameter quartz capillaries and sealed with epoxy and then placed in a custom fabricated 8-capillary heated stage during the experiments. Samples were heated stepwise in increments of 10 °C and allowed to anneal for 10 min at each temperature, approximating a 1 °C/min temperature ramp. 2D scattering patterns were collected during 1 s exposures to λ = 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 noise. The 2D SAXS data were integrated azimuthally yielding 1D scattering patterns plotted as intensity versus the magnitude of the scattering wave vector q = (4π/λ) sin(θ/2) covering the range 2.35 × 10−3 to 0.137 Å−1; θ is the scattering angle. SAXS patterns obtained at 80 °C were modeled using the SASView software package.23 A power-law background was subtracted from each sample to account for water and quartz scattering from the solvent and capillary, respectively. A semiflexible cylinder form factor with a disperse radius was fit to the scattering patterns,24,25 where the scattering length density and scale terms (volume fraction of polymer multiplied by the fibril volume) were combined into a single amplitude fitting parameter. The fiber length and length dispersity were chosen based on results from cryo-TEM presented in this work. An additional power law term was added to account for the upturn at low q. A power of 3.5 was chosen based on previous USANS results.16 Small-Angle Light Scattering. MC solutions were contained in quartz cuvettes with a 1 mm path length and annealed in a copper heating block for 30 min at 80 °C. Scattering patterns were produced on black paper at a sample distance of 94 cm and recorded with a Nikon D5000 digital camera. Perspective correction and radial integration of the images were performed in MatLab. The radial average of the grayscale values for each sample was subtracted from the solvent scattering. The grayscale values, which are proportional to the relative intensity, were plotted as a function of pixel distance as I vs q. Cryogenic Transmission Electron Microscopy. Solutions of various MC at 0.1 wt % were annealed for 30 min at 80 °C. 5 μL of annealed sample was pipetted onto a lacey carbon Formvar grid (Ted

EXPERIMENTAL SECTION

Materials. A library of commercially available MC and model low molecular weight MC (Mw = 22−550 kg/mol) was chosen to investigate the impact of M on the structure of the associated gels (Table 1). Each sample is named for the corresponding Mw; e.g.,

Table 1. Characteristics of Methylcellulose Samples Examined name

Mwa,b (kg/mol)

Đa

Lwc (nm)

[η] (mL/g)

c*d (g/L)

MC22S MC50S MC83S MC100S MC180S MC290S1e MC290S2f MC400S MC550S

22 49 83 99 180 290 290 400 550

2.3 2.8 3.3 1.9 4.2 5.4 11 5.1 4.3

80 190 310 370 670 1100 1100 1500 420

72 130 200 270 450

14 7.5 5.1 3.7 2.2

830 1050

1.2 0.95

a

Based on size exclusion chromatography, using methods reported previously,22 where Đ denotes molar mass dispersity (Mw/Mn). bAll polymers investigated had a degree of methoxy substitution (DS) of 1.8 mol per mol of anhydroglucose unit. cThe contour length of the polymer chain based on the weight-average molecular weight. Calculated from an average repeat unit molecular weight (M0) of 187 g/mol and a repeat unit length of 7 Å.2 This M0 corresponds to a DS of 1.8 dCalculated from 1/[η]. eSample prepared by blending MC180S and MC400S. fSample prepared by blending MC50S and MC550S.

MC400S denotes a polymer with Mw = 400 kDa, and “S” denotes samples that were prepared using a staged or multiaddition procedure that differs from “standard” commercial MC. The staged addition process has been demonstrated for various cellulose derivatives as a way to add additional substituents19,20 or to modulate the regularity of the substitution.21 For MC the staged addition procedure provides a more regular substitution pattern, by controlling the rate at which the methoxy substituents are added to the three potential positions of the glucosyl unit. The more regular substitution generally results in a reduction in the gelation temperature and a higher hot gel modulus. To fill out the large gap in Mw between the commercial materials MC180S and MC400S, we also prepared two blended samples: MC290S1 was obtained by blending equal weight fractions of MC180S and MC400S; MC290S2 was prepared by blending MC50S and MC550S targeting the same Mw as MC290S1. Acid Hydrolysis of MC. The MC is partially depolymerized by heating the powderous samples with gaseous hydrogen chloride at a B

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Macromolecules Pella), inside a FEI Vitrobot Mark IV set to 60 °C and 100% relative humidity. The grid was blotted for 1 s with the instrument defined blot force set to −1 to −3 and then equilibrated for 1 s before being plunged into liquid ethane at −183 °C. All grids were stored under liquid nitrogen prior to imaging. The sample grids were transferred to a Gatan-626 single tilt cryo-holder at −179 °C. Images were taken on a FEI Techni G2 Spirit Bio-Twin with a FEI Eagle CCD camera. To mitigate the effects of beam damage on the samples, electron exposure was reduced by using spot sizes greater than 5. The spot size is a unitless value inversely related to the strength of the first condenser (c1) lens. By reducing the strength of the c1 lens, less beam current is projected onto the sample.

nucleate and grow fibrils. Tsol on cooling is analogous to the melting temperature, which represents the equilibrium transition from MC fibrils to dissolved chains. Consistent with this analogy, Tgel is a strong function of heating rate, whereas Tsol is relatively independent of cooling rate. For comparative purposes we define the hot gel modulus as G′ at 80 °C, and values of this mechanical property are plotted as a function of molecular weight for 0.3 wt % solutions in Figure 1b; results for 1 wt % are presented in Figure S1. The elastic modulus increases monotonically with increasing molecular weight, including the blended samples MC290S1 and MC290S2. For each molecular weight, the scaling relationship for the hot gel modulus as a function of concentration (Figure S1b) is approximately consistent with a densely cross-linked filamentous gel (G′ ∼ c2.5),27 and in good agreement with the previous concentration scaling found for nonstaged addition MC (Figure S1c).13 Additionally, this scaling is comparable to what is observed for long entangled chains of microfibrillated cellulose.28 For a network of 5−6 nm diameter microfibrillated cellulose fibrils, it was found that G′ ∼ φn, where 2 < n < 3. At 0.3 wt % microbrillated cellulose, the modulus was ca. 20 Pa,28 which is comparable to what is observed for the lower molecular weight MC gels in Figure 1b. Structural Characterization. SAXS was used to quantify the fibrillar structure in the MC gels at 80 °C as a function of molecular weight and concentration. Scattering patterns were collected from MC solutions varying from 0.1 to 1 wt %. Qualitatively, the scattering patterns across all molecular weights investigated appear similar in the intermediate qrange (Figure 2), exhibiting a shoulder around q = 2 × 10−2 Å−1, which develops with increasing temperature (Figure S2a). This behavior is consistent with the transition from a homogeneous solution of semiflexible polymer chains to fibrils, as previously documented by SANS.15,16,26,29 At low q the scattering profiles exhibit slight differences as a function of M, which we attribute to spatial heterogeneity. In particular, slight but distinct upturns in intensity are evident for MC22S and MC50S at 0.3 wt %. To quantify the dimensions of the fibrils, the scattering patterns were fit to a model for semiflexible cylinders with a disperse radius (eq S1).24,25 This model fits the scattered intensity normalized by the fibril volume (Vfib) in terms of the scattering contrast (Δρ)2, fibril volume fraction (ϕfib), contour length (Lc), Kuhn length (lk), radius (r), and radius dispersity (PDrad) as a function of the scattering vector, q. This multi parameter model was previously fit to SANS profiles of MC and hydroxypropyl methylcellulose.16,30 To assess the sensitivity of this model with respect to each of the key variables, the scattered intensity normalized by Vfib was plotted as a function of q while systematically varying each of the parameters (Figure S4). For fitting purposes (Δρ)2 and ϕfib were combined into a single scale factor since they have a common influence on the intensity. The SAXS results were then fit to r, PDrad, (Δρ)2φfib, lk, and a power law scale factor while holding Lc and PDlength constant for each molecular weight based on the TEM results presented in this work and the power law exponent to 3.5. Example fits are provided in Figure 2b for 1 wt % solutions of MC for Mw = 22−550 kg/ mol and for MC100S at various concentrations between 0.1 and 3 wt % in Figure S2b. Figure 3 shows a summary of the parameters extracted from fitting the SAXS data; tabulated results can be found in Table S1. The fits yield remarkably constant values of the fibril

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RESULTS Rheological Behavior. Small-amplitude oscillatory shear measurements were conducted to probe the viscoelastic properties of MC solutions as functions of temperature and molecular weight. All solutions investigated undergo a sol−gel transition upon heating, characterized by a large increase in the magnitude of the complex modulus |G*| over a narrow temperature interval (Figure 1a). In all cases, we attribute the

Figure 1. (a) Complex modui for 0.3 wt % solutions of MC22S, MC100S, and MC550S at 1% strain, 1 rad/s, and 1 °C/min. Filled and open symbols denote heating and cooling traces, respectively. (b) Hot gel modulus (G′ at 80 °C) as a function of molecular weight (Mw) for 0.3 wt % solutions.

sharp increase to the formation of a fibrillar network. The transition is reversible and exhibits hysteresis, with a temperature gap of ∼30 °C between Tgel and Tsol when heating and cooling at 1 °C/min. The sol−gel and gel−sol transitions in MC have been compared to a first-order thermodynamic transition such as crystallization.26 Tgel on heating is comparable to a crystallization temperature, which is kinetically determined through the ability of polymer chains to C

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Figure 3. Results from fitting SAXS curves to the flexible cylinder model: the diameter (a) and the scattering scale factor A divided by the volume fraction of MC in the solution (b).

Figure 2. (a) Unshifted and (b) vertically shifted SAXS patterns obtained from 0.3 wt % MC solutions at 80 °C. Scattering patterns were shifted vertically in increments of half an order of magnitude for clarity. The black lines indicate fits to a semiflexible cylinder model with a disperse radius.

in modulus is not a result of a decreased conversion of MC polymer chains to fibrils at lower M. The Kuhn length (Figure 3c) is ∼60 nm across the range of M. The model does not account for interactions between fibrils, which in addition to any heterogeneity at low concentration and the limited q-range available impacts the fit for Kuhn length at low concentration for the lower M samples (Mw ≤ 100 kg/mol). Additionally, the value of lk is rather unreliable due to the limitation of the q range in SAXS; aspects of lk will be covered more thoroughly in the Discussion section. Fairclough et al.12 reported that phase separation accompanies gelation in MC solutions based on optical microscopy performed at 90 °C. Using Fourier transforms of microscopy images, they found that the gel of 1.5 wt % MC300 at 90 °C had a correlation length ξcor ≈ 5 μm, reflecting heterogeneity of fibril-rich and fibril-deficient domains; ξcor is larger than the length between fibrillar cross-links. To determine a similar ξcor as a function of M, we conducted small-angle light scattering (SALS) experiments to access much smaller values of q, hence larger structures than are probed by SAXS. The grayscale intensity obtained by SALS was plotted as a function of q as illustrated in Figure 4a. The decay in the scattered intensity with increasing q was fit to the Ornstein−Zernike relation A I(q) = 1 + q2ξcor 2 (1)

diameter d = 18 ± 1, with 1 representing the standard deviation of the fits across the range of concentration and molecular weight (Figure 3a). This value is slightly larger than previous reports due to the difference in fitting software.15,16,26,29 SASView accounts for dispersity using the number-average distribution function while the NIST Igor Pro small-angle scattering analysis package utilizes the second moment of the distribution function.23,31 As a result, SASView reports a higher mean when fitting the same curve. Using the NIST Igor Pro analysis package, the fits yielded a diameter of 15.0 ± 0.5, with 0.5 representing the standard deviation of the fits across the range of concentration and M, which is comparable to previous studies. The fitted values of the composite prefactor term, (Δρ)2φfib (eq S2), were divided by the polymer concentration (φpolym) to render a scaling parameter independent of initial concentration (Figure 3b). This quantity varies by roughly a factor of 2 over the range of M and concentrations investigated with no clear trend as a function of M. This difference alone is not significant enough to account for the factor of 10 and factor of 5 difference in G′ for 0.3 and 1 wt % MC gels, respectively. The difference is most significant at a concentration of 0.1 wt %, where the scattered intensity is lowest. The fits are also impacted by variations in sample thickness due to differences in the diameter of the capillaries, differences in the thickness of the capillary wall, and any differences in sample heterogeneity; these effects will be strongest at the lowest concentration. Overall, the data suggest that the total volume fraction of fibrils remains constant with respect to M, and therefore the decrease

where ξcor is the structural correlation length associated with the fibril-rich and fibril-deficient domains, and A is the scattered intensity scale factor. Within experimental uncertainty ξcor ≈ 1.4 ± 0.3 μm, independent of M; however, the D

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those reported previously in gels of higher molecular weight MC. However, the fibril length appears to decrease with decreasing M. To quantify this difference, hundreds of fibrils appearing in cryo-TEM micrographs obtained from 0.1 wt % MC solutions of each M (annealed at 80 °C for 30 min) were measured. The results, presented in Figure 6, reveal distributions of fibril lengths that shift to shorter average values with decreasing M. For MC22S nearly half of the population of fibrils are shorter than 100 nm.

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DISCUSSION There is a strong correlation between the average length of MC fibrils, the molecular weight of the constituent polymer chains, and the elastic modulus of the MC gels at elevated temperatures. A decrease in the polymer chain length leads to a decrease in the fibril length without influencing the radius, which results in a less connected fibrillar network with decreased elasticity. This provides insight into how chains are organized within the fibril and into the connectivity of the fibrillar network. It has been proposed that the uniform 15 nm diameter of the fibrils is a consequence of the Kuhn length of MC chains, bK ≅ 14 nm. Recent simulations of MC fibril formation suggest that due to the semiflexible nature, at elevated temperatures individual MC chains wrap around themselves to form hollow toroids ∼14 nm in diameter. This morphology ultimately produces MC fibrils.33−36 Our results suggest that although the toroidal radius might set the fibril diameter, in more concentrated systems chains are likely to be arranged in less twisted morphologies within the fibril. The predicted dimensions of a polymer chain capable of forming a toroidal structure are 16 kg/mol to fully wrap around the inside of the torus and 25−30 kg/mol for the outside diameter. We observed no quantifiable decrease in conversion from polymer chains to fibrils based on the SAXS results across all the M investigated. Based on a 0.7 nm repeat unit length for MC,2 over half of the weight distribution of MC22S polymer chains would not be able to completely wrap around the outside of such a toroidal fibril (Table 1). Moreover, considerably smaller fractions of the chains would satisfy the geometric constraints imposed by a toroidal tube for MC22S, MC50S, and MC83S based on Mn values of 10, 18, and 25 kg/mol, respectively (see Table 1). A decreasing fibril length with decreasing M suggests that the fibril length is influenced by or perhaps even controlled by

Figure 4. (a) SALS of MC400S at 80 °C. Line represents a fit to an Ornstein−Zernike decay. (b) Correlation length for SALS scattering for MC50S to MC550S.

slight increase in ξcor as a function of Mw could be a result of increasing fibril length. Cryo-TEM was used to visualize the MC fibrils and to determine any structural differences across the range of M. Images were taken of vitrified samples of MC50S, MC100S, MC400S, and MC550S after annealing at 80 °C (Figure 5 and Figure S5). In all cases fibrils are observed. To the best of our knowledge, these are the first cryo-TEM images demonstrating the presence of fibrils in MC gels with Mw below 300 kg/ mol.14−16,32 The MC50S fibrils appear structurally similar with respect to diameter to those associated with MC550S and

Figure 5. Cryo-TEM images of MC solutions annealed at 80 °C for 30 min for samples of (a) MC400S and (b) MC50S. The fibrils for MC50S appear substantially shorter than those from MC400S. E

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Figure 6. Histograms of fibril length measured from cryo-TEM of 0.1 wt % solutions annealed at 80 °C for 30 min prior to vitrification compared with Schulz−Zimm distribution of the polymer chain contour length of (a) MC50S, (b) MC100S, (c) MC400S, and (d) MC550S. The fibril length distributions and the distribution of the length of the constituent polymer chains are strongly correlated, particularly for the two lower molecular weights. The distributions of fibril length are shifted toward smaller fibril length for the lower molecular weight MC.

Figure 7. Cartoon of proposed fibril structure. We propose that the fibril comprises a core of axially oriented chains with subsequent chains bundled and wrapped around this core, with a graded helical pitch.

crystals.37 The geometric constraints on these structures have been studied by Grason and co-workers,37−39 where filament assembly reflects a balance between the surface energy of the bundle and the geometric packing frustration. For MC the average distribution of chemical composition along the backbone is assumed to be constant across the various M investigated; hence, the Kuhn length would be invariant. On the basis of SANS results, we showed previously that MC fibrils comprise about 60% water and 40% polymer.16 Significantly, cryo-TEM images have never revealed a hollow tube-like morphology, which suggests the water is distributed throughout the radial dimension of the fibrils. We therefore propose that MC fibrils are composed of bundled chains that are packed with a graded helically as modeled by Grason and co-workers and as illustrated in Figure 7. We speculate that the average chain length controls the overall length of the fibril, while the bundle morphology is controlled by chain bending and the interactions between the chains mediated by the presence of water.38

the MC chain contour length. To explore this possibility, the distribution of MC chain contour lengths was calculated assuming a Schulz−Zimm distribution based on Mw and Đ as measured by SEC (Table 1) and plotted in Figure 6. Comparison with the histograms of fibril contour lengths reveals similarities, particularly for Mw ≤ 100 kg/mol. We expect the final structure of the fibrils to have some dependence on the thermal history employed (annealing at 80 °C for 30 min). Strikingly, the fibrils do not appear to grow beyond the average contour length of individual polymer chains. A plausible explanation for this phenomenon is that the fibril length is controlled by polymer chains that are oriented along the fibril axis. The torodial structure model accounts for the uniform fibril diameter as a consequence of the dihedral potential.33,36 For axially oriented MC chains, the diameter could be controlled by the combination of the tendency to bundle and the ability to assume a helical pitch related to the Kuhn length. Twisted filament bundles are common in many biological systems such as collagen, fibrin, cellulose microfibrils, and chiral liquid F

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Macromolecules This fibril model is consistent with several aspects of the results presented here and elsewhere. First, there is no difference in fibril diameter as a function of M, which indicates that the balance between chain bending and chain interactions is constant with M, consistent with the expectation that chain Kuhn length and chemical composition are invariant with respect to M. We also observe that lower Mw MC chains produce shorter fibrils, consistent with the notion that the core chains are aligned axially. The M dependence of the gel modulus is also compatible with this packing model. Longer MC chains produce longer fibrils and more connected networks. The molecular interpretation embodied in the illustration in Figure 7 naturally lends itself to the formation of branches and accommodates individual solvated polymer molecules that enter and leave fibrils, resulting in tie-chains. Correlated alignment of fibrils as shown in Figure 8 is a

that are capable of significant bending, which thereby reduces the apparent lk,fib. To understand how the fibril length impacts the gel modulus, we consider a mechanical model developed for flexible filaments,27,42 which has previously been applied to MC fibrillar networks:29 G′ ∝

κ 2 −2 −3 ξmeshLj kT

(3)

This relationship relates G′ to the filament bending modulus κ, the mesh size (average distance between cross-links) of the fibrillar network ξmesh, and the fibrillar length between crosslink junctions Lj. Although this scaling relationship is derived for an idealized cross-linked network, the scaling relationships provide insight into how the connectivity of MC fibrillar networks changes as a function of M. Based on the constant Kuhn length measured by SAXS, κ is constant with M and concentration. The length scale, ξmesh, for an idealized uniform network of fibrils is distinct from ξcor, the length scale of heterogeneity of fibril-rich and fibril-deficient domains measured using SALS. For the case of a highly entangled network, with fiber dimensions and properties independent of concentration, where Lj ≃ ξmesh, the modulus of a filament network is given by G′ ∝

κ 2 −5 ξmesh kT

(4)

The mesh size is related to the concentration of the monomers cA and the monomer length a by ξmesh ≈ 1/ acA

which, when combined with eq 4, leads to the scaling with fibril concentration, c

Figure 8. TEM of MC180S highlighting the structural motifs of branching and connected fibrillar segments.

G′ ∝ c 5/2

(6)

The 5/2 power law concentration scaling for a highly entangled network is observed in Figure S1b,c for each M.27 Although the connectivity of the network is not entirely a result of permanent fibril cross-links, but could include mechanisms such as entanglements and connections from tie-chain-like polymers, this model can be used to gain insight into how differences in structure would impact the resulting modulus. If the fibers in the network were longer, we would expect more fibril cross-links and entanglements between fibrils, resulting in a smaller mesh size. Based on the scaling, G′ should depend on ξmesh−5 for a cross-linked fibrillar network. For 0.3 wt % MC, decreasing M from 550 to 22 kg/mol results in a change of G′ by a factor of 10, which corresponds to a 1.6fold increase in ξmesh for the ideal cross-linked fibrillar network. For 1 wt % gels the difference in G′ when decreasing M from 550 to 22 kg/mol differs by a factor of 5, which would correspond to a 1.4-fold increase in ξmesh for the ideal crosslinked fibrillar network. When comparing MC fibrillar networks to the predicted response of a cross-linked fibril network, not only do small changes in the apparent ξmesh result in large variations of G′, but also the difference in ξmesh between highest and lowest Mw decreases with increasing concentration of MC. In the context of MC fibrils the difference in the apparent ξmesh could be manifested through fewer entanglements and cross-links, which would also depend on concentration as observed in Figure S1a.

manifestation of such tie-chains, which would be very difficult to resolve in cryo-TEM. We anticipate that the tendency to form such invisible bridges would increase with increasing molecular weight, which would contribute to network connectivity hence increasing the elastic modulus of the gel. Longer fibrils are also likely to influence entanglements and other cross-links in the networks. Additionally, chirality has been reported for MC gels using circular dichroism measurements.40 Because of preferential absorption of right-handed circularly polarized light, there is a preferred handedness to the MC chains in a fibril, while MC chains in solution do not exhibit a net handedness. For filament bundling the value of the Kuhn length for a homogeneous bundle is predicted to be related to the number of chains in the bundle N lk,fib ∼ N xlk,polymer

(5)

(2)

where x varies between 1 and 2 for chains which are completely decoupled and coupled, respectively.41 Based on the fibril diameter of 18 nm and polymer chain diameter of ca. 0.7 nm, the fibril comprises a bundle of 200−300 chains. For the case x = 1 (decoupled chains), lk,fib ∼ 4.6 μm. This value is an estimate that assumes a constant density, which might not be realized. The defective nature of MC fibrils results in fibrils G

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Macromolecules To understand the magnitude of lk,fib, MC can be compared to other systems. Lin et al. have studied the mechanical behavior of vimentin and neurofilaments (NF).43 The value of G′ for MC at 80 °C ranges from 10 to 100 Pa as a function of molecular weight. Neurofilaments (NF) and vimentin at 3 mg/ mL have moduli of ca. 10 and 80 Pa, respectively. Lin et al. argue the difference between NF and vimentin is a result of strong associations with Mg2+ for NF and more effective crosslinking. Because the chemical composition of MC fibrils does not change as a function of molecular weight, the interaction between fibrils should not change. For MC fibrillar networks, cross-linking is more effective at higher molecular weight due to more entanglements and cross-links. The increase in entanglements is a result of the increase in fibril length, while the increase in cross-links is from an increase in threepoint junctions.

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 operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. The SAXS fitting in this work benefited from the use of the SasView application, originally developed under NSF Award DMR-0520547. SasView contains code developed with funding from the European Union’s Horizon 2020 research and innovation programme under the SINE2020 project, Grant Agreement No. 654000. The cryo-TEM images were collected at the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program.

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SUMMARY MC hydrogels have a hot gel modulus that is dependent on M. MC with a weight-average molecular weight as low as 22 kg/ mol can produce fibrils. The overall volume fraction of fibrils is independent of M, and certain structural features of the fibrils (specifically the radius and Kuhn length) exhibit no change with varying M as demonstrated by SAXS. The heterogeneity of the network is also constant with M. Cryo-TEM demonstrates that the fibril length is strongly dependent on the contour length of the polymer chains that assemble into fibrils. Substantially shorter fibrils lead to a less connected network and as a result a less elastic gel. As a result of these new findings, we propose that the polymer chains are primarily oriented axially along the fibril, with a diameter that reflects the tendency for the outer layer of macromolecules to twist in a helical fashion when swollen with water.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01292. Additional rheology and SAXS data (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

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

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

The authors declare no competing financial interest. 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. The SAXS measurements were taken at the DuPont−Northwestern−Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by H

DOI: 10.1021/acs.macromol.8b01292 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b01292 Macromolecules XXXX, XXX, XXX−XXX