Structure and Properties of Aqueous Methylcellulose Gels by Small

Article pubs.acs.org/Biomac

Structure and Properties of Aqueous Methylcellulose Gels by SmallAngle Neutron Scattering Tirtha Chatterjee,*,† Alan I. Nakatani,*,‡ Roland Adden,§ Meinolf Brackhagen,§ David Redwine,† Hongwei Shen,∥ Yongfu Li,† Tricia Wilson,⊥ and Robert L. Sammler⊥ †

Analytical Sciences, The Dow Chemical Company, Midland, Michigan 48667, United States Analytical Sciences, The Dow Chemical Company, Spring House, Pennsylvania 19477, United States § Dow Wolff Cellulosic, The Dow Chemical Company, Bomlitz 05161, Germany ∥ Formulation Sciences, The Dow Chemical Company, Spring House, Pennsylvania 19477, United States ⊥ Material Science and Engineering, The Dow Chemical Company, Midland, Michigan 48674, United States ‡

S Supporting Information *

ABSTRACT: Cold, semidilute, aqueous solutions of methylcellulose (MC) are known to undergo thermoreversible gelation when warmed. This study focuses on two MC materials with much different gelation performance (gel temperature and hot gel modulus) even though they have similar metrics of their coarse-grained chemical structure (degree-of-methylether substitution and molecular weight distribution). Small-angle neutron scattering (SANS) experiments were conducted to probe the structure of the aqueous MC materials at pre- and postgel temperatures. One material (MC1, higher gel temperature) exhibited a single almost temperature-insensitive gel characteristic length scale (ζc = 1090 ± 50 Å) at postgelation temperatures. This length scale is thought to be the gel blob size between network junctions. It also coincides with the length scale between entanglement sites measured with rheology studies at pregel temperatures. The other material (MC2, lower gel temperature) exhibited two distinct length scales at all temperatures. The larger length scale decreased as temperature increased. Its value (ζc1 = 1046 ± 19 Å) at the lowest pregel temperature was indistinguishable from that measured for MC1, and reached a limiting value (ζc1 = 450 ± 19 Å) at high temperature. The smaller length scale (ζc2 = 120 to 240 Å) increased slightly as temperature increased, but remained on the order of the chain persistence length (130 Å) measured at pregel temperatures. The smaller blob size (ζc1) of MC2 suggests a higher bond energy or a stiffer connectivity between network junctions. Moreover, the number density of these blobs, at the same reduced temperature with respect to the gel temperature, is orders of magnitude higher for the MC2 gels. Presumably, the smaller gel length scale and higher number density lead to higher hot gel modulus for the low gel temperature material.

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INTRODUCTION Physical hydrogels are interesting materials since the change in their transition from liquid-like to solid-like states can be controlled reversibly using external stimuli such as temperature, pH, light, and solvent composition.1 Physical hydrogels are distinct from chemical hydrogels in that their network junctions are transient rather than permanent. The binding energy of physical cross-links is of the order of thermal energy so that physical network junctions can be created, as well as be destroyed, by the thermal motion of polymers. In thermoreversible hydrogels, temperature acts as an external trigger, and the sol-to-gel transition is reversible in nature.1c For example, aqueous solutions of semidilute methylcellulose (MC),2 Nisopropylacrylamide (NiPAAM)3 or poly(ethylene oxide)− poly(propylene oxide)−poly(ethylene oxide) (PEO-PPOPEO) triblock copolymer (Pluronic)4 all undergo thermoreversible gelation upon heating. MC, an ether derivative of © 2012 American Chemical Society

cellulose, is traditionally used as a binder, thickener, and/or emulsifier in food, hair shampoos, tooth pastes, liquid soaps, and cosmetic applications. It is also used in industrial applications in mortar, cement, and ceramic pastes to control water retention, workability, open time, viscosity, yield stress, and thixotropy.5 MC exhibits a thermoreversible sol−gel transition with a specific lower critical solution temperature (LCST) phase behavior,5c,6 and has recently attracted attention in bio- and nanoengineering fields. For example, MC/alginate hydrogel blended with salt shows excellent pH controllable protein drug release and is a promising candidate for protein based drug delivery.7 MC (64630 methylcellulose, Fluka, Switzerland)-phosphate buffered saline hydrogel coated with Received: July 18, 2012 Revised: August 27, 2012 Published: September 20, 2012 3355

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expected to aggregate/associate in water (hydrophobic interaction) to reduce the energy of the system, and these aggregated hydrophobic chain portions develop into the junctions of the three-dimensional gel network when warmed.5a,c It follows that the gelation process would be expected to depend on many factors such as the number of aggregates per unit volume, the average size of the aggregate, the junction structure, their association strength, and the connectivity between two junction points. This entropic argument has merit, and undoubtedly does play a role in one or more types of association of MC chains in water. However, the importance of this concept toward the gelation mechanism remains an open question. Surprisingly, while MC gels are well documented in terms of their rheological and thermal properties;5a,c,e,12 very little work has been done to understand their gel structure.13 Lodge and co-workers13c working with Metolose SM-4000 (from Shinetsu Chemical Co., Japan) found that, for this particular MC, the gelation process is not only a function of temperature but also depends on the value of reduced MC concentration (c/c*, where c* is the chain overlap concentration). Dilute aqueous MC materials (c < c*) form clear solutions at cold temperatures, and the chains in these dilute solutions are thought to be partially aggregated/self-assembled.13a At semidilute concentrations (c > c*), MC solutions form a gel once the gel temperature is reached and on further heating the sample synereses, often forming a transparent polymer-poor fluid phase and a high modulus opaque, polymer-rich gel phase at high temperature. A recent small-angle light scattering (SALS) study by Viletti and co-workers found that phase separation of Metolose SM-4000 (aqueous solution in the presence of 5% NaCl) follows a spinodal decomposition mechanism with a spinodal temperature of ∼41 °C.14 This interpretation is also supported by the theoretical treatment of thermo-reversible gels by Tanaka and co-workers.15 In contrast, Takeshita and co-workers, based on laser speckle analysis on light scattering data and small-angle X-ray scattering studies, concluded that gelation of an aqueous MC solution (Metolose, Shin-Etsu Co., molecular weight (MW) = 5.4 × 104; DS = 1.76) was accompanied by liquid−liquid phase separation.16 According to their study, an apparent increase in MW due to cross-link formation induces the phase separation process. Later, Takahashi and co-workers17 developed a temperature− concentration phase diagram for an MC solution, where they found two coexisting gels with different polymer concentrations at high temperature. Rheological measurements by Li and coworkers12b show a weak and a strong gel regime depending on the equilibrium modulus scaling to the gel temperature or to the renormalized gel temperature. A recent simulation study proposes that a micellar phase connected by hydrophilic strands gives rise to a weakly interacting gel as opposed to a hydrophobic chain network at high temperature responsible for strongly interacting gels.18 It is known that the gel temperature, and the hot gel modulus, of aqueous MC materials depends on the process and process conditions used to synthesize the MC material;19 several water-soluble MC examples in this patent are reported to have gel temperatures between about 30 and 60 °C. In this context, understanding the macroscopic structure−property relation is fundamental to design novel MC gels with suitable properties to meet desired end-applications. In this study, we examine two MC materials with similar coarse-grain chemical structure parameters (e.g., MW and MeO DS). They are of

tissue culture polystyrene (TCPS) can harvest living cell sheets, which may be used for tissue reconstructions. 8 The combination of shear-thinning hyaluronan with MC (METHOCEL A15, The Dow Chemical Company, USA) produces a fast gelling (at body temperature), noncell adhesive, biocompatible, and injectable gel suitable for spinal cord injury repair.9 Recently, the Dow Chemical Company has developed an MC solution-based food supplement that when ingested by an individual forms a gel mass in the stomach and temporarily reduces the stomach void volume as well as caloric intake of the individual.10 Undoubtedly, the availability of different grades of MC that gel at a broad range of temperatures and biocompatibility enables them to be used in a wide range of biological applications. Cellulose, the raw material for MC, is the most abundant natural polymer on earth. Interestingly, cellulose is water insoluble even though the three hydroxyl groups per anhydroglucose unit (AGU) (Figure 1) are hydrophilic in

Figure 1. Chemical structure of the cellobiose repeat unit (1.4-linked β-D-glucopyranose).

nature. Historically, it has been accepted that the regular spacing of these hydroxyl groups along the chain enables the formation of inter- and intrachain hydrogen bonds and, ultimately, three-dimensional water-insoluble semicrystalline domains. However, the contribution of hydrophobic interactions on the insolubility of cellulose in water as postulated by Medronho et al. is currently under discussion.11 To break these hydrogen bonds, some of the hydrophilic hydroxyl (−OH) groups on the chain are replaced with hydrophobic methoxy (−OCH3) groups. The level of substitution is expressed as the degree of substitution (DS), defined as the mean number of −OCH3 groups (MeO) per anhydroglucose unit (AGU). A close look at Figure 1 reveals that the DS value can range from 0 to 3 mol MeO/mol AGU, and eight (8) unique MC repeat units are possible depending on the regio-selective (position and level of methoxy) substitutions. The number (N = 23n) of chemically distinct chains for any given number, n, of AGUs rises with n, and often reaches astronomical values for most commercial MC materials (100 < n < 4000). This clearly emphasizes the diverse and complex chain chemical structure of MC materials. While MC materials with low DS are insoluble due to their semicrystalline nature, materials with very high DS (DS → 3.0) are also insoluble due to their hydrophobic nature. To make MC chains water-soluble, a balance between the hydrophobic methoxy and hydrophilic hydroxyl groups in each repeat unit should be maintained. This is satisfied by an intermediate DS range. Therefore, most water-soluble commercial MC products have DS values ranging from 1.7 to 2.2. The current hypothesis is that the chemical composition of the high-molecular weight (200 < n < 4000) cellulosic ether chains is nonuniform along the chain backbone. The highly substituted chain portions are more hydrophobic, while the other portions are hydrophilic. According to an entropic argument, the hydrophobic chain portions (of MC) are 3356

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fractal dimension, D = 8/5. For even smaller length scales (q > 1/ξr), the scattering intensity varies as ∼q−1/υ, where υ is the classical excluded-volume exponent (υ = 3/5 in good solvent and 1/2 in a θ solvent). However, experimentally, the scattering intensity decays slower than predicted by eq 2a.23 To accommodate this difference, Burchard and co-workers23 introduced a cutoff function, and the fitting equation for 1/ ζc < q < 1/ ξr becomes a1 I1(q) = [1 + g (q)qrc/ 2 ] exp( −q2rc2/2) [1 + g (q)q2ζc2]

interest in that both are commercially important, and one material (MC2) was produced with an alternative process that has resulted in a much lower gel temperature (Tgel[MC1] − Tgel[MC2] ≈ 15 °C) and higher hot gel modulus.19 Small-angle neutron cattering (SANS) experiments provide new insight to their gel structure and contrasting thermal gelation performance.

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SANS BACKGROUND AND DATA ANALYSIS Case I: T < Tgel. Aqueous MC at pregel temperatures and concentrations above c* behave like polymer solutions in the semidilute regime. At low scattering vector, q [= (4π/λ)·sin(θ/ 2), where θ is the angle between the incident and scattered beam and λ is the incident neutron wavelength], the scattering intensity I(q) resembles a power-law relation followed by a shoulder at intermediate/high q values. Considering these two effects as independent contributors, the total scattering intensity profile can be expressed as a sum of three terms with five fit parameters. I(q) = aq−m +

I(0) + bgd (1 + q2ξr2)

(3)

where the expression for g(q) is given in eq 2b. The introduction of a new length scale, rc, physically represents the finite radius of polymer strands. At even higher length scales, scattering is observed from the soft gel or the concentration fluctuations of the thermally excited chains and can be expressed through an Ornstein−Zernike relation (for q > 1/ξr, I(q) ∼ q−2). A modified version of the “Coviello−Burchard”23 fitting routine was used by Lodge and co-workers13c while fitting SANS data from a thermoreversible MC gel (Metolose SM4000). While the low and intermediate q intensity data were modeled after eq 3, a Debye−Bueche term (for q > 1/ξr, I(q) ∼ q−4) was introduced to fit the high-q data. The selection of a Debye−Bueche term over an Ornstein−Zernike type of equation depends on the nature of the experimental data. From a physical point of view, the high-q (or smaller/local length scale) scattering should be associated with the concentration fluctuations of thermally excited chains (semidilute polymer solution like scattering) and represented by the Ornstein−Zernike equation [ I(q) ∼ q−2]. On the other hand, a highly phase-separated structure (evolved through gel formation) may lead to surface dominated high-q scattering (Porod scattering, where I(q) ∼ q−4), which can be modeled using the Debye−Bueche term. To overcome this conflict, a generalized high-q scattering term is proposed,24 which is given for q > 1/ξr as a2 I2(q) = d f /2 df + 1 ⎡ 2 2⎤ 1 q + ξ r ⎣ ⎦ 3

(1)

It includes a power-law term (aq−m), the Ornstein−Zernike relation,20 and a constant background term (bgd). The parameter a is a prefactor and the power-law exponent, m, is typically between 2 and 3 for mass fractal systems. The Ornstein−Zernike relation (2nd term) is a truncation of the series expansion for the Debye function; f(x) = (2/x2){x − 1 + exp(−x)}, where x = (qξr)2, after dropping terms of order O(q3). The parameter ξr is referred to as the polymer concentration fluctuation length. The concentration fluctuation length scale can be interpreted as the length scale of perturbations of the polymer chains. Beyond this length scale, the solution behaves homogeneously. I(0) is a thermodynamic term known as the zero-scattering-vector structure factor. Case II: T ≥ Tgel. Model 1. A scattering model for the largescale heterogeneity in randomly cross-linked networks was originally proposed by Bastide and Leibler.21 This model assumes that the effective interchain tie points (or network junctions) are statistically distributed in the solution matrix. When two such cross-linking nodes are adjacent to each other, a frozen blob is formed. Formation of such frozen blobs provides a topological constraint to the chains, and clusters are formed. For semidilute concentrations of high-MW polymers, high concentrations of cross-linking must be introduced to reach the blob percolation threshold and attain complete gelation. In this case, even below the gel point, strong crosslinking density inhomogeneities are observed. Thus close to and above the gel temperature, a new length scale appears, which is the frozen blob concentration correlation length (ζc) and ζc ≫ ξr. Scattering from such a system is given for 1/ ζc < q < 1/ ξr as

I(q) ≈

(

(

(2a)

where the crossover function is of the form: g (q) =

1 1 + (qζc)2 − D

(4)

where df is the fractal dimension associated with the structure represented by the high-q scattering (or polymer chains in solutions). For Gaussian chains, df = 2, and eq 4 represents the Ornstein−Zernike equation. In contrast, for df = 4, eq 4 becomes the Debye−Bueche term. Combining this approach with the Coviello−Burchard fitting routine,23 we propose to fit the SANS data at and above the gel temperature according to the following functional form (referred to as Model 1): a1 I(q) = [1 + g (q)qrc/ 2 ] [1 + g (q)q2ζc2] a2 exp( −q2rc2/2) + + bgd d f /2 df + 1 ⎡ 2 2⎤ 1 q + ξ r ⎦ ⎣ 3

φζc D 1 + g (q)q2ζc 2

)

)

(5)

Further, Model 1 (eq 5) has two scaling factors (a1 and a2), three length scales (ζc, rc, and ξr), and two fractal dimensions D (embedded in the g(q) term) and df. Here ζc is the gel correlation length or the blob size (the average length scale between two adjacent network junctions), and ξr is the

(2b)

At the limiting condition q→0, eq 2a approximates I(q = 0) ∼ φζDc . Analogy with the percolation cluster theory22 predicts the 3357

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Table 1. Properties of MC Materials and Aqueous Solutions sample

DS (mol MeO/mol AGU)

Mwa (kg/mol)

Mw/Mn

T(G′ = G″) c (°C)

η0 (20 °C)d (Pa·s)

T(pinf) (°C)

Rga (nm)

Lpb (nm)

|G*(60 °C)|c (Pa)

[η]e (mL/g)

MC1 MC2

1.827 1.897

526 ± 8.2 410 ± 6.9

4.23 ± 0.02 3.73 ± 0.2

53.0 34.5

26.5 ± 1.0 12.0 ± 1.0

57.4 43.6

75.2 ± 0.4 63.8 ± 0.4

13.6 13.0

546 4090

1071.4 ± 5.5 925.9 ± 14.1

a Data from size exclusion chromatography (SEC) measured with refractive index, differential viscosity, and multiangle laser light scattering detectors on dilute aqueous solutions. (Detail in Supporting Information). bCalculated with the Kratky−Porod chain model and SEC data. cMeasured at 1.5 wt.% MC in D2O at 0.5 Hz while warming at 1 °C/min. dMeasured at 1.5 wt.% MC in D2O. eMeasured in water at 28 °C, and used to estimate c* (=1/[η]) for the same materials in D2O

concentration fluctuation length. To reduce the number of fitting variables and attribute a physical meaning to the third length scale, after Lodge and co-workers,13c we also assumed that rc = ξr.13c This assumption also provides the compatibility of scattering from two different length scales and guarantees the continuity of the scattering intensity over the entire experimental q range. Further, the D and bgd parameters are also held constant. The first fractal dimension, D, can be obtained independently from the low-q scattering data where intensity varies as I(q) ∼ q−D. Therefore, the fitting parameters are reduced to two length scales (ζc and ξr), two scaling factors (a1 and a2), and one fractal dimension (df). Model 2. This model considers cross-links that evolved during gel formation, restricts the free movement of polymer chains, and builds up regions of excess polymer concentration.25 Therefore, the total concentration fluctuations (which provide the scattering contrast) can be approximated by the sum of two parts: a dynamic and a static part. The dynamic part arises from the solution-like matrix and can be represented by using an Ornstein−Zernike-like expression. The static component is assumed to have the form of stretched exponential: exp(−qsΞs), where Ξ is the mean length scale associated with static nonuniformity (or the gel) and s (stretched exponential coefficient) is a positive constant. The parameter s depends on the nature of the network structure and is ∼0.7 for a randomly cross-linked gel (e.g., poly(vinyl acetate) in toluene)25b,26 or ∼2.0 for an end-linked gel (poly(dimethyl siloxane)).25c,27 Further, as discussed previously, polymer solution-like asymptotic behavior at high q is not always found, and a generalized high-q scattering term (eq 4) is often used. Incorporating this generalized term, a second functional form (referred to as Model 2) used to fit our data is given as I(q) = I1(0) exp( −q s Ξs) +

I2(0) ⎡ ⎣1 +

(

df + 1 3

⎤ q2ξr2 ⎦

)

d f /2

temperature and high hot gel modulus. Note that the intrinsic viscosities ([η]) for these samples are comparable. On the basis of the [η], the calculated chain overlap concentrations (c*) are 0.093 and 0.108 wt% for MC1 and MC2 grades, respectively. More details about the process used to prepare them may be found elsewhere.19 The samples were selected for their similar molecular weights (Mw) and degrees of substitution (DS) as reported in Table 1. Solution Preparation. All (rheological, NMR, and SANS) studies were performed on 1.5 wt % MC solutions prepared in D2O. The solution concentration (c = 1.5 wt %) for both MC1 and MC2 is ∼15 times stronger (c/c* ∼ 15) than their chain overlap concentration. The MC powders were used as received. Before use, the powder was dried overnight in a vacuum oven at 70 °C in order to eliminate any residual absorbed water. About half the volume of D2O needed for the given solution (1.5 wt % here) was introduced into a clean glass vial. The vial was warmed on a hot plate with stirring (propeller type magnetic stirrer) until the D2O temperature exceeded about 70 °C. The MC powder was then introduced with stirring into the hot solvent. The MC powder/hot solvent slurry was stirred for another 5 minutes before diluting with the remaining room-temperature D2O to reach the target concentration. After addition of all D2O, the solution vial was placed in an ice bath with stirring until the temperature approached about 0 °C and the solution was optically clear. The vial was capped and stored in a refrigerator (at 4 °C) for 24 h to complete hydration. SANS. SANS measurements were performed at the NG3 30 m SANS beamline28 at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR) in Gaithersburg, MD. An incident neutron wavelength (λ) of 8.403 Å was used for all measurements. Three different sample-to-detector distances (SDDs) of 1.33 m, 4.0 and 13.0 m were utilized, which cover a scattering vector range of q = 0.001−0.3 Å−1 [q = (4π/ λ)·sin(θ/2), where θ is the angle between the incident and scattered beam]. At the longest SDD (13.0 m), a lens configuration was used for beam collimation, whereas for the other SDDs standard pinhole collimation was used. At 1.33 m SDD, the detector was offset to increase the accessible high-q range. The MC solutions were allowed to equilibrate at 4.5 °C in a refrigerator at the NCNR for at least 48 h before SANS measurements. The solutions were loaded into quartz microcylindrical cells (NSG Precision cells Type 31, 22 mm o.d., 19 mm i.d., 5-mm path length) with graded seal tubes (overall height approximately 92 mm) using a syringe with hypodermic needle. To minimize evaporation (and any change in solution concentration) during the high temperature measurements, a small amount of low-viscosity silicone oil was placed on the top of the MC solutions. Finally, the cell stem was covered using plastic NMR tube caps. A circulating water bath was used to control the temperature of the 10CB (a 10 position sample changer with circulating bath temperature control system) sample block. The temperature-dependent SANS study was performed at comparable T− Tgel values for the MC1 and MC2 samples, where T is the measurement temperature and Tgel is the respective gel temperature. The SANS measurements were started at the lowest temperature. The temperature was increased in a stepwise fashion between measurements. The heating rate was not directly controlled and was later calculated from the time-temperature log. The nominal heating rates during a temperature change were 0.5 °C/min. At each temperature, an equilibration time of 20 min was imposed to allow the sample to

+ bgd (6)

We note that for both Model 1 and 2, the equation parameters depend on the how the gel is formed and treated after the preparation. The parameters used in these models, especially the gel correlation lengths (ζc and Ξ), concentration fluctuation length (ξr), and the fractal dimension of the polymer chains in solution (df) are directly comparable.

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MATERIALS AND METHODS

MC Preparation. All the MC samples used in this study are either of commercial grade or made in the laboratory following the commercial manufacturing process. Commercial samples are manufactured by The Dow Chemical Company under the trade name of METHOCEL brand cellulose ethers.5b Two different MC samples, referred to as MC1 and MC2, respectively, were prepared from ground cellulose pulp. MC1 is the material with a high gel temperature and low hot gel modulus, whereas MC2 is the material with the low gel 3358

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Automated-Temperature-Ramp Nuclear Magnetic Resonance (ATR-NMR). Sample Preparation. MC NMR samples were prepared by weighing the desired amount of polymer into an 8-mm NMR tube. Warm D2O (at approximately 80 °C) was measured into the tube, and the mixture was agitated using a vortex mixer (Fisher). The resulting suspension of polymer in heavy water was allowed to cool slowly by placing it in an insulated cup containing warm tap water. Occasionally, the sample was removed from the warm water and further agitated on the vortex mixer. This sequence was repeated until the polymer had dissolved or the suspension no longer settled due to the increased viscosity of the sample. The sample was then placed in a lab refrigerator at approximately 5 °C for at least 12 h before use. Before being placed in the NMR magnet for measurement, a capillary NMR tube containing a small amount of silicone pump oil was placed inside the 8-mm tube. The signal from this silicone oil was used as a quantitation reference for the ATR-NMR experiment. Data Collection. NMR spectral data were collected using a Varian 8-mm gradient inverse-detection probe with a 600-MHz Varian Inova NMR spectrometer. Sample temperature was controlled by the Inova’s built-in Varian L900 temperature control unit. Spectral collection, temperature control, and experimental timing delays were all controlled by the spectrometer using VNMR 6.1C. The temperature ramp was programmed in one of two methods. The first method used the VNMR array feature to collect 81 spectra. The temperature variable in VNMR was arrayed from 10 to 90 to 10 °C in 2 °C increments. Using this method, a minimum preacquisition delay time (pad) of 5 min was required between each temperature jump for reliable synchronization between data acquisition and the temperature of the probe. The second method used a series of MAGICAL30 programs to initiate and automate the data collection. This method eliminated the timing requirements imposed by the array method; however, for the data presented in this report, the preacquisition delay is still set to 5 min. A set of 600-MHz 1D proton NMR spectra were acquired during the warming and cooling ramps; there is one spectrum for each of the 81 temperature set points. Each spectrum was composed of eight transients with 10 seconds between each 90° pulse. NMR Data Processing. Each spectrum was automatically phased and baseline corrected by the VNMR command string ‘aph bc’ as the second argument to the dliarray program. Baseline and integral zero points were set to integrate the regions 5.4 to 3.675 ppm, 3.675 to 2.09 ppm, and 1.65 to −0.985 ppm. The raw integrals were imported into an Excel spreadsheet for the calculation of % association (p). % Association (p) Calculation. The MC % association (p) for each temperature was ultimately calculated as the ratio of observed NMR integral to the expected NMR integral for the MC polymer: p(T) = 100 × Observed Integral(T)/Expected Integral(T). However, before this ratio can be computed, corrections to the raw MC integral must be performed. To correct for the temperature dependence in the tuning of the NMR probe, the raw integral was normalized to the integral obtained for the reference silicone oil signal (which had first been corrected for changes to the density of the silicone oil) using the following expression: Observed Integral(T) = Raw Integral(T)/ [Silicone Oil Integral(T)/Density(T)]. The expected integral for the MC was calculated from data obtained over the range of 10 to 90 °C using a 1.5 wt % sample of sucrose, which had been referenced to the same silicone oil-filled capillary. Probe Temperature Correction. The probe temperature was corrected using a 5-mm sample tube containing neat ethylene glycol inserted into an 8-mm NMR tube using dimethyl sulfoxide (DMSO) as a heat transfer fluid. The temperature was determined from the chemical shift difference of the two resonance lines of the ethylene glycol using the Varian tempcal command.

reach a constant temperature. We note that this thermal equilibration time may be insufficient for the gel structure to reach equilibrium. The thermal equilibration time was adequate to deliver an average and maximum temperature variation during the SANS measurement time of ±0.4 and ±2 °C, respectively. The reported temperature is the average temperature attained during the measurements. In order to check the thermo-reversibility of the gelation process, after the highest temperature measurement, the sample holder was quickly connected to another circulating bath temperature controller preset to the lowest measured temperature. Adequate equilibration time was allowed before repeating the lowest temperature SANS measurement. Details of low-temperature data reproducibility are presented in the Supporting Information. At each temperature, counting times of 4500, 1500, and 300 s were used for the SDDs of 13.0, 4.0, and 1.33 m, respectively. Transmission measurements were made for the open beam and the aqueous MC materials at each temperature. The recorded two-dimensional (2D) data were corrected for empty cell and parasitic background scattering. The background corrections were made from a blocked beam measurement, and Jacobian corrections due to curvature of the detector were made from an isotropic scattering file (Plexiglas). All data were placed on an absolute intensity scale using an attenuated empty beam. Further, the 2D data were reduced to one dimension (intensity vs q) by circular averaging of the 2D patterns using software29 available from the NCNR. The total scattering intensity is composed of a coherent component and an incoherent component. Only the coherent scattering contains information about the structure of the sample, as it arises from the interference of scattered waves over a large correlation volume. For SANS (or elastic scattering), the incoherent scattering (arising from uncorrelated motion of individual atoms) does not contain information on interference effects and forms a flat background. To remove the incoherent scattering background, the high-scatteringvector data (q > 0.2 Å−1) are assumed to follow a linear relationship in q4I(q) against q4 coordinates: q4I(q) ∼ Bq4 + A. Subtraction of the constant B from I(q) yields incoherent-background corrected data. All fits of the experimental scattering to models discussed below were performed using the IGOR Pro (Wavemetrics, Inc.) based data analysis software/macro available from the NCNR.29 Rheology. Small-amplitude oscillatory shear flow measurements were used to probe thermoreversible gelation of aqueous MC solutions while warming as well as the redissolution (melt back) of these gels while cooling. The data were collected using a straincontrolled Rheometric Fluids Spectrometer (RFSIII) with Couette (cup and bob) fixtures between 5 and 90 °C while warming/cooling at ±1 °C/min. The Couette geometry was preferred over parallel-plate geometry to minimize solvent evaporation at elevated temperatures. The key Couette fixture dimensions were: 34 mm i.d. for the cup, and 32 mm o.d. and 33.33 mm height for the bob dimensions. The bob had a convex cone bottom and was fabricated in-house. About 3 mL of a low density water-immiscible polydimethylsiloxane oil (3 cSt, 0.898 g/mL, 550 g/mol, flash point = 100 °C, Clearco Products Company) was layered/floated over the aqueous solution by disposable pipet after the solution level rose above the bob top to minimize solvent evaporation at elevated temperature. The oscillation frequency during the thermal ramp was held at 0.5 Hz (π rad/s). The amplitude of oscillatory studies was selected to be sufficiently low to be in the linear viscoelastic regime. The amplitude selections were based on a set of amplitude sweeps on freshly prepared fully hydrated MC solutions at three temperatures (20 °C, gelation onset temperature, and 90 °C) for each sample. For the oscillatory flow measurement, the data can be reported as complex shear viscosity (η*) and complex shear modulus (G*). Interconversion of these parameters (G*= −iωη*, where i = √(−1)) are straightforward and involve the angular frequency (ω). These complex quantities can be written in terms of their real and imaginary parts: η*= η′ − iη″ and G* = G′ + iG″. Here, both the real (G′) and imaginary (G″) components of the modulus are reported as a function of temperature. The real and imaginary part of the modulus, G′ and G″, are also known as the shear storage and shear loss modulus, respectively.

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RESULTS AND DISCUSSION Thermoreversible Gelation of MC: Rheological Measurements. Small-amplitude oscillatory flow studies have been widely used to probe gelation for many types of associating materials.5c−e,13c,31 Small-amplitude oscillation minimizes the perturbation of the chains and/or the network from their 3359

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Figure 2. Temperature dependence of the shear storage modulus (G′) (rheology data, red curves) and % association, p, (NMR data, black curves) for a 1.5 wt % (a) MC1 and (b) MC2 solution in D2O warmed (solid lines) and cooled (dotted lines). For a 5 to 90 to 5 °C thermal ramp (with ramp rate ±1 °C/min), the rheological data were collected at every 0.1 °C temperature interval and at a frequency 0.5 Hz. ATR-NMR data were collected from 10 to 90 to 10 °C in 2 °C increments. The reported plots are constructed by drawing line segments between adjacent points; symbols (filled circles for G′ and filled triangles for p) are marked on the points for clarity. The plots show that temperature-dependent upturn (in heating ramp) and downturn (in cooling ramp) in both G′ and p coincides in these two different measurements. G′ data for MC2 sample during the cooling cycle has not been reported since the collected data were erroneous (for details please see the discussion in text).

(mostly T > ∼ 60−65 °C), the rate of growth slows. The origin of slower growth is not well understood. It could stem from approaching a maximum-associated state analogous to the isothermal curing of the thermosets.32 Alternatively, it could arise from a change in the gel microstructure at that temperature range. Further, for the MC2 sample (Figure 2b), around T ∼ 60 °C a maximum in G′ is observed in the heating curve. The sharp decrease in G′ at temperature range ∼65−80 °C is not well understood, and is suspected to be an artifact since this portion of the curve does not reproduce very well. The suspected origin of this decrease may be due to a partial/ complete loss of contact between the gel and the concentric cylinder fixtures as the gel dimensions contract and syneresis appears. Therefore, cooling cycle rheological data are not reported for this sample. The upper temperature range of the study is limited to around 90 °C to minimize excessive water loss from the solution when approaching the solvent boiling point. During the cooling cycle, a clear hysteresis is observed, which suggests that the system never reaches thermal equilibrium in the gelled state. It also indicates that the dissociation in the MC gel−sol transition is not an exact reversal of the association process. It is worth noting that for associating polymers, Rubinstein and Semenov suggested that besides binding energy there is an additional potential energy barrier related to the dissociation, and it restricts the process.33 By contrast, the hysteresis may simply be due to the inhomogeneity of the water (or D2O) when cooling from a hot gelled/syneresis state. The inaccessibility of the syneresed water domains to all the gelled material may contribute to slowing the gel dissolution rate when cooling. Similarly, the higher MC concentration of the gel in water after syneresis occurs at hot temperatures may contribute to slowing the gel dissolution rate when cooling. A crossover temperature during the cooling cycle is also found, which is generally lower than the same observed during the heating cycle (Figure S1, Supporting Information). In the lowtemperature regime, for MC1 T < ∼ 25 °C, the heating and cooling curves superpose, confirming minimal solvent loss and the thermoreversibility of the process. Other interesting features revealed from these rheological measurements are the enhanced gel properties displayed by the MC2 sample. As a

equilibrium configurations. In Figure 2, the shear storage modulus (G′) obtained from temperature sweep test for different 1.5 wt % MC solutions in D2O are presented. Initially, at low temperature (5 °C), G′ < G″ (the temperature dependence of both G′ and G″ are shown in Supporting Information, Figure S1) which confirms the expectation that this system is liquid-like (at 0.5 Hz frequency). With increasing temperature, the G′ slowly decreases, reaches a minimum at a temperature referred to as T(G′min), and then rises rapidly as the aqueous MC material gels. The rate of decrease of G′ at pregel temperatures parallels that of the viscosity of water (not shown); this dependence is not surprising since the fluid is 98.5% water. It is possible, after Haque and Morris,5c the decrease of G′ with increasing T may also arise from melting out of low-temperature self-assembled structure analogous to globular protein unfolding prior to network formation. The temperature at which G′ is minimum, T(G′min) is one of the many metrics of the onset of gelation. Further, upon heating, G′ exceeds G″, and this crossover temperature is an important rheological metric marking gelation (reported in Table 1 and also shown in Figure S1, Supporting Information). From the data, it is evident that gelation occurs at much lower temperatures for MC2 compared to the MC1 aqueous solution. The rheological gel temperatures (the crossover temperatures) are 53.0 and 34.5 °C for the MC1 and MC2 samples, respectively. Besides the crossover temperature, other rheological metrics, such as temperature for minimum G′ value in G′ versus T data, T(G′min), temperature for the inflection in the post gel G′ versus T data, and so on, are also considered to define the Tgel of MC solution. In our case, all these different metrics convey a gel temperature in the same ballpark of the crossover temperature indicating that the crossover temperature (even when temperature sweep data were collected at a fixed frequency, 0.5 Hz) is also a reasonable metric to determine the onset of gelation. At postgel temperatures, G′ increases with temperature and G′ > G″. In this regime, the system is considered to be a soft elastic solid or gel. However, a close examination of the slope of G′ value with temperature (i.e., d(log G′)/dT) shows two distinct regions. Initially, just above the T(G′min), the G′ value increases rapidly, and after a certain temperature is reached 3360

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Figure 3. Incoherent background-corrected temperature-dependent scattering profile (intensity as a function of scattering vector) at selected temperatures for 1.5 wt % MC, (a) MC1 and (b) MC2 solutions in D2O. As temperature increases, a clear transition from solution to gel is evident through the change in scattering profile. The error (±one standard deviation) in measurements of SANS intensity is less than the size of the markers used unless explicitly shown using error bars.

the MC1 and MC2 samples are also presented in Figure 2. The major temperature-dependent features related to sol−gel transition, such as upturn in G′ or p occurs at almost the same T, change of slopes with temperature (i.e., d(log G′)/dT or dp/dT), hysteresis during the cooling cycle, and finally complete reversibility at low temperature are markedly similar. This observation clearly confirms that NMR measurement can successfully probe thermoreversible gelation of aqueous MC solution. A close look at Figure 2 reveals that p values start at a nonzero value at cold temperatures, and show an initial decrease in association as a function of temperature followed by a rapid increase in association beginning at approximately 55 and 35 °C for MC1 and MC2 gels, respectively. The association shows an inflection at higher temperature and then plateaus at approximately 95% association due to the presence of a small sol (soluble) MC component. The nonzero cold-temperature association indicates that some fraction of MC is associated even at 10 °C. The meaning of this result is not well understood. The solution at this condition is optically clear and homogeneous. Some portion of the chains may have intramolecular associations that may persist at any MC concentration; another portion of the chains may associate into dimers, trimers, and so on since the data were measured at a concentration (1.5 wt %) well above the critical association concentration (20−50 ppm) of these aqueous materials. Further, the extent of associated chains is higher for MC2 (% association 56.2) compared to MC1 (% association 40.0) at 10 °C. The cooling (meltback) curve shows a significant hysteresis but eventually reaches the starting association level at 10 °C. For the MC2 sample, the association is not completely reversible at the ramp rate chosen due to kinetic effects. A sigmoidal function is fit to the heating data, and the inflection point, T(pinf) is assigned as the gel temperature (Tgel) and reported in Table 1. These temperatures are later used to renormalize temperature scale of the SANS measurements. We mention that (unlike rheological measurements) ATR-NMR technique does not distinguish between intra- and interchain association, and only interchain associations are thought to be relevant for the formation of network junctions. A systematic bias exists between the independent metrics of the gelation temperature probed by rheology and NMR at low concentrations. This difference is often observed to be minimized at

very simple and crude measure of the gel strength, we compare the complex modulus (|G*| = √[(G′)2+(G″)2] for different samples at the same absolute temperature. From the heating curve data |G*| values at 60 °C are found to be ∼545 Pa and ∼4100 Pa for MC1 and MC2 gels, respectively. It should be noted that the rheology of MC solutions in D2O is characteristically the same as observed for the H2O solutions (not displayed). However, the gel temperatures are typically about 3 to 4 °C higher for 1.5 wt.% solutions in H2O, and the solution viscosities in H2O are about half those in D2O. Thermoreversible Gelation of MC: ATR-NMR Characterization. Metrics of macroscopic phase separation such as turbidity, cloud point, and rheological measurements are limited by their nonlinear response to the thermal event. These methods are also not directly sensitive to the underlying chemistry or chemical structure. An ATR-NMR technique has been developed as a molecular probe to directly measure the extent of associative processes. Applied to aqueous MC materials, it probes inter- and intramolecular association at any given temperatures. One can imagine that the level of association will be altered by the phase separation process, so additionally it can be used as a metric of gelation and/or precipitation during a thermal cycle. The data shown in Figure 2 illustrates this use. Moreover, the thermal cycle data compares well to that of rheological metrics of the gelation process. The NMR approach is especially valuable in that one always obtains complete S-curves during the thermal ramp study of the gelation (and/or precipitation) process; it is not limited by loss of contact to the sample container at high temperature as found for some materials (MC2) with high-levels of syneresis. The technique yields quantitative data relating the extent of immobilizing associations or cross-links. As the MC sample is heated, the polymer solidifies as a gel or precipitates, resulting in an increase in the line-width for the protons that are in a local region of low mobility.34 For solid precipitates or glassy gels (on the NMR time scale of 600 MHz), this results in a complete loss of signal in the solution NMR spectrum for the portion of the polymer that has experienced the loss of mobility. Previously, Haque and Morris also utilized NMR signal to study heat-induced gelation and subsequent dissociation on cooling for an aqueous A4M (Dow Chemical Company) solution.5c For direct comparison with rheological data, the fully processed ATR-NMR data (% association, p) for 3361

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Figure 4. Kratky representations of the SANS intensity data at selected temperatures for (a) MC1 and (b) MC2 samples. Scattering from sol does not show any peak. After gelation, MC1 gel exhibits a clear gel peak, whereas MC2 gel exhibits two distinct peaks. Gel peaks are denoted by arrows.

scattering intensity by the square of scattering vector, a higher weighting factor is assigned to the intermediate q range intensities, and the relative importance of low q as well as high q scattering is diminished.37 Such a representation is helpful in identifying the sol−gel transition since the scattering from a gel has a peak, whereas that from a sol does not.24,38 In Figure 4a, the Kratky representation of the MC1 scattering data shows peak arising due to gel formation at q ∼ 0.008−0.01 Å−1 (above Tgel). The peak is broad in nature, indicating high dispersity associated with the characteristic size scale of the gel structure. More interestingly, for the MC2 gel, the Kratky representation of scattering intensity clearly exhibits two distinct peaks at q ∼ 0.007−0.02 Å−1 and at q ∼ 0.04 Å−1. This result indicates that two different length scales are present in the aqueous MC2 gel at postgel temperatures. Further, the peak in MC1 appears to shift, albeit slightly, toward higher q at the highest temperatures (T > 60 °C). For MC2, the low-q peak tends to move toward higher q values as temperature rises, or equivalently the characteristic length scale associated with this structure decreases with temperature. However, the position of the high-q peak is preserved for all temperatures. At this point it is arguable whether only the MC2 sample exhibits two length scales or two length scales are also present in MC1, but the second length scale is concealed by greater heterogeneity present in the system. This idea can be verified by performing SANS on contrast matched systems, where scattering signals (as a function of T) from deuterated methoxy (−OCD3) substituted (full or partial) and protonated (−OH) unsubstituted parts can be tracked independently. In the absence of such experimental evidence, we treat MC1 gel as having one characteristic gel length scale while the MC2 gel possesses two characteristic gel length scales. Extension of the SANS Models. The Kratky representation of scattering data showed one length scale for MC1 as opposed to two distinct length scales for the MC2 sample. During the model fitting exercise, MC1 data are fitted using a single gel length-scale model as presented in eq 5 (Model 1) and eq 6 (Model 2). For the MC2 sample, an extension of those models is used where an additional term accounting for the second characteristic gel length scale is introduced. The equations used to fit these data are For Model 1:

much higher concentrations (c/c* > 8) when interchain entanglements dominate the intrachain associations. Thermoreversible Gelation of MC: SANS Study. Temperature-Dependent SANS. The scattering intensity, I(q), as a function of scattering vector (q) collected at selected temperatures is illustrated for each MC material in Figure 3. All data have been reduced and corrected according to the experimental SANS section. A close look at the figures reveals the following salient points: (a) For any given MC sample and temperature, the scattering profile does not show any discernible sharp scattering peak in the experimental q window over the temperature range studied. Instead, broad shoulders/ humps are observed, which are more typically associated with disordered systems. (b) Second, for T < Tgel, the scattering profiles are almost independent of temperature. As the sample temperature increases toward the gel temperature, a change in the scattering intensity profile is encountered. In an intermediate q region (q ∼ 0.005−0.05 Å−1) a broad shoulder/hump (or, a weak peak) in the intensity profile develops. This shoulder arises from the presence of a characteristic gel length scale assumed to arise from blob/ cluster formation. Hence, following the temperature dependence of the SANS intensity profiles, a clear transition from semidilute polymer solution scattering to gel scattering can be observed. (c) The transition from solution-like to gel-like scattering occurs at lower absolute temperature for the MC2 sample compared to the MC1 sample. (d) Finally, in the low-q region in the experimental window, the scattering intensity never reaches a q-independent plateau value, which clearly suggests the presence of a larger spatial inhomogenity (or length scale), which is presently inaccessible through the q range covered by the SANS. Physically, an aqueous solution of MC becomes turbid upon heating indicating the presence of length scales comparable to the wavelength of light. Further, in the low-q region (q ∼ 0.001−0.005 Å−1), the slope of I(q) versus q is independent of T, suggesting that the fractal dimension of the larger length scale is independent of temperature. Such a temperature (and also concentration) invariant, large-scale fluctuation was previously reported for MC gel,13c polyelectrolytes,35 and self-assembled oligoelectrolytes.36 In the future, ultrasmall-angle neutron scattering (USANS) or optical microscopy experiments can be utilized to probe this length scale. To emphasize the shoulder observed at intermediate q, a “Kratky plot” (q2I(q) vs q) is prepared. By multiplying the 3362

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Figure 5. Nonlinear fits of eq 1 to (a) MC1 and (b) MC2 SANS data. Deconvolution of eq 1 into the power-law component (dashed line) and the Ornstein−Zernike component (solid line) are also shown. In this representation, the “bgd” term is added with the power-law component. Fitting parameters are reported in Table 2.

a1

I(q) =

[1 + g1(q)q2ζc12]

Table 2. Fit Parameters for the MC1 and MC2 Materials at Pregel Temperatures Based on Eq 1a

[1 + g1(q)qζc2/ 2 ]

exp( −q2ζc22/2) +

a2 [1 + g2(q)q2ζc22]

T (°C)

exp( −q2ξr2/2)

[1 + g2(q)qξr / 2 ] a3 + + bgd d f /2 df + 1 ⎡ 2 2⎤ 1 q + ξ r ⎦ ⎣ 3

(

)

(7a)

T− Tgel(NMR) (°C)

10.9

46.5

20.6

36.8

35.4

22.0

5.8

37.8

15.0

28.6

where, for i = 1−2: gi(q) =

1 1 + (qζci)2 − Di

(7b)

Here a new length scale ζc2 and the corresponding fractal dimension D2 are introduced. Any length scale is connected hierarchically to the next length scale through the cutoff function, which provides scattering continuity and compatibility. The fitting parameters in eqs 7a and 7b are three length scales (ζc1, ζc2 and ξr), three scaling factors (ai, i = 1−3) and two fractal dimensions (D2 and df). Note that between single (eq 5) and two-gel length scale models (eqs 7a- and 7b), the characteristic gel length scale (ζc or ζc1), gel fractal dimension (D or D1), Ornstein−Zernike, or concentration fluctuation length scale and fractal dimensions (ξr and df, respectively) are the same and comparable between MC gels. For Model 2, using a similar extension approach, eq 6 can be rewritten as

I3(0) ⎡ ⎣1 +

(

df + 1 3

⎤d f /2 q2ξr2 ⎦

)

MC1 7.4 × 10−6 ± 3.9 × 10−8 7.8 × 10−6 ± 4.0 × 10−8 9.3 × 10−6 ± 4.8 × 10−8 MC2 1.05 × 10−5 ± 6.1 × 10−8 1.26 × 10−5 ± 7.5 × 10−8

I(0) (cm−1)

ξr (Å)

0.096 ± 0.001

19.0 ± 0.2

0.11 ± 0.001

22.0 ± 0.3

0.18 ± 0.002

31.0 ± 0.4

0.37 ± 0.004

40.0 ± 0.3

0.67 ± 0.008

52.0 ± 0.4

Error reported to ± one standard deviation; all the length scales are reported to their nearest integer value.

a

of the scattering intensity is a much stronger function compared to the Ornstein−Zernike relation (∼q−2). To minimize the effect of the power law exponent, m, on independent determination of the concentration fluctuation length (ξr), the value of m was fixed at 2.4. This value is obtained from the slope of I(q) versus q in the low-q regime (0.001 Å−1 < q < 0.005 Å−1). It is evident from Table 2 that with increasing temperature, ξr increases. Over a more limited temperature range (for the same T−Tgel) the MC2 sample shows a higher concentration fluctuation length compared to MC1. The increase in ξr with temperature is expected as the thermal fluctuations become enhanced at higher temperatures. As the system approaches the critical point (Tgel), all the fluctuation length scales associated with the system are expected to diverge. (T > Tgel). Both Model 1 (eq 5 for MC1 and eqs 7 for MC2) and Model 2 (eq 6 for MC1 and eq 8 for MC2) were used to fit the SANS data above the gel temperature. The Model 1 fits to the SANS data at representative temperatures (Figure 6a,c) along with examples of the deconvoluted independent contributors to the total scattering intensity (Figure 6b,d) are presented. Similar plots for the Model 2 fits are shown in the Supporting Information (Figure S4). A slight mismatch between the experimental data and the model fit is found at low q. This is because these models assume that, beyond the largest length scale (ζc or Ξ for MC1 and ζc1 or Ξ1 for MC2), the system behaves homogeneously without any spatial

I(q) = I1(0) exp( −q s Ξ1s) + I2(0) exp( −q s Ξ 2 s) +

a (cm−1)

+ bgd (8)

Here Ξ2 represents the second gel length scale. The power-law coefficient, s, remains the same for both gel length scales, since it depends on the nature of the gel formation process, not on the length scale hierarchy.25 SANS Fitting. (T < Tgel). The scattering profiles at low temperature (or before the gel formation) were fitted using eq 1. Representative fitting with deconvolution of the overall fitting into the Ornstein−Zernike function and power law contributions are presented in Figure 5. The fitting parameters for the MC1 and MC2 samples at different temperatures are tabulated in Table 2. Generally, the observed power law decay 3363

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Figure 6. (left: a,c) Fits of scattering data for the (a) MC1 and (c) MC2 samples to Model 1 at selected postgel temperatures. (right: b,d) The fits for each term in the model are shown for a selected postgel temperature. The temperature was selected such that each aqueous MC material is at a comparable T−Tgel condition. MC1 data are modeled with a single gel term (eq 6). Two gel terms (eq 7a) are used to model MC2 SANS data. The error (±one standard deviation) in measurements of SANS intensity is less than the size of the markers used unless explicitly shown using error bars.

Table 3. Characteristic Gel Length Scales for the MC1 and MC2 Materials at Postgel Temperatures Obtained from Model 1 and 2 Fitsa MC1

a

MC2

T (°C)

ζc (Å) model 1

ζc (Å) model 2

T (°C)

ζc1 (Å) model 1

ζc1 (Å) model 2

48.0 53.0 55.5 57.9 63.0 75.2 89.9

1029.0 ± 13.0 1056.0 ± 15.0 1071.0 ± 6.0 1094.0 ± 2.0 1163.0 ± 14.0 1149.0 ± 13.0 1092.0 ± 12.0

1037.0 ± 17.0 1029.0 ± 2.0 1019.0 ± 14.0 1081.0 ± 13.0 1078.0 ± 26.0 1078.0 ± 23.0 1049.0 ± 14.0

27.0 30.3 32.3 34.8 37.3 42.3 54.9 69.8 88.9

1046.0 ± 19.0 807.0 ± 12.0 767.0 ± 11.0 688.0 ± 14.0 611.0 ± 15.0 544.0 ± 9.0 515.0 ± 15.0 468.0 ± 1.0 450.0 ± 5.0

970.0 ± 50.0 684.0 ± 18.0 640.0 ± 15.0 727.0 ± 20.0 604.0 ± 3.0 573.0 ± 2.0 535.0 ± 4.0 487.0 ± 5.0 494.0 ± 3.0

ζc2 (Å) model 1 139.0 137.0 130.0 155.0 147.0 118.0 203.0 200.0 234.0

± ± ± ± ± ± ± ± ±

5.0 0.4 3.0 4.0 0.5 2.0 2.0 3.0 0.5

ζc2 (Å) model 2 219.0 ± 36.0 129.0 ± 3.0 125.0 ± 2.0 150.0 ± 3.0 139.0 ± 1.0 155.0 ± 1.0 215.0 ± 3.0 177.0 ± 2.0 151.0 ± 1.0

Error reported to ± one standard deviation; all the length scales are reported to their nearest integer value.

(s ∼ 2.0 in that case). The same s values were obtained previously for a randomly branched poly(vinyl acetate) gel network swollen in toluene.25b,26 Rheological and NMR data revealed that the gel temperatures differ between these samples. For the MC1 sample, using the NMR method, the gel temperature is 57.4 °C, whereas the gel temperature for MC2 is substantially lower (43.6 °C). To account for the difference in Tgel, structural parameters for MC1 and MC2 samples are compared using a renormalized temperature scale: (T − Tgel)/Tgel and presented in Figure 7. The characteristic gel length (ζc) for MC1 is found to increase slightly as T approaches Tgel and then decreases slowly above the Tgel. However, the temperature dependent variation for this length scale is relatively small (compared to the MC2 gel, discussed next), and the average value of this length scale is ∼1090 ± 50 Å. This finding is in close agreement with previous SANS work performed by Lodge and co-workers13c on

correlation, therefore the scattered intensity reaches an asymptotic limit as q → 0. Different characteristic gel length scales, obtained from Model 1 and Model 2 fittings, are presented in Table 3. The reported data show that the agreement between different length scales extracted using these two model fits is quite good. Because of agreement found between returned parameters for Model 1 and Model 2; only the parameters obtained from Model 1 fitting are used in the remaining discussion of the temperature dependent gel structure. However, it is interesting to note that, using Model 2, satisfactory fits are obtained with a stretched-exponential coefficient s ∼ 0.7. This finding is in agreement with the expected broad-spectrum of nonuniformities (network junctions) originating from random crosslinking.25b,26 For a network developed through a site percolation process, the spatial distribution of network junctions is expected to deviate from a Gaussian distribution 3364

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Figure 7. Renormalized temperature representation of the (a) characteristic gel length scales, (b) fractal dimension associated with gel structures, (c) concentration fluctuation length scale (ξr), and (d) fractal dimension associated with ξr. The error (±one standard deviation) in model fit parameters is less than the size of the markers used unless explicitly shown using error bars.

Metolose SM-4000 gels where they reported an average gel length scale of ∼1200 Å, which is independent of temperature. This length scale is perceived to be the average blob size or the chain length between two adjacent network junctions. For the MC2 sample, the equivalent length scale (ζc1) below Tgel is ∼1000 Å and progressively tends to decrease approaching the Tgel. Further, above the gel temperature [i.e., (T − Tgel)/Tgel > 0], it reaches a limiting value of ∼450−500 Å. Comparing the temperature-dependent length scale fluctuation in MC2 (ζc1), the equivalent length scale in MC1, ζc, can be considered almost temperature invariant. For the MC2 sample, primarily below and vicinity of the Tgel, a drastic change in ζc1 is observed, which appears to plateau off above the gelation. This observation suggests that the densification of gel structure (for T ≤ Tgel) may be an outcome of the incipient gelation where close to the critical temperature (Tgel) drastic changes in gel structure take place. Alternatively, it may be argued that this effect is a manifestation of the chain collapse events that are typically encountered well beyond the Tgel for this system. Note that the sharp decrease in G′ data for the MC2 gels occurs at much higher temperature, T ∼ 65 °C, or at a fully developed gel state. Similarly, the % association, p, value, calculated from the NMR signal, approaches a plateau value (p ∼ 95%) at T ∼ 60 °C. Presently, the SANS experiment is inconclusive regarding the chain collapse at high temperature. However, one would have expected a major change in high-q scattering, reflecting the chain collapse, as the individual chain fractal dimension would have changed for that event. We do not observe any such effect in our high-q scattering profile. Undoubtedly, single-chain experiments, using deuterated MC chains should be conducted to look for chain collapse. In the

absence of such experimental data, we cannot conclusively declare whether the chain collapse is responsible for gel densification close to and above the Tgel observed here. The second characteristic gel length (ζc2) (Figure 7a) for the MC2 sample is about 150 Å. Above Tgel, a slight increase in ζc2 with increasing T is observed. The concentration fluctuation length scale, ξr, for both MC1 and MC2 samples, initially increases with temperature and then becomes independent of temperature at postgel temperatures (Figure 7c). This length scale arises from the thermal concentration fluctuations of the polymer chains. Before gelation, ξr increases as the thermal perturbation increases monotonically with T and all the fluctuation length scales tend to diverge approaching the critical point (Tgel). Beyond that critical point; the concentration fluctuation length attains a maximum and is pinned to a constant value (arrested motion due to gel formation). The constant value is found to be higher for the MC1 (∼75 Å) compared to the MC2 sample (∼60 Å). The fractal dimensions associated with the gel structures, D for the MC1 gel and D1 for the MC2 gel, were held constant at 2.4 during fitting to reduce the number of fitting parameters. This value is different from the theoretical prediction (percolation cluster theory predicts D = 1.6) or experimental findings of Lodge and co-workers13c for thermoreversible Metolose SM-4000 MC gelation (D = 1.8) or Coviello and Buchard’s23 findings on exopolysaccharide gels (D = 1.6 ± 0.2). Syndiotactic polystyrene (SPS) gels38 in different organic solvents exhibit fractal dimensions between 2 and 2.5. A percolated network of carbon nanotubes in low-MW PEO and different epoxy matrices also exhibits a fractal dimension between 2.2 and 2.5.39 Fractal dimensions between 2 and 3 3365

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The physical origin of the second length scale (ζc2), found in MC2 gel is less clear. This length scale is of the order of the persistence length of the MC2 chains. Further, the fractal dimension, D2, associated with this length scale steadily decreases with increasing temperature, and at postgel conditions it becomes ∼1.4, which approaches the rigid rod fractal dimension (1.0). However, beyond this similarity, there is no further experimental proof available to identify the physical origin of this structure. As discussed before, a second length scale may be present in MC1 sample as well but overshadowed by the existing structural heterogeneity associated with ζc length scale. Another possibility is that in MC2 sample, the two length scales represent the hydrophobic and hydrophilic parts of the MC chains, respectively. In the future, this hypothesis can be verified by studying temperaturedependent SANS in contrast matched gels. To the best of our knowledge, no previous study on MC gel has reported a length scale that is of the same order of magnitude as ζc2. However, recent cryogenic transmission electron microscopy (cryoTEM) imaging of MC gels (samples annealed at 65 °C for 30 min followed by transfer to the TEM grid and subsequent vitrification of structure under cryogenic condition), reported by Lodge and co-workers, revealed a fibrillar structure with a fiber width of 150 ± 20 Å.41 Note that these images are collected for MC gels with Mw ∼ 300 000−400 000 g/mol, similar to our systems, but at a much lower concentration (∼0.2−0.4 wt %). It will be interesting to extend the cryo-TEM study to a much more concentrated (c > 10 c*) MC gel. The scattering prefactors (a1, a2 or a3 in Model 1 or I1(0), I2(0), etc. in Model 2) are a collection of parameters including scattering contrast factor, number density, and volume of a single scattering particle. They can be expressed as ai(L−1) = Γ(L−3) × (Δρ)2(L−4) × V2P(L6), where Γ is the number of scatterers per unit volume, (Δρ) is the scattering contrast, and VP is the volume of a scattering particle. In the absence of exact information about the shape of the individual scatterer, we assume it to be spherical. For a characteristic gel correlation length or blob size, ζc or ζci, the number of such blobs present per unit volume (Γ) can be estimated as Γ ≈ ai/[(Δρ)2 × {(4π/3) × (ζci/2)3}2]. The contrast factor used for this calculation is the difference between the neutron scattering length densities (SLDs) of the MC and solvent, D2O. The neutron SLD for D2O is 6.33 × 10−6 Å−2. The neutron SLD for MC1 and MC2 polymers are calculated as 1.24 × 10−6 and 1.23 × 10−6 Å−2, respectively. The major assumption associated with the above calculation is that the whole blob is considered an individual scattering particle. More rigorously, inhomogeneities exist inside the blob as the scattering power of the network junctions (or the polymer rich domains) is higher (and much smaller in size) than the connections between the junctions. There is also a contribution to the scattering signal from the contrast between randomly substituted and nonsubstituted parts of a single MC chain. This contribution is completely ignored here. Nevertheless, for both samples, these frozen blob Γ values (associated with length scale ζc and ζc1 for the MC1 and MC2 gels, respectively) are calculated and plotted as a function of renormalized temperature (Figure 8). At similar distance away from their respective gel points [or at the same (T − Tgel)/Tgel], the number density of frozen blobs for MC2 is an order of magnitude higher than for the MC1. The Γ calculated for the smaller length (ζc2) of MC2 (data not shown) is almost 3 orders of magnitude higher than the Γ calculated for the larger length scale (ζc1).

represent a mass fractal system. Interestingly, a decrease in the ζc2 fractal dimension, D2, with increasing temperature is observed for the MC2 gels (Figure 7b). Close to and above the Tgel, D2 becomes ∼1.4, indicating a stretched structure. The fractal dimension, df, associated with ξr is shown in Figure 7d. As discussed earlier, the df value should lie between 2.0 (Ornstein−Zernike relation for Gaussian chains) and 4.0 (Porod scattering for phase separated structure). Previously, most of the authors found df to be constant. For example, Lodge and co-workers13c used a value of 4.0 (based on high-q scattering profile), anticipating a phase-separated structure for MC gels; Horkay and co-workers found that a df value 2.0 works well for poly(vinyl acetate) gels in toluene;25b,26 Shibayama and co-workers24 reported a df value between ∼2.6 and 2.8 for poly(vinyl alcohol) gel in water. The deviation from the Ornstein−Zernike relation was attributed to the presence of hydrogen bonding.24 We found for both MC gels, the df value gradually increases from 2.0 to 4.0 with increasing temperature. This observation clearly demonstrates that with increasing temperatures, as the gel forms and starts to grow, an increasing degree of phase separation takes place. This phaseseparated structure leads to an increase in surface area, and well above the postgel temperature, the surface scattering dominates the high-q scattering. Physical Interpretation of Gel Length Scales and Structure−Property Relation. Previously, applying rubber elasticity theory20 to rheological measurements, Sammler and co-workers showed that network junctions in MC1 gels are separated by their chain entanglement molecular weight (Me), which is 23000 g/mol for aqueous MC materials at 1.5 wt % .40 A similar Me value (27 500 g/mol) was previously reported for Metolose SM-4000 by Li and co-workers.5a MC chains can be considered as worm-like polymer chains. Such polymer chains, due to their stiff backbone, show negligible fluctuations along the contour of the chain and locally (at small length scale) behave like a rod. The rod-like behavior of polymer chains is described by their persistence length (Lp), which is 136 and 130 Å for the MC1 and MC2 samples, respectively. Moreover, for worm-like chains, the Kuhn length (b) is exactly twice the persistence length.20 As per the freely joined chain model, long polymer chains can be represented as an end-to-end attachment of Kuhn segments, where each segment has the same mean square end-to-end distance. Also the combined length of all the Kuhn segments is equal to the maximum end-to-end distance of the original polymer chain. The Kuhn length (b) is 272 and 260 Å for MC1 and MC2 polymer chains, respectively. A repeat unit in MC is 7 Å long, and the molar mass of each repeat unit of MC1 (with DS = 1.827) is ∼187 g/mol. Therefore, the molar mass of each Kuhn segment is (272 × 187/7) ∼ 7266.3 g/mol. Using this data, the number of Kuhn segments present between two network junctions (or equivalent to the Me) is calculated to be ∼3.2. By comparison, the number of Kuhn segments within the characteristic gel length scale for MC1 (ζc ∼ 1090 ± 50 Å) is equal to ∼ 3.8−4.2. Within the limits of measurement uncertainties, the SANS and rheological measurements are in quite good agreement and reveal that the gel length scale (ζc) for MC1 is consistent with the distance between network junction points, which is equal to the chain Me at pregel temperatures. A similar exercise cannot be performed for the MC2 sample since even at the lowest SANS experiment temperature (5.8 °C) the chains probably did not attain their low-energy fully expanded time-independent conformation in solvent. 3366

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strong function of the substituent distribution.2 Substituent distribution changes the aggregation tendency, which significantly affects the cellulose derivative solution behavior and later gel structure. In this study, the MC1 and MC2 materials were selected for their similar MW and DS values. This study clearly suggests that MW and DS are not complete descriptors of the MC gel properties, and other chemical parameters are necessary to understand the gel behavior completely. It is important to understand the distribution of the substituents along various hierarchical levels (within the glucose unit, along the polymer chain, and in between polymer chains) to obtain more descriptors that enable a differentiation between the samples based on chemistry. The main purpose of this study is to demonstrate that for the same MW and DS, the MC gel structure may be different (and thereby affect the hot gel modulus). The analysis of the differences in substituent distribution is an active area of research in our laboratory and will be treated in detail in a separate publication. Combining all the information related to the temperaturedependent macroscopic structure of MC gels, the MC1 gelation process is found to be in agreement with the gel formation route proposed by Li and co-workers.5a Below the gel temperature, in the semidilute concentration regime, MC chains overlap in solution, giving rise to an entangled system. As the temperature increases, the solvent (D2O or H2O)−MC chain interaction also changes, entangled physical cross-links phase separate from solvent, and network junctions are formed. However, during this thermal process, the polymer chain mean distance between network junctions is preserved and is equal to their entanglement molecular weight (Me). As the temperature increases, more and more of such structures are formed (described by Li et al. as the “hydrophobic effective unit”),5a which accounts for the increase in gel modulus. In other words, the gel structure is influenced by the low-energy, fully expanded, time-independent chain conformation in solvent. Tuning the solution state structure, the gel state structure and properties can be modified to accommodate end use performance. For the MC2 gel, close to and at the Tgel, two distinct length scales are formed. The characteristic length scales in MC2 gels are much shorter than the MC1 gel characteristic length scale. Presently, the physical interpretation of this second (smaller) length scale and its role in the gel rheological properties is still not clear.

Figure 8. Frozen blob number density as a function of the renormalized temperature. The error (±one standard deviation) is less than the size of the markers used unless explicitly shown using error bars.

The number density of frozen blobs exhibits two temperature-dependent regimes resembling the behavior of G′ as a function of temperature. Initially, close to the Tgel, the Γ increases rapidly with increasing temperature, and well above the Tgel the rate of blob formation slows down. This frozen blob number density is either too low or the blobs are too large in length scale to account for G′ values, which are in the range of 100−1000 Pa for these systems. However, such deviation is expected since only the network junctions present in the blob, not the entire blob, are actually responsible for the modulus. The network junctions are presumably orders of magnitude smaller than ζc or ζc1. Further, the modulus in polymeric systems depends on both the number of bonds (or network junctions) and bond strength (spring constant).The connectivity between the network junction points, i.e., the characteristic gel length scales, are much shorter for MC2 gels (ζc1 < ζc). As the spring constant of a bond varies with ⟨L−2⟩,42 the shorter gel length scale suggests a stiffer bonds. Moreover, as mentioned before, the smaller length scale (ζc2) found in this system (MC2) is of the order of the polymer persistence length, suggesting an extremely rigid structure with orders of magnitude higher number density. Thus a combined effect of higher number of network junctions and shorter connections between those network points are presumably responsible for the superior gel properties displayed by the MC2 gel. At this point, we have shown that even when the MW and DS of the MC1 and MC2 materials are very similar, their gel temperature and hot gel moduli are different, and the latter difference arises from the difference in the respective gel structures. According to an entropic argument, the hydrophobic parts of the chain aggregate/associate in water and phase separate at elevated temperature to form gel. The gel strength depends on both the number of network junctions as well as the distance between them. Therefore, the lower gel temperature and higher hot gel modulus in MC2 presumably arises from a different substitution pattern of MeO groups compared to MC1 materials. It is well reported in the literature that changes in the substitution pattern have a strong effect on the phase transition of the MC and other cellulose derivatives in water.43 Previously, using cellulose sulfate with similar DS and MW but markedly different substituent distribution, Clasen and Kulicke showed that the shear rate dependent viscosity is a

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SUMMARY Using rheology, ATR-NMR, and SANS measurements, we probe the structure of MC gels and try to understand their structure−property relations. Two MC materials were studied with similar coarse-grained chemical structure (DS, Mw) but with much different gelation performance (Tgel, G′(90 °C). One material (MC1: high Tgel; low G′(90 °C)) showed a characteristic gel length scale of ∼1090 ± 50 Å, which is relatively temperature independent with respect to MC2 gel length scales. This length scale is interpreted to be the distance between network junctions and is indistinguishable from the MC Me measured at pregel temperatures. By contrast, the other material (MC2: low Tgel; high G′(90 °C)), exhibits two distinct characteristic gel length scales. The larger of the two length scales decreases sharply as the temperature approaches Tgel and reaches an asymptotic limit after the gelation. Above the Tgel, this length scale is ∼450−500 Å, much shorter than the corresponding length scale for MC1. The smaller length scale in this sample is ∼150 Å in size. Presently, the physical 3367

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Viscoelastic Properties and Structure of Gels; Springer: New York, 1997; Vol. 130. (2) Clasen, C.; Kulicke, W. M. Determination of Viscoelastic and Rheo-optical Material Functions of Water-Soluble Cellulose Derivatives. Prog. Polym. Sci. 2001, 26 (9), 1839−1919. (3) Shibayama, M.; Tanaka, T.; Han, C. C. Small-Angle NeutronScattering Study on Poly(N-isopropyl acrylamide) Gels near Their Volume-Phase Transition-Temperature. J. Chem. Phys. 1992, 97 (9), 6829−6841. (4) Bromberg, L. Scaling of Rheological Properties of Hydrogels from Associating Polymers. Macromolecules 1998, 31 (18), 6148− 6156. (5) (a) Li, L.; Thangamathesvaran, P. M.; Yue, C. Y.; Tam, K. C.; Hu, X.; Lam, Y. C. Gel Network Structure of Methylcellulose in Water. Langmuir 2001, 17 (26), 8062−8068. (b) http://www.dow.com/ dowwolff/en/. (c) Haque, A.; Morris, E. R. Thermogelation of Methylcellulose 0.1. Molecular-Structures and Processes. Carbohydr. Polym. 1993, 22 (3), 161−173. (d) Haque, A.; Richardson, R. K.; Morris, E. R.; Gidley, M. J.; Caswell, D. C. Thermogelation of Methylcellulose 0.2. Effect of Hydroxypropyl Substituents. Carbohydr. Polym. 1993, 22 (3), 175−186. (e) Sarkar, N.; Walker, L. C. Hydration Dehydration Properties of Methylcellulose and Hydroxypropylmethylcellulose. Carbohydr. Polym. 1995, 27 (3), 177−185. (6) Chevillard, C.; Axelos, M. A. V. Phase Separation of Aqueous Solution of Methylcellulose. Colloid Polym. Sci. 1997, 275 (6), 537− 545. (7) Liang, H. F.; Hong, M. H.; Ho, R. M.; Chung, C. K.; Lin, Y. H.; Chen, C. H.; Sung, H. W. Novel Method Using a TemperatureSensitive Polymer (Methylcellulose) to Thermally Gel Aqueous Alginate As a pH-Sensitive Hydrogel. Biomacromolecules 2004, 5 (5), 1917−1925. (8) Chen, C. H.; Tsai, C. C.; Chen, W. S.; Mo, F. L.; Liang, H. F.; Chen, S. C.; Sung, H. W. Novel Living Cell Sheet Harvest System Composed of Thermoreversible Methylcellulose Hydrogels. Biomacromolecules 2006, 7 (3), 736−743. (9) Gupta, D.; Tator, C. H.; Shoichet, M. S. Fast-gelling Injectable Blend of Hyaluronan and Methylcellulose for Intrathecal, Localized Delivery to the Injured Spinal Cord. Biomaterials 2006, 27 (11), 2370−2379. (10) Adden, R.; Anderson, W. H.; Huebner, B.; Knarr, M. Methods and Compositions for Inducing Satiety. US Patent 0269711 A1, 2011. (11) (a) Glasser, W. G.; Atalla, R. H.; Blackwell, J.; Brown, R. M.; Burchard, W.; French, A. D.; Klemm, D. O.; Nishiyama, Y. About the Structure of Cellulose: Debating the Lindman Hypothesis. Cellulose 2012, 19 (3), 589−598. (b) Medronho, B.; Romano, A.; Miguel, M. G.; Stigsson, L.; Lindman, B. Rationalizing Cellulose (In)Solubility: Reviewing Basic Physicochemical Aspects and Role of Hydrophobic Interactions. Cellulose 2012, 19 (3), 581−587. (12) (a) Sarkar, N. Kinetics of Thermal Gelation of Methylcellulose and Hydroxypropylmethylcellulose in Aqueous-Solutions. Carbohydr. Polym. 1995, 26 (3), 195−203. (b) Li, L. Thermal Gelation of Methylcellulose in Water: Scaling and Thermoreversibility. Macromolecules 2002, 35 (15), 5990−5998. (c) Desbrieres, J.; Hirrien, M.; Ross-Murphy, S. B. Thermogelation of Methylcellulose: Rheological Considerations. Polymer 2000, 41 (7), 2451−2461. (d) Funami, T.; Kataoka, Y.; Hiroe, M.; Asai, I.; Takahashi, R.; Nisbinari, K. Thermal Aggregation of Methylcellulose with Different Molecular Weights. Food Hydrocolloids 2007, 21 (1), 46−58. (e) Li, L.; Shan, H.; Yue, C. Y.; Lam, Y. C.; Tam, K. C.; Hu, X. Thermally Induced Association and Dissociation of Methylcellulose in Aqueous Solutions. Langmuir 2002, 18 (20), 7291−7298. (13) (a) Guillot, S.; Lairez, D.; Axelos, M. A. V. Non-Self-Similar Aggregation of Methylcellulose. J. Appl. Crystallogr. 2000, 33 (1), 669− 672. (b) Bodvik, R.; Dedinaite, A.; Karlson, L.; Bergstrom, M.; Baverback, P.; Pedersen, J. S.; Edward, K.; Karlsson, G.; Varga, I.; Claesson, P. M. Aggregation and Network Formation of Aqueous Methylcellulose and Hydroxypropylmethylcellulose Solutions. Colloids Surf., A 2010, 354 (1−3), 162−171. (c) Kobayashi, K.; Huang, C. I.;

interpretation of this length scale is not clear. However, the smaller length scale shows negligible temperature dependence compared to the larger length scale and is of the same order of magnitude as the MC persistence length. For both gels, the polymer concentration fluctuation length diverges as the critical point Tgel is approached and reaches a constant value above Tgel. The formation and growth of the gel as well as the poorer solvent−polymer interaction at high temperature (T ≫ Tgel) arrest the local chain motions. The gel structures are mass fractal in nature with fractal dimensions of ∼2.4. Due to gel formation, phase separation takes place, which results in an increase in surface area. As a result, the fractal dimension of the polymer chains (concentration fluctuation length) progressively rises from about 2 (Gaussian chains in solution) at low temperature to about 4 (phase separated surface scattering dominance) at high temperature. Both rheological and ATR-NMR studies showed a lower gelation temperature for the MC2 gel. Further, rheological measurements show that MC2 materials exhibit higher shear storage modulus (G′) compared to MC1 materials when compared on a renormalized temperature scale (Supporting Information, Figure S2). An estimate of the number density of frozen blobs reveals that on a renormalized temperature scale, the numbers of blobs in MC2 gels are an order of magnitude higher than at the same renormalized temperature in MC1 gels. This observation signifies that in MC2 gels, there are more network junctions, and, further, the connections between the network junctions are much less flexible (as ζc in MC1 > ζc1 in MC2), or their bond energy is high. We conclude that the higher number density and stiffer connectivity between network junctions are presumably responsible for the higher gel modulus displayed by MC2 gels.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental sections on size exclusion chromatography, additional rheology and SANS data, and model 2 fit to SANS data are available in the Supporting Information. This information is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (T.C.); [email protected] (A.I.N.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.C. and A.I.N. acknowledge Dr. David Mildner, Dr. Paul Butler, and Dr. Boualem Hammouda for their help at the NG3 30 m SANS beamline at the NCNR. T.C. also acknowledges Dr. Steve Kline at the NCNR for help in model fitting to the experimental SANS data. This research was supported by Dow Wolff Cellulosics,5b a business unit of The Dow Chemical Company.

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REFERENCES

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