Letter Cite This: ACS Macro Lett. 2017, 6, 1274-1279
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Conformation of Methylcellulose as a Function of Poly(ethylene glycol) Graft Density Svetlana Morozova† and Timothy P. Lodge*,†,‡ †
Department of Chemistry and ‡Department of Chemical Engineering and Material Science, University of Minnesota, Minneapolis, Minnesota 55455, United States S Supporting Information *
ABSTRACT: Low molecular weight thiol-terminated poly(ethylene glycol) (PEG) (M ≈ 800) has been grafted onto a high molecular weight methylcellulose (MC, Mw ≈ 150000) by a facile thiol−ene click reaction; graft densities varied from 0.7% to 33% (grafts per anhydroglucose unit). Static and dynamic light scattering reveals that the overall radius of the chain increases systematically with graft density, in a manner in excellent agreement with theory. As the contour length remains unchanged, it is apparent that grafting leads to an increase in the persistence length of this semiflexible copolymer, by as much as a factor of 4. These results represent the first experimental verification of the excluded volume theory at low grafting densities, and demonstrate a promising synthetic platform for systematically increasing the persistence length of a model semiflexible, water-soluble polymer. length of MC is ∼8 nm,13,15,25 or about half the diameter of the resulting fibers, it has been suggested that the geometry of the structures depends on the folding mechanism and the stiffness of the polymer and, in particular, that the individual chains wrap around in toroidal or helical forms.3,6,8−13 Modifying MC stiffness promises to develop further insight on the folding mechanism of MC as well as provide an straightforward way to tune the strength of MC fibrillar networks. In this Letter, we demonstrate that the persistence length, lp, of 150 kg/mol MC can be systematically increased by grafting low molar mass thiol-terminated poly(ethylene glycol) (PEG) onto the MC backbone by aqueous thiol−ene click chemistry. Using dynamic (DLS) and static light scattering (SLS), we quantify the size and overall shape of the resulting copolymers as a function of grafting density, σ. We show that, in accordance with theory, the grafts effectively stiffen the MC backbone while the copolymer contour length and shape remain constant (Figure 1).16,18,31 These findings open a path to further investigation of grafting effects on MC polymer self-assembly. There are many possible synthetic approaches for grafting to MC.32−34 We have chosen thiol−ene click chemistry because of its reported ease and efficiency.35−38 MC (Mw ≈ 150 kg/mol, Đ ≈ 3.6, degree of methyl substitution, DS = 1.8) was provided by the Dow Chemical Company. The remaining reagents, including PEG with Mw = 800 g/mol and Đ < 1.1, were purchased from Sigma-Aldrich and used without further purification. PEG grafting densities were quantified by 1H
M
ethylcellulose (MC) is an abundant and sustainable cellulose derivative that enjoys an impressive range of consumer applications, from clinical excipients to construction materials.1,2 One of the most interesting and rheologically significant properties of MC is its ability to self-assemble into highly elastic fibrous networks, upon heating in aqueous solution.3−7 Interestingly, the detailed mechanism and internal structure of the fibrils is still an open fundamental question;8−13 further addition of relatively few hydroxypropyl groups, to produce hydroxypropyl methylcellulose (HPMC), suppresses fibril formation.14,15 Other straightforward chemical modifications to the MC backbone could also tune physical properties and thereby broaden the breadth of applications. For example, small molecular grafts are predicted to increase the stiffness of an otherwise flexible or semiflexible polymer.16−19 Increasing stiffness is expected to modify MC self-assembly, thereby enabling new application opportunities, and also could ultimately contribute to a more detailed understanding of the nature of MC fibril formation. MC is a chemical derivative of cellulose characterized by methoxy residues that substitute on average 1.5−2.0 out of every 3 hydroxyl groups along the backbone. MC is soluble in water at low temperature because the methyl groups disrupt inter- and intramolecular hydrogen bonds, but phase separation and gelation are observed upon heating.20−23 It is a semiflexible polymer in aqueous solutions.24,25 The property of fibril assembly is not unique to MC and occurs frequently in biological systems, for example, protein misfolding in diabetes and Alzheimer’s disease and structural protein assembly such as actin and collagen.26−30 Intriguingly, MC fibers are always ∼15 nm in diameter, regardless of the concentration, molecular weight, and temperature of formation. Since the persistence © XXXX American Chemical Society
Received: September 30, 2017 Accepted: October 28, 2017
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water and freeze-dried. The grafting density per monomer, σ, was calculated by integrating the MC hydrogen peak at 4.5 ppm, and comparing it to the PEG hydrogen peaks at 3.6 ppm (Figures 2d and S1 in Supporting Information). This synthetic method afforded a series of MC-g-PEG copolymers with grafting densities from 0.7−33% (Table 1 and Figure 2d). Table 1. Solution Parameters of MC-g-PEG Copolymersa NMR σ
Figure 1. Persistence length, lp, increases as a function of polymer graft density, σ, defined as number of grafts per anhydroglucose unit.
0 0.007 0.026
NMR analysis using a Bruker Advance III HD spectrometer with SampleXpress. First, remaining hydroxyls along the MC backbone were allylated in 1 M NaOH. Different molar quantities of allyl bromide were added to a 1.6 wt % MC solution, from 0.1 to 4 mol/mol hydroxyl groups of MC. The solution was left to stir at room temperature overnight, neutralized with 1 M HCl, and precipitated in acetone. The reaction does not go to completion during this time, but the stoichiometric imbalance results in different degrees of allylation of MC, as shown in Figure 2. Percent allylation was quantified by integrating the MC hydrogen peak at 4.5 ppm and comparing it to the allyl hydrogen peaks at 5.25 and 6 ppm (Figures 1b and S1 in Supporting Information).39 For these reaction conditions, the addition of 4 mol/mol allyl bromide: hydroxyl groups resulted in 28% allylation (gray line in Figure 2b, where % means fraction of allylated anhydroglucose rings along the backbone), and the addition of 0.1 mol/mol allyl bromine: hydroxyl groups resulted in 0.6% allylation (black line in Figure 2b). Allylated MC was redissolved in water with 5% mol/mol IRGACURE:MC and 3x excess thiol-ended PEG (Figure 2c). The samples were exposed to broadband UV light (254−365 nm) for 1 h while stirring, then dialyzed against
0.05 0.11 0.22
SLS σ 0 0.011, 0.018 0.03, 0.01 0.041, 0.041 0.28, 0.31
0.28 0.33
0.47, 0.5
Mw (kg/mol)
A2 (mol cm3/g2)
b
44, 43 47, 48
151 158, 163
49, 49, 50b 53, 51
170, 160
Rg (nm)
180, 180
χeff
ψ
0.0017 0.0008, 0.0013 0.0009, 0.0009 0.0007, 0.0008
0.444 0.475
0.03 0.02
0.475
0.02
0.479
0.01
55b 62, 59
330, 340
0.0006, 0.0006
0.485
0.02
67,b 70b 69, 68
450, 480
0.0007, 0.0008
0.484
0.03
a
Multiple entries are taken from two trials of Zimm plots shown in Figure S2. bRepresents data from Guinier plots.
To quantify the coil dimensions in solution as a function of grafting density, SLS measurements were taken on a Brookhaven BI-200SM instrument with a 5 mW laser for q=
2π n 0 λ
( θ2 ) ranges of 6.79−22.7 × 10
sin
6
m−1 (30−120°).
Here, n0 is the solvent refractive index and λ is the laser wavelength (637 nm). The samples were filtered through a 0.45 μm filter before analysis. The excess intensity (ΔRθ) in a static light scattering experiment depends on the polymer size (Rg), molecular weight (Mw), concentration (c), and solvent-
Figure 2. Chemical modification of MC to yield MC-g-PEG. (a) In the first step, the MC backbone is allylated in 1 M NaOH by the addition of allyl bromide. The mol/mol ratio of allyl bromide to hydroxyl groups controls the degree of allylation. (b) 1H NMR spectra after precipitation and dissolution of allyl MC. (c) In the second step, thiol-ended PEG is clicked onto the backbone allyl groups in water in the presence of the photoinitiator IRGACURE and UV light of wavelength 254−365 nm. (d) Subsequent 1H NMR analysis shows the appearance of PEG hydrogens. This synthesis results in a range of grafting densities from 0.7−33%. 1275
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ACS Macro Letters mediated interactions (A2). In a Zimm plot, Rg and 1/Mw are determined from the slope and intercept of the inverse intensity ( Kc ) vs q2 line, and the slope of the inverse excess intensity ΔR θ
versus concentration yields the second virial coefficient, A2.40 The optical constant K is equal to
2
( ddnc ) and depends on the N λ4
4π 2n02
A
refractive index increment
dn . For dc 13,41
MC,
dn dc
= 0.136 mL/g, and
for PEG, dn = 0.132 mL/g. For the copolymers, dn was dc dc calculated from the relative volume fractions of the backbone polymer and graft polymer. In a Guinier plot, Rg is calculated from the slope of the natural log of the excess intensity versus q2. DLS was measured at a 20 mW laser power for a q range of 1.31−2.27 × 107 m−1 (60−120°) in pure water after filtration with a 0.45 μm filter. Relaxation times were calculated using the Laplace inversion routine REPES for each angle.42 For a diffusive molecule in a solvent, the relaxation rate of the intensity−intensity correlation function is a linear function of q2.43 The slope gives the diffusion coefficient, D, which is related to the hydrodynamic radius, Rh, by the Stokes−Einstein equation.43−46 From the Zimm (Figure S2) and Guinier plots (Figure S3) we observe that Rg and Mw both increase monotonically as a function of grafting density, while A2 decreases slightly (Table 1). The increase in size is shown in Figure 3a as a function of the grafting density, σ. The increase in the molecular weight from 150 kg/mol to 450 kg/mol is due to the grafted PEG chains and is consistent with NMR determination of σ (Table 1). The increase in Rg from 44 nm for σ = 0 to 70 nm for σ = 0.33 is consistent with theoretical prediction. The free energy of a grafted coil is a sum of the free energy of the backbone and the excluded volume of the grafts with their respective interactions (Figure 3b):17−19,47,48
Figure 3. PEG grafts increase the size of MC due to excluded volume effects. (a) Rg from Zimm and Guinier plots as a function of the grafting density plotted against eq 2 (black line). (b) Schematic showing the possible excluded volume interactions in MC-g-PEG.
3R g2 v3R m3(σbN )2 v1a3N 2 v2V 3σbN 2 ΔF = + + + kBT 2Na 2 R g3 R g3 R g3
parameter, χeff, which is a measure of the copolymer-copolymer interactions relative to copolymer−solvent interactions, as49
(1)
2 ⎛1 ⎞ V ̅p ⎜ ⎟ A2 = − χeff ⎝2 ⎠ M 02Vs̅
where Rg is the radius of the copolymer, N is the number of statistical segments of length a, b is the number of anhydoglucose units per statistical segment length, v1a3 is the monomer−monomer excluded volume, v2V3 is the graftmonomer excluded volume, v3R3m is the graft−graft excluded volume, and R3m is the volume of a graft (Figure 3b). Minimization with respect to Rg leads to
(3) −1
where V̅ s is the solvent molar volume, equal to 18 cm mL , V̅ p is the polymer molar volume, equal to the volume fraction weighted average of MC (140 cm3 mL−1) and PEG (39 cm3 mL−1). M0 is the repeat unit molecular weight, equal to the volume fraction weighted average of MC (187 cm3 mL−1) and PEG (44 cm3 mL−1). χeff increases from 0.444 for 0 σ to 0.485 for 0.33 σ, that is, tending toward θ conditions with increasing graft density. Another way to interpret A2 is through a dimensionless “interpenetration parameter”, Ψ = 2A2M2w/(4π)3/2R3gNA. For linear chains, ψ increases from 0 for θ solvents to a constant value of 0.269 at good solvent conditions. For branched architectures, the local density increases relative to that in a linear chain, resulting in an increase in ψ. For MC-g-PEG the values of ψ are listed in Table 1. As a function of grafting density, ψ first decreases to 0.1 at σ = 0.05 and then increases to 0.3 at σ = 0.33, possibly due to both a change in the interactions between monomers and local density effects.50,51 One prediction of eq 2 is that, for low grafting densities, the radius scaling with molecular weight will remain unchanged at R ∼ N3/5. The Flory exponent, ν = 3 is equivalent to a swollen 3
1/5 ⎛ v3R m3 2 2⎞ v2V 3 R g = R 0 ⎜1 + bσ + b σ ⎟ ∼ R 0(1 + ασ )1/5 v1a3 v1a3 ⎝ ⎠
(2)
for which α is a prefactor that depends on the graft radius and excluded volume and R0 is the ungrafted polymer radius. eq 2 predicts that for small σ, the graft−backbone interactions dominate the increase in the copolymer size. The graft−graft interactions are quadratic in σ and do not contribute significantly to the size increase. In Figure 3a we plot the predicted radius as a function of σ against eq 2, with α as a fitting parameter (smooth curve). The experimental trend is captured nicely by the theory, with α = 26. From light scattering the second virial coefficient decreases with σ (Table 1). We can therefore estimate the effective χ
5
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density, the ρ values are around 1.9−2.1, which is consistent with disperse semiflexible polymers. We note that the slight upturn in this value at low grafting densities is consistent with lower A2 values, determined with SLS and with Franken and Burchard’s prediction that at higher grafting density ρ decreases due to an increase in local density.46 Lastly, since the contour length, L, remains fixed, we estimate the persistence length lp from light scattering measurement of Rg using the Kratky−Porod wormlike chain model:52
coil configuration. We assess this prediction by quantifying the graft copolymer shape, using the dimensionless ratio ρ = Rg/Rh as a metric. For Gaussian coils, ρ is expected to equal 1.5−1.7, depending on the molecular weight distribution.44−46 Burchard has summarized the effect of dispersity (Đ) on ρ. For Đ = 1.3, ρ increases to 1.6, and for Đ > 2, ρ asymptotes to 1.7. For monodisperse systems in a good solvent ρ is greater than 1.7 and can be estimated by a semiempirical equation:44 ρ=
6 (1 − v)(2 − v)(3π (1 + v)(1 + 2v))1/2
(4)
R g2 =
For disperse good-solvent systems, Burchard and Franken have estimated that the shape ratio is between 1.77 for monodisperse chains and 2 for disperse chains.44,45 We have measured the shape ratio by independently measuring Rg using SLS and Rh using DLS. For DLS experiments, the normalized intensity−intensity correlation functions g2 − 1 are plotted in Figure S4. As the grafting density increases, the relaxation time of the correlation functions increases (Figures S4 and S5). The diffusion coefficient is determined from the slope of the relaxation rate (Γ) as a function of q2, from which the hydrodynamic radius is found kT using D = 6πηB R , where η is the solvent viscosity.43 Rh is plotted
⎞ 2l 3 2lp4 ⎛ ⎛ L ⎞ 1 p lpL − lp2 + 2 ⎜⎜exp⎜⎜ − ⎟⎟ − 1⎟⎟ + 3 L L ⎝ ⎝ lp ⎠ ⎠
(5)
The calculated lp from eq 5 is shown in Figure 5. As grafting density increases, the chains stiffen due to excluded volume
h
in Figure 4a. Just like Rg (Figure 3a), Rh increases with σ, and ρ ranges from 1.5 to 2, consistent with chains in a swollen coil configuration (Figure 4b). At 0 = σ and at the lowest grafting
Figure 5. Calculated persistence length of MC-g-PEG as a function of grafting density.
interactions. At low grafting densities, however, the shape of the chains remain unchanged. This result is consistent with the calculation of persistence length. Even at the highest grafting density (σ = 0.33), for which lp = 30 nm, the contour length of 560 nm, calculated by assuming a monomer length of 0.7 nm15 and multiplying it by monomer number N = Mw/M0, is still much higher such that the stiffer polymer chains remain in the semiflexible regime. In summary, using a simple chemical grafting method we have systematically and substantially increased the stiffness of methylcellulose. The size scale of the resulting MC-g-PEG copolymer increases monotonically with grafting density, and is consistent with classical excluded volume theories. As the radius increases, the copolymer backbone stiffens but the shape, quantified by Rg/Rh, remains consistent with that of a semiflexible polymer. This approach is an intuitively appealing method designed to modulate the persistence length of methylcellulose, and possibly other relevant polymer systems. The self-assembly of MC chains into fibrous networks makes the polymer an extremely valuable consumer product. Modifying the stiffness is expected to influence chain folding, and represents a new parameter by which to systematically modulate MC fibril formation.
Figure 4. Summary of DLS of MC-g-PEG. (a) Rh plotted versus σ. (b) Shape factor Rg/Rh ranges from 1.5 to 2 for all grafting densities, consistent with good-solvent swollen coil configuration of the copolymers. 1277
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00776. Figures S1−S4 and extended Materials and Methods, pages S1−S6 (PDF).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Timothy P. Lodge: 0000-0001-5916-8834 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We would like to acknowledge NSF MRSEC (Award DMR1420013) for providing funding and Dow for generously providing the MC samples. Helpful discussions with Dr. Jukuan Zheng, Dr. Piril Ertem, and Prof. Theresa Reineke are appreciated.
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REFERENCES
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