Diffusion of Rodlike Polymers - ACS Publications - American Chemical

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Diffusion of Rodlike Polymers: Pulsed Gradient Spin Echo NMR of Poly(γ-stearyl-α,L‑glutamate) Solutions and the Importance of Helix Stability Cornelia Rosu,†,‡,§ Ernst von Meerwall,∥ and Paul S. Russo*,†,‡,§,⊥ †

J. Phys. Chem. B Downloaded from pubs.acs.org by TULANE UNIV on 12/05/18. For personal use only.

Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803, United States ‡ School of Materials Science & Engineering, §Georgia Tech Polymer Network, and ⊥School of Chemistry & Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ∥ Department of Physics, University of Akron, Akron, Ohio 44325, United States S Supporting Information *

ABSTRACT: Many natural and synthetic polymers and particles have a rodlike shape, leading to important and intriguing solution behavior, such as high intrinsic viscosities and liquid crystalline phases. Much of what is known about suspensions of rods has been learned by studying helical polypeptides, even though such molecules are not perfectly rigid, smooth cylinders. Previous optical tracer self-diffusion studies of poly(γ-benzyl-α,L-glutamate) (PBLG) revealed that the molecule initially resists topological constraints imposed by neighboring molecules, but diffusion strongly decreases as concentration rises beyond a certain number density. In contrast, the tracer self-diffusion coefficient of truly rigid tobacco mosaic virus begins decreasing immediately with concentration. We used pulsed gradient spin echo NMR to measure another polypeptide, poly(γ-stearyl-α,L-glutamate) (PSLG), to gain physical insight into the question of polypeptide diffusion in crowded isotropic solutions. The PSLG molecule, with long alkyl sidechains, is semiflexible like PBLG but does not exhibit the same ability to evade topological constraints. Instead, PSLG follows a simple exponential decay, D/DKR = A e(−κν/ν*) + B, where DKR is the Kirkwood−Riseman expectation for rod diffusion, ν is the number density of rods, ν* is the Onsager expectation for the number density at the onset of liquid crystal formation, A = 1 ± 0.1, B = 0.1 ± 0.01, and κ = 4.5 ± 0.5. The results emphasize the importance of helix stability when choosing rodlike polypeptides as model systems, particularly with regard to the chain ends.

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INTRODUCTION

predicted to drop by 50% because of loss of sideways motion.2,3 Model experimental systems have included rodlike viruses,6,7 DNA,8,9 mineral fibers,10 polyphenylenes,11 and cellulose nanocrystals.12 Helical polypeptides have played an important role because of their relatively high stiffness, good solubility in common solvents, and modest polydispersity.13−17 Nevertheless, the diffusion of helical polypeptides is poorly understood in relation to very stiff particles. In a previous study,6 this laboratory pointed out the striking difference between the most heavily studied of the rodlike plant viruses, which is tobacco mosaic virus (TMV), and the most heavily studied of the rodlike helical polypeptides, which is poly(γbenzyl-α,L-glutamate) (PBLG). The optical tracer self-diffusion of TMV begins to decrease immediately with concentration,

The diffusive transport of macromolecules governs many biological processes, including replication, viral infection, and network formation. Industrially, diffusion underlies the dissolution of polymeric solids for solution processing or its reverse, drying solutions to form a solid film. By relaxing entanglements that stabilize transient networks, diffusion also contributes to the viscoelastic response of polymeric systems. The diffusion of random flight polymers has received much attention, often associated with the entanglement concept.1 Rodlike polymers do not experience entanglement in the conventional sense, but topological constraints do diminish their transport in solutions.2,3 Understanding the transport of rods has special importance because many of them, particularly those with conjugated backbones and short sidechains, cannot be processed in melt form.4 Accordingly, a number of theoretical2,3 and computational5 studies have appeared. In the simplest treatments for thin rods, translational diffusion is © XXXX American Chemical Society

Received: September 13, 2018 Revised: November 19, 2018

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DOI: 10.1021/acs.jpcb.8b08974 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Table 1. Sample Name, Number-Average Molecular Weights, PDIs, Length and Predicted Diffusion Coefficients of PSLG Polymers sample name

Mn/kDa

PSLG-33000 PSLG-55000 PSLG-81000 PSLG-210000

33 ± 2.2 55 (±4c) 81 ± 1.4 210 ± 7.3

Đ ≡ Mw/Mn 1.08 1.04 1.19 1.09

± 0.10 (±0.04c) ± 0.03 ± 0.05

Lna/nm

DKRb/10−7 cm2 s−1

13.0 21.7 31.9 82.7

10.4 8.64d 7.10 3.90

Calculated by using the formula Ln = (Mn/Mo) × 0.15 nm, where Mo is the PSLG repeat unit molar mass, 381 g·mol−1, and 0.15 nm is the pitch, or spacing between the PSLG repeat units in the direction of the α-helix. bCalculated from Ln and d = 3.4 nm using eq 3. cEstimated uncertainty; other uncertainties measured by repeat GPC-MALS measurements. dDiffusion coefficient for PSLG-55000 was calculated for 36 °C, the measurement temperature for this sample; all other calculations were done at 30 °C. a

a ZnSe single crystal. Polymers were analyzed in the powder state. Gel Permeation Chromatography. The molecular weight of PSLG was measured by GPC−MALS. An instrument equipped with an Agilent 1100 solvent degasser, Agilent 1100 pump and Agilent 1100 autosampler, was used for separation. The column set was a 10 μm, 50 × 7.8 mm guard column and two Phenogel 300 × 7.8 mm columns from Phenomenex, Torrance, CA: (1) 10 μm, 105 Å (10−1000 kDa) and (2) 10 μm, MXM (100 Da to 10 000 kDa). A Wyatt Dawn DSP-F multi-angle light-scattering detector used a He−Ne laser. A Hitachi L-7490 differential index detector (32 × 10−5, refractive index full scale) served as a concentration detector. An injection volume of 100 μL was used for separation. The mobile carrier was THF (1 mL·min−1) stabilized with 250 ppm butylated hydroxytoluene. A value of 0.080 ± 0.002 mL·g−1 was used for the specific refractive index increment of PSLG in THF.25 NMR Diffusion Measurements. All measurements were performed in the wide-line proton resonance at 33 MHz, using either the principal Hahn spin echo with radio frequency (rf) pulse spacing τ = 20 ms or the three-pulse stimulated spin echo with τ = 15 ms and spacing Δ = 70 ms between the first and third rf pulse, hence also between the carefully matched pair of field-gradient pulses. Single-side-band phase-sensitive detection, offset by 3 kHz from the reference frequency, was followed by measurement of echo signal height A using integration across the echo after Hamming-filtered magnitude Fourier transformation with rms correction for magnitude baseline noise. The pulsed-field gradient magnitude, G, was 714.5 ± 3.5 G/cm. A steady-field gradient, Go = 0.3 G/cm, was also applied for convenience in data reduction. Gradient pulse length δ was varied in 5−20 steps between 0.026 and 1.4 ms, obtaining incremental echo attenuations between the original echo height Ao (for δ = 0) and the value δ(max) for which the signal/noise ratio fell below unity. Each measurement was averaged over six to ten repetitions. Most measurements were made at 30 ± 1 °C. A few extra measurements for PSLG55000 were performed at 36 °C. Details of the equipment and implementations have been described in earlier work.28 The echo attenuation is expected to follow the general form

whereas that of PBLG is initially at level with concentration but dives quickly as concentration rises above a particular value. TMV can be thought of as a hard cylinder with dimensions ∼300 × 18 nm.18 Although PBLG is often thought of as a cylinder too, it is thinner and more flexible than TMV.19,20 Also, even though PBLG was measured in a strongly helicogenic solvent, the probability of a chain segment being in the α-helical conformation decreases near its ends.21−23 If the chain ends assume the coil conformation, that may permit one chain to evade another, easing topological constraints to diffusion. The purpose of this paper is to shed further light on the translational diffusion of helical polypeptides in semidilute solutions. Pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) spectroscopy was used to measure self-diffusion of poly(γ-stearyl-α,L-glutamate) (PSLG). Its long, waxy sidechains confer good solubility in a wide variety of solvents, and the many protons provide a strong signal to dominate any residual protons in the deuterated solvents. PSLG exhibits only modest flexure even at the highest molecular weights studied here.24 The diameter of PSLG (3.4 nm)25 is about twice that of PBLG (1.6 nm),26,27 so it is expected to have a harder time evading topological constraints provided by other rods. If this hypothesis is true, we should expect the diffusion of PSLG to fall off more quickly with concentration than that of PBLG. This expectation is met, but the differences between the two polypeptides vanish at concentrations near the isotropic-to-liquid crystalline transition.

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MATERIALS AND METHODS Materials. PSLG was synthesized and characterized for molecular weight by gel permeation chromatography with multiple-angle light scattering (GPC−MALS) detection, as described elsewhere.25 Deuterated tetrahydrofuran-d8 (THF, ≥99.5 atom % D) was purchased in sealed ampoules from Sigma-Aldrich. Custom quartz tubes (L = 20 cm, o.d. = 0.5 cm) with a flat bottom were made in the glass shop. Sample Preparation. Solutions were prepared in 4 mL s c in t i l l a t i o n v i a l s e q ui p p e d w i t h a t i g h t p o l y(tetrafluoroethylene) cap seal. They were equilibrated at ambient conditions (∼1 week). Then, the solutions were transferred with glass pipettes into the quartz tubes and sealed by flame under reduced pressure. Each step was monitored gravimetrically. Fourier-Transform Infrared Spectroscopy. Synthesis of PSLG polymers was confirmed by the presence of the characteristic infrared adsorption bands. Spectra were obtained with a Bruker TENSOR 27 FTIR instrument equipped with a Pike Miracle single-bounce attenuated total reflectance cell and

A (X ) = Ao

2

∑ ai e[−γ D X ] i

i

with ∑ ai = 1 i

(1)

where ai represents the fractional amplitude of component i, γ is the proton gyromagnetic ratio, Di are the component diffusion coefficients, and X = δ 2G2(Δ − δ /3) + small correction terms in G ·Go (2) B

DOI: 10.1021/acs.jpcb.8b08974 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B Data reduction was performed by our Fortran routine DIFUS5K29 in its current version. The program derives the best fit of a postulated model, providing adjusted model parameters and their uncertainties. To account for biexponential echo profiles, the fraction f(fast) of the spin echo arising from the lower-M, faster-moving species reflects the relative concentrations weighted by the species’ spin−spin relaxation times (T2). Any slower-diffusing component is postulated to arise from polymer with a known Mn and polydispersity index (PDI) from GPC−MALS, which is incorporated in the model but not adjusted in the fit. The reference molecular weight is given as the number average Mn. The corresponding diffusivity distribution is based on a scaling M-exponent, in this case D ≈ M−1. and in our code, it was generated via a coordinated ensemble of ai and Di = D(Mi) in eq 1; nine M-fractions were sufficient to approximate the continuous distribution. Whenever the slow component’s echo signal or its attenuation was not measurable, the model reverted to a single (fast) component.

Figure 1. Typical echo recovery plot for PSLG in d8-THF showing biexponential character. Each measurement was averaged over six to ten repetitions. Error bars represent a single standard deviation; when smaller than the data point markers, they are not shown.

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RESULTS AND DISCUSSION Molecular weights and PDIs of the PSLG polymers used in this study were evaluated by GPC−MALS, and the results are summarized in Table 1. Selected GPC−MALS traces and Fourier-transform infrared spectroscopy (FTIR) spectra that confirm the synthesis of PSLG appear in the Supporting Information. Four polymers were considered: PSLG-33000 (Đ ≡ Mw/Mn = 1.08 ± 0.10), PSLG-55000 (Đ = 1.04 ± 0.04), PSLG-81000 (Đ = 1.19 ± 0.03), and PSLG-210000 (Đ = 1.09 ± 0.05). The determination of molecular weight values enabled the calculation of other essential parameters. For polypeptides, the rod length, L, can be computed from the molecular weight, M, as L = 0.15 nm × M/Mo, where for PSLG the monomer molecular weight, Mo, is 381 g/mol. The range of Ln was 13.0−82.7 nm, whereas that of Lw was 13.8−89.8 nm.25 The predicted diffusion coefficients of PSLG were calculated using the expression developed by Kirkwood and Riseman30 DKR = kBT ln(L /d)/3πηL

recovery (Figure 3). The fractional amplitude does not decline in the same manner for all molecular weights, though; we attribute this to variations in the amount of residual protonated solvent. The solvent likely experiences many environments from solvent-rich to solvent-poor in fast exchange. The decrease in the fast component diffusion coefficient with polymer molecular weight, as evident in Figure 2, suggests interaction between the solvent and PSLG, particularly its sidechains. Any solvent associated strongly with the PSLG would diffuse at the polymer rate for the duration of that association; when impeded by the larger polymers, the THF will diffuse more slowly. This impeded solvent interpretation is consistent with the decrease in the fast component selfdiffusion coefficient by a large amount, about an order of magnitude (Figure 2A). Various theories for solvent diffusion through non-interacting polymer solution have been summarized.34 A reasonable expectation would be that diffusion is reduced according to the volume occupied by polymer impediments: D = Do(1 − ϕ), where ϕ is the volume fraction of polymer. Thus, at our highest concentrations (20% by weight, which is also about 20% by volume), we might have expected a reduction of only ∼20% if the solvent were not entrained with the polymer. Alternative explanations for the fast contribution to the decay profiles were considered. Baldwin et al.35,36 developed a theory explicitly for PGSE of rodlike filaments; it adds terms to the usual Stejskal−Tanner analysis37 to account for end-overend rotation. For the measurement conditions and rodlike polymers used in the present study, these terms are negligible, so we ruled out end-over-end rotation as a contributor to our signals. Kanesaka et al. reported a fast component in PGSE recovery profiles measured during a study of the diffusion of poly(β-benzyl-L-aspartate) (PBLA), dissolved in deuterated chloroform. The primary goal of their study was to follow diffusion across the helix-to-coil transition, induced by the addition of trifluoroacetic acid (TFA). The fast component was observed at high TFA and therefore attributed to polymers in the random coil state. PSLG exists only as a helix in THF, and in any case, our fast-component diffusion coefficient is too high to associate with a polymeric diffuser regardless of shape. The slower echo attenuation recovery process (Figure 2B) is associated with PSLG self-diffusion. This assignment was

(3) 25

where d is the rod diameter, measured for PSLG at 3.4 nm, and η is the viscosity of the solvent. More accurate expressions have been critically evaluated,31 but eq 3 will suffice for our purposes. Any difference between the viscosity of deuterated and hydrogenated THF was ignored; viscosities were estimated using data for hydrogenated THF as η = 0.0044 and 0.0041 P for T = 30 and 36 °C, respectively.32 Solution concentrations were adjusted for the slight density difference between THF and d8-THF by assuming that the density of the latter (0.985 g/mL at 25 °C from the vendor) has the same temperature dependence as that of non-deuterated homologue (0.889 g/ mL at 25 °C).33 As shown in Figure 1, the PGSE signals were biexponential, characterized by fast and slow decay terms. Figure 2 shows the concentration dependence of the diffusion coefficient associated with each decay term, whereas Figure 3 shows the concentration dependence of the fast component amplitude relative to the total. We attribute the fast recovery to residual protonated solvent, based on the value of the associated diffusion coefficient (2−4 × 10−5 cm2 s−1) at low PSLG concentrations. This assignment is consistent with the overall decrease in the amplitude of the fast component term, expressed as a fraction of the total echo C

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Figure 2. Self-diffusion coefficients as a function of weight percent PSLG in THF from PGSE NMR showing (A) fast component decay and (B) slow component decay. Error bars to ln(D) supplied by the DIFUS5K program29 have been propagated to D.

Riseman theoretical expectations. At the same time, we follow ref 13 and scale the concentrations by a critical number density ν* = 16/πdL2

(4)

that represents the appearance of the liquid crystalline phase according to the theory of Onsager.38 The result displayed in Figure 5 shows that for all molecular weights, PSLG diffusion

Figure 3. Fast D-echo fraction for PSLG-33000, PSLG-81000, and PSLG-210000.

confirmed by the good agreement between PGSE and dynamic light scattering (DLS), which cannot detect the diffusion of solvent (Figure 4). Additionally, the PGSE data can be compared to the theoretical value expected from eq 3 using known parameters for PSLG rods, as described in Table 1. A convenient way to make the comparison is to normalize all measured diffusion data by their dilute-solution Kirkwood−

Figure 5. Slow self-diffusion coefficients normalized to DKR as a function of concentration from PGSE showing two trends.

starts near the expected Kirkwood−Riseman value. Thus, although rotation can cause PGSE NMR to return diffusion coefficients that are too high when measuring very long rods,35,36 our PSLG samples are short enough that the measured results conform to theoretical expectations in dilute solution. As concentration increases, the rate of diffusion declines smoothly, and the PSLG data (except at the lowest molecular weight) collapse to the same curve D/DKR = A e(−κν / ν*) + B

(5)

where A = 1 ± 0.1, B = 0.1 ± 0.01, and κ = 4.5 ± 0.5. Thus, in consideration of eq 4, by the time the number density, ν, reaches about one rod per volume, dL2, the diffusion coefficient, has declined by a factor of 1/e ≅ 0.4 or 40%. Petekidis et al. provided an exhaustive analysis and review of the transport of semiflexible polymers in an isotropic solution.11 The experimental part of their study concerned polydisperse substituted polyphenylenes with contour lengths well in excess of the estimated persistence length of ∼25 nm.

Figure 4. Diffusion of fast and slow components from PGSE NMR compared to DLS results for PSLG-55000 in d8-THF. Error bars for PGSE NMR data: similar to data point size. D

DOI: 10.1021/acs.jpcb.8b08974 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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helical polypeptides is not matched by the ease of synthesis of high-M samples. Thus, all available polypeptides exhibit only modest flexure. This problem confounds the precise measurement of persistence length, but most reported values exceed 70 nm.19,24 Concerning Figure 6, it is not the existence of a lowconcentration plateau that matters. This much is guaranteed for a log-scale plot provided the experiments can be conducted at sufficiently low concentrations (and without aggregation). The remarkable feature of Figure 6 is the sharing across varying contour lengths of a common “knee,” that is, a scaled concentration where diffusion begins to decline. It has been known for a long time13 that this knee exists even in a linear plot for the PBLG/pyridine system. As shown in the inset to Figure 6, it occurs at approximately ν = 0.2ν*. This linear representation, highlighting the lower concentrations, makes clear the difference between PBLG/pyridine and either TMV/buffer or PSLG/THF. There is no reason to accept aggregation as the cause of the quicker decline of both TMV and PSLG. TMV enjoys charge stabilization, whereas positive virial coefficients consistent with a reasonable rod diameter have been observed for PSLG/THF.25 There is also no reason to suspect the addition of a fluorescent tag altering the PBLG molecule; this possibility was considered at length by Bu et al. and ruled out.13 Nor is it likely that fluorescent labeling altered the TMV structure. It is therefore reasonable to assert that the tracer self-diffusion measurements and PGSE NMR measurements can be compared directly. Before suggesting a plausible explanation of the difference between the three systems, we return to the aforementioned work of Kanesaka et al., who used PGSE to study the diffusion in deuterated chloroform of PBLA, in the isotropic phase.14 PBLA is a polypeptide similar to PBLG, minus one methylene group in the sidechain. Although a wide range of concentrations was studied, using varying amounts of TFA to interrupt the helical segments, only one molecular weight (Mw = 59 900, corresponding to Lw = 44 nm) of a commercially available sample was used; therefore, it is not possible to tell whether the kind of scaling evident in our Figure 6 applies. Nevertheless, for PBLA in the helical form, the authors’ Figure 3 (a log−log plot of diffusion vs weight percent of PBLA) shows an initial decline with concentration, followed by a steeper slope that starts at ∼1 wt %. Using a diameter of 1.5 nm for PBLA, an estimated partial specific volume of 0.8 mL·g−1, and the density of deuterated chloroform (1.50 g/mL), this knee corresponds to ν ≈ 0.1ν*, about half the knee concentration observed for PBLG/ pyridine. We also briefly consider the work of Kuroki and Kamiguchi,16 who studied diffusion of PBLG in 1,4-dioxane using PGSE. In dilute solutions, these authors found values somewhat higher than predicted by the Kirkwood−Riseman expression (eq 3) but little reduction in diffusion at high concentrations in the isotropic phase, even though PBLG is known to aggregate in dioxane.40 The focus of the study was on diffusion in different phases, including oriented ones, and not on concentration dependence in the isotropic phase, so we do not consider it further. Of the three systems comparedPSLG in THF, PBLG in pyridine, and TMV in aqueous bufferonly PBLG in pyridine exhibits linear-scale plots featuring a long plateau with sharp turn-down shared by polymers at all lengths. This result is consistent with the idea that PBLG in pyridine is more adept at escaping “entanglements” than the other systems, as though

Accordingly, they considered terms ignored in the earliest theories of simple rods.2,3 Their eq 10 begins just as our eq 5 does, with a simple exponential decrease in diffusion coefficient with concentration, but adds terms for rotation, flexibility, hydrodynamic interaction, and the ability of the filaments to pass through “holes” in the topologically constrained assembly of semiflexible polymers. The lead term (κ in eq 5) is associated with a normalized excluded volume. Our experiments are silent on the other terms; they are not required to fit the available data. We now combine the PGSE results on PSLG with the optical tracer results from TMV6 and PBLG13 (Figure 6). Like

Figure 6. Diffusion coefficients reduced by values at zero concentration against number density, scaled by the critical number density, ν*, for TMV (ref 6), five samples of fluorescently labeled PBLG (molecular weights indicated, ref 13), and three samples of PSLG (this work). The measured diffusion coefficients were normalized by zero-concentration extrapolations (TMV and LPBLG) or by eq 3 (PSLG). Additionally, the LPBLG values are normalized by estimated solvent diffusivity reduction, a minor effect.

TMV in buffer, the diffusion of PSLG in THF begins to decline almost immediately with concentration. There is no extended plateau at low concentrations, as in PBLG/pyridine. On the other hand, whereas the diffusion coefficient of TMV in buffer declines to ∼50% before reaching the liquid crystalline phase, as predicted on the grounds of simple topological constraints to sideways motion,2,3 PSLG in THF declines to ∼10% of its initial value, much the same as PBLG/pyridine. This result invites comparison to work by Tinland, Maret, and Rinaudo,39 who studied diffusion of the polysaccharide xanthan in semidilute solutions. In particular, our Figure 6 calls to mind their Figure 5, a log−log plot in which xanthan diffusion coefficients scaled to their zero-concentration values are plotted against concentration scaled by an estimated overlap concentration. As in the PBLG results of Figure 6, the “knee” of the Tinland, Maret, and Rinaudo curve (where diffusion suddenly decreases) is shared by polymers having different contour lengths. Their experiments were performed at contour lengths well in excess of persistence length. In contrast to these xanthan macromolecules, our polypeptides have contour lengths shorter than, or sometimes comparable to, their persistence lengths. Though not rigid, they are quite stiff. There is little point to being more specific: the great stiffness of E

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The Journal of Physical Chemistry B the ends of the chain are not fully helical, as first suggested by Zimm and Bragg in their treatment of the helix-coil transition.21,22 This possibility is sometimes acknowledged in modern studies of polypeptides; for example, in a recent simulation of PBLG liquid crystals, the apparent length of spherocylinders representing PBLG was varied to take conformation into consideration.41 In their study of pHinduced helix-coil conformational transitions of surfacetethered poly(L-glutamic acid) (PLGA), for which PBLG is the progenitor, Adiga and Brenner included molecular dynamics simulations of the untethered PLGA that clearly show unmade helices at the end of the molecule.42 The question remains whether unmade helices at the chain ends can be distinguished from overall flexibility of the chains. Here we can put forth an argument based on a comparison of dynamics and thermodynamics. The studies of Miller and coworkers27 showed that PBLG displays a transition to the liquid crystalline phase beginning at a volume fraction, ϕ, consistent with the lattice Flory theory43 of rods: ϕ = 8/x(1 − 2/x), where x is the axial ratio, L/d. These studies were conducted on high-M PBLG samples. The phase boundary shifted slightly toward higher concentrations at higher temperatures, a sign of increasing flexibility. On the other hand, Kubo and Ogino44 studied shorter PBLG molecules. They found the onset of LC formation at ϕ ≈ 4/x, consistent with the Onsager theory.38 Yet the results of Figure 6 show that, dynamically, both short and long PBLG molecules exhibit similar behavior when the concentrations are scaled, as though the molecules share an essential feature for escaping entanglements: flexible ends because of unmade helices.

Paul S. Russo: 0000-0001-6009-2742 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Foundation Science Grant NSF DMR-1505105. C.R. acknowledges support from the Hightower Family Fund (Georgia Institute of Technology). The authors thank Dr. Rafael Cueto (Department of Chemistry, Polymer Analysis Laboratory, Louisiana State University) for help with GPC−MALS measurements. The authors acknowledge helpful comments by a reviewer.

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(1) McLeish, T. C. B. Tube Theory of Entangled Polymer Dynamics. Adv. Phys. 2002, 51, 1379−1527. (2) Doi, M.; Edwards, S. F. Dynamics of Rodlike Macromolecules in Concentrated Solution. Part II. J. Chem. Soc., Faraday Trans. 2 1978, 74, 918−932. (3) Doi, M.; Edwards, S. F. Dynamics of Rodlike Macromolecules in Concentrated Solution. Part I. J. Chem. Soc., Faraday Trans. 2 1978, 74, 560−570. (4) Kwolek, S. L.; Morgan, P. W.; Schaefgen, J. R. Encyclopedia of Polymer Science and Technology, 2nd ed.; Wiley: New York, 1987; Vol. 9. (5) Doi, M.; Yamamoto, I.; Kano, F. Monte Carlo Simulation of the Dynamics of Thin Rodlike Polymers in Concentrated Solution. J. Phys. Soc. Jpn. 1984, 53, 3000−3003. (6) Cush, R. C.; Russo, P. S. Self-Diffusion Of a Rodlike Virus in the Isotropic Phase. Macromolecules 2002, 35, 8659−8662. (7) Lettinga, M. P.; Barry, E.; Dogic, Z. Self-diffusion of Rod-like Viruses in the Nematic Phase. Europhys. Lett. 2005, 71, 692−698. (8) Scalettar, B. A.; Hearst, J. E.; Klein, M. P. FRAP Studies and FCS Studies of Self-diffusion and Mutual Diffusion in Engangled DNA Solutions. Macromolecules 1989, 22, 4550−4559. (9) Robertson, R. M.; Smith, D. E. Self-Diffusion of Entangled Linear and Circular DNA Molecules: Dependence on Length and Concentration. Macromolecules 2007, 40, 3373−3377. (10) Donkai, N.; Inagaki, H.; Kajiwara, K.; Urakawa, H.; Schmidt, M. Dilute Solution Properties of Imogolite. Macromol. Chem. Phys. 1985, 186, 2623−2638. (11) Petekidis, G.; Vlassopoulos, D.; Fytas, G.; Fleischer, G.; Wegner, G. Dynamics of wormlike polymers in solution: Self-diffusion and Zero-shear Viscosity. Macromolecules 2000, 33, 9630−9640. (12) Lima, M. M. D. S.; Wong, J. T.; Paillet, M.; Borsali, R.; Pecora, R. Translational and Rotational Dynamics of Rodlike Cellulose Whiskers. Langmuir 2003, 19, 24−29. (13) Bu, Z.; Russo, P. S.; Tipton, D. L.; Negulescu, I. I. Self Diffusion of Rodlike Polymers in Isotropic Solutions. Macromolecules 1994, 27, 6871−6882. (14) Kanesaka, S.; Kamiguchi, K.; Kanekiyo, M.; Kuroki, S.; Ando, I. Diffusional Behavior of Poly(β-benzyl l-aspartate) in the Rodlike, Random-Coil, and Intermediate Forms as Studied by High FieldGradient 1H NMR Spectroscopy. Biomacromolecules 2006, 7, 1323− 1328. (15) Phalakornkul, J. K.; Gast, A. P.; Pecora, R. Rotational and Translational Dynamics of Rodlike Polymers: A Combined Transient Electric Birefringence and Dynamic Light Scattering Study. Macromolecules 1999, 32, 3122−3135. (16) Kuroki, S.; Kamiguchi, K. Diffusional Behavior of Poly(γ-benzyl L-glutamate) in Concentrated Solution As Studied by the FieldGradient 1H NMR Methods. Polym. J. 2008, 40, 223−227. (17) Ando, I.; Yin, Y.; Zhao, C.; Kanesaka, S.; Kuroki, S. Diffusion of Rod-Like Polypeptides in the Liquid Crystalline and Isotropic Phases as Studied by High Field-Gradient NMR Spectroscopy. Macromol. Symp. 2005, 220, 61−74.

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CONCLUSIONS In order to improve the understanding of polypeptides as model systems for rods, particularly for questions of molecular motion, the diffusion of PSLG in THF has been measured by PGSE NMR studies of four low-polydispersity samples in the molecular weight range of 33 000−210 000, corresponding to lengths of 13−82.7 nm at concentrations spanning the isotropic phase. No extended low-concentration plateau followed by a sudden downturn comparable to that seen in PBLG/pyridine was observed. Rather, the rate of diffusion decreases exponentially with concentration. These results indirectly suggest that the nature of topological constraints in isotropic solutions of rods, when probed using helical polypeptides, may require consideration of the helix stability, particularly at the molecular ends. Given the importance of polypeptides as model systems for rodlike polymers, and the great wealth of literature already generated, direct observation of these end effects deserves attention.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b08974. GPC and FTIR spectra of PSLG; tabulation of data in Figure 6 (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Cornelia Rosu: 0000-0001-8687-7003 F

DOI: 10.1021/acs.jpcb.8b08974 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcb.8b08974 J. Phys. Chem. B XXXX, XXX, XXX−XXX