Complementary-DNA-Strand Cross-Linked Polyacrylamide Hydrogels

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Complementary-DNA-Strand Cross-Linked Polyacrylamide Hydrogels Cong Du and Reghan J. Hill* Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, QC H3A 0C5, Canada

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ABSTRACT: We examine networks of complementaryDNA-strand cross-linked polyacrylamide, with and without covalent N,N′-methylene(bis)acrylamide cross-linking, using rheological time−temperature superposition (TTS) to ascertain how temperature and composition influence the microstructure. A higher DNA-cross-linking efficiency is ascribed to the larger cross-linker imparting greater steric hindrance to the formation of self-terminating loops. TTS unifies the rheological spectra of DNA cross-linked and dual cross-linked gels at low frequencies, furnishing the effective activation energy for DNA-cross-link disengagement. Temperature sweeps also show that the temperature dependence of the dynamic moduli is reversible. The activation energy is temperature-independent (≈318 kJ mol−1) at low temperatures but decreases significantly and systematically with increasing temperature (and varying cross-linker composition). We interpret the varying activation energyrelative to the lowtemperature limitas a measure of DNA-cross-linker disassociation, and infer from TTS a cooperative relationship between the DNA-cross-linker disengagement and network connectivity. At low temperature, DNA cross-linked samples exhibit hallmarks of star-polymer-melt relaxation, including a superexponential divergence of the longest relaxation time with increasing cross-linker concentration, increasing from ≈2 to 20 entanglements per arm. At high temperature, a new “associative-reptation” scaling furnishes a robust interpretation of the network and longest relaxation times.

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INTRODUCTION DNA cross-linked polyacrylamide (PA) hydrogels are physical gels cross-linked by hydrogen bonds and base stacking between double-stranded DNA. Unlike chemically cross-linked polyacrylamide gels, such as those cross-linked by N,N′-methylene(bis)acrylamidehereafter termed “bis-acrylamide” (bis), DNA cross-links (a type of “macro-cross-linker”1) are dynamic, and their length and sequence are programmable. These characteristics impart a variety of specialized functions: heating and cooling reversibility,2 photoresponsivity,3 volume control,4,5 pH-responsivity,6,7 shape-memory and self-healing,6,8 and a tunable gel−sol transition temperature.9 When aptamers are adopted as a “toehold”, cross-links dissociate when the aptamer binds to target molecules, such as adenosine and human thrombin.10 Such gels have demonstrated potential for drug delivery,11,12 molecular separation,13 tissue engineering,2 and biosensing.4,14 To arrest creep and prevent dissolution, permanent chemical cross-links have been combined with physical cross-links.4,14−16 In the foregoing applications, it is important to know the time scales on which samples are solid- and liquid-behaving, viscoelastic response through the DNA melting temperature, and durability under load. Note that DNA-cross-linking has been used to trigger swelling as a biosensor.12,15,17 To maximize such a response, it may be desirable to minimize the covalent cross-linking while maintaining a percolating © XXXX American Chemical Society

network. Little is known on how to optimize the microstructure for this purpose, and the viscoelastic properties of gels with coexisting DNA and bis cross-links have not been studied hitherto. The present study therefore focuses on the rheology of very weakly cross-linked structures, for which the presence of a percolating network may be ambiguous, particularly when the network comprises dynamic and permanent junctions. Among studies of the mechanical properties of DNA crosslinked hydrogels, Lin et al.18 and Lin et al.19 correlated the Young modulus of DNA cross-linked polyacrylamide gels with DNA concentration using video-microscopy of an embedded steel ball subjected to a magnetic force. Using the same method, Jiang et al.20 showed that the Young modulus of such gels can be varied from 100 Pa to 30 kPa according to the length of cross-linker, monomer concentration, and degree of cross-linking. Chippada et al.21 developed a method to determine the shear modulus, Young modulus, and Poisson ratio by applying a force or torque to embedded magnetic microneedles. Previtera et al.22 demonstrated a stiffness-tuning process by adding various amounts of DNA to gels supported on an elastic cushion, measuring the cushion displacement. In each of these microrheological testing platforms, gel viscosities Received: June 27, 2019

A

DOI: 10.1021/acs.macromol.9b01338 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Schematics of the chemically, physically, and dual cross-linked hydrogel networks in this study.

energy and provides a mechanism with which to restore gel structure and mechanical properties.31−36 The activation energy has been demonstrated to measure the strength of ionic cross-linking bonds that influence self-healing efficiency.34 One way to determine the activation energy is by applying TTS. However, there is controversy over the applicability of TTS for physically cross-linked gels.37 For example, Noro et al.38 superposed the dynamic moduli for a thermosensitive gel cross-linked by hydrogen bonds, whereas Nair et al.39 were unable to superpose both the storage and loss moduli. An Arrhenius plot linking the rheological properties and temperature had previously been applied to physical gels to obtain the activation energy.40 For example, Peng et al.23 correlated the zero-shear-rate viscosity with temperature using the Arrhenius equation, obtaining the energy required to disengage the hydrophobic chains from micelles (≈25−56kBT at 25 °C). Similarly, Sun et al.34 reported the apparent activation energy of weak and strong ionic bonds in polyampholyte hydrogels (≈29−124kBT at 25 °C) and Kim et al.41 demonstrated similarity of nanoemulsion network activation energies from rheological tests and dynamic light scattering. The large activation energy for the multiple-base-pair disassociation in DNA cross-linked gels suggests distinct viscoelastic characteristics when compared to those of physical gels cross-linked by hydrogen bonds, ionic bonds, or micelles. Moreover, permanent bis cross-linking in DNA cross-linked networks complicates their viscoelastic response. Recent studies have examined the rheological properties of gels with dual cross-linked architectures. For example, it has been shown by Loveless et al.42 that multiple types of cross-links affect the mechanical properties of poly(4-vinylpyridine) gels additively. For poly(vinyl alcohol) (PVA) cross-linked with borate ions as physical cross-linkers, with and without glutaraldehyde as a chemical cross-linker, Narita et al.24 identified the associative Rouse mode of Indei and Takimoto43 (evident by G′ and G″ spectra scaling as ω1/2). Long et al.44 developed a theory to describe the linear mechanical response of dual cross-linked PVA gels, predicting torsional rheometry data, and Liu et al.45

and/or shear moduli were obtained at times that are evidently much shorter than microstructural relaxation times. For example, the shear modulus of 10% w/v DNA cross-linked gels20 has been reported to exceed the plateau storage modulus of an ideal network by ≈80%, suggesting a strong frequency dependence that has hitherto been unknown. Spectral rheological characterization, using a macroscale rheometer, is a powerful tool for studying dynamic crosslinks.23,24 However, in contrast to microrheological platforms, much larger sample volumes are required. Dynamic moduli from macroscale rheometry have been reported at a single frequency to highlight DNA cross-linked hydrogel stimuli responsiveness.7,8,25 Guo et al.6 reported dynamic modulus spectra of a DNA cross-linked hydrogel, at frequencies where the gels are solid-behaving. Dynamic modulus spectra can be extended using time−temperature superposition (TTS) to probe the microstructure over a wide range of time scales. This permits materials to be rigorously identified as a liquid or gel/ solid.26,27 In the present study, TTS furnishes relaxations on time scales that are commensurate with microstructural relaxation times, thus providing new and clear distinctions of liquid- and solidlike behavior, also highlighting a remarkable temperature dependence of rheological properties, which reflects the underlying dynamic state of DNA hybridization. Topuz and Okay28 and Okay29 reported dynamic moduli during gelation and dynamic modulus spectra of chemically cross-linked double-stranded DNA hydrogels. In these studies, however, DNA served as the polymer chains, so its influence on the rheological response is different than when it is the cross-linker, as addressed in the present study. Diffusing-wave spectroscopy (DWS) was recently used by Xing et al.30 to measure the dynamic moduli of Y-shaped DNA “nanostar”based hydrogels over a wide range of frequencies and temperatures. The apparent activation energy of physical cross-linking influences the gel melting temperature and yield stress. Moreover, some physical- and dual cross-linked gels can exhibit self-healing properties, achieved by introducing breakable cross-links. Dynamic, reversible cross-linking dissipates B

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Macromolecules Table 1. Compositions of DNA- and Dual Cross-Linked Polyacrylamide Gels sample B0D0.2 B0D0.4 B0D0.6 B0D0.8 B0.6D0.2 B0.4D0.4 B0.2D0.6 B0.1D0.4

A

Bis-A/A

DNA/A

A

DNA+Bis-A

(% w/v)

(mmol mol−1)

(mmol mol−1)

(mol L−1)

(mmol L−1)

10 10 10 10 10 10 10 10

0 0 0 0 0.6 0.4 0.2 0.1

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.4

1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4

0.28 0.56 0.84 1.12 1.12 1.12 1.12 0.70

applied TTS to dual cross-linked PVA gels, finding that the activation energies from TTS are comparable to those for physically cross-linked PVA gels. To the best of our knowledge, no mechanical or rheological properties of polyacrylamide gels in which DNA and bis cross-links coexist have been reported. In the present study, we performed bulk rheological measurements in the linear viscoelastic regime for DNA- and dual cross-linked polyacrylamide gels. Schematics of the gel synthesis and comparison with bis cross-linked gels are shown in Figure 1. Two acrydite-modified DNA strands were complemented to a third DNA strand to form the DNA cross-links. The third strand contains an aptamer segment that can bind to adenosine. The base sequences of DNA are adopted from Yang et al.12 With and without bis, the DNA cross-linker is copolymerized with acrylamide as the monomer. The protocol is modified from Lin et al.18 to produce dual cross-linked gels with associated DNA-cross-linking centers prior to acrylamide polymerization. Using dynamic rheology during the polymerization and cross-linking reaction, gelation kinetics were examined, and frequency-sweep spectra at various temperatures following gelation were used to interpret the complementary DNA-cross-link dynamics and ascertain the apparent activation energy.

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linker concentration to the acrylamide concentration (ratio as mmol mol−1) in the pre-gel solution. After adding 10 μL of freshly prepared 10% w/v APS and 3.6 μL of TEMED per ml of pre-gel solution, the solution was pipetted onto the bottom plate of a parallel-plate sample holder of an ARES-G2 rheometer (TA Instruments) and the 25 mm diameter top plate was lowered to achieve a 0.5 mm gap. An “evaporation blocker” and silicon oil applied to the sample edge were used to minimize evaporation. Oscillatory shear during gelation was applied at 21 °C with an angular frequency ω = 1 rad s−1 and strain amplitude γ = 1% to ensure a linear viscoelastic response. After the dynamic moduli reached steady values, frequency sweeps were performed in the range ω =0.1−100 rad s−1 with γ = 1% and temperatures from 21 to 56 °C, controlled using a thermoelectric chiller (ThermoCube 10-300, Solid State Cooling Systems). An average gap compensation factor that accounts for the sample holder and gel expansions was set at ≈2.9 μm/°C for TTS.

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RESULTS AND DISCUSSION Gelation Kinetics. Time series of the storage and loss moduli are available in Figures S1 and S2. For DNA crosslinked gels, which have various DNA-cross-linker ratios, cDNA/ ca, the storage moduli G′ increase systematically with the DNA-cross-linker ratio, whereas the loss moduli have weak and nonsystematic variation with the composition. As gelation progresses, G′ reaches maximum values at t ∼ 1000 s and then decreases on a time scale that is about an order of magnitude slower. Whereas qualitative characteristics of the G′ time series are similar to those of dual cross-linked gels (Figure S2) and weakly bis cross-linked polyacrylamide gels,46 the G″ time series for DNA-containing gels have a local maximum occurring in the initial gelation stagethat is absent for bis cross-linked polyacrylamide gels. This might be attributed to the higher molecular weight of the DNA cross-linker, hindering the formation of self-terminating loops, which would change the manner in which the size of growing clusters depends on their molecular weight. The role of cluster size is supported, in part, by the peak in G″ being more pronounced when increasing the accelerator concentration. With the growth of polymer chains connected to DNAcross-linking centers, the increasing cluster size eventually promotes cluster aggregation and a transition from a dilute to an entangled solution with a rapid increase in the dissipation, as measured by G″. However, when clusters attach to the network, they contribute to the elasticity; the friction between the solvent and the network reduces, decreasing G″. Fluctuations in the G″ time series are from instrumental adjustments to the top plate to maintain a constant axial force (set to 0 N).

MATERIALS AND METHODS

Acrylamide (40% w/v, Fisher Scientific), N,N′-methylene(bis)acrylamide (2% w/v, Fisher Scientific), acrydite-modified oligonucleotides (standard desalting, Integrated DNA Technologies), ammonium persulfate (APS, ≥98%, Fisher Scientific), N,N,N′,N′tetramethylethylenediamine (TEMED, 99%, GE Healthcare Life Sciences), and DNA suspension buffer (10 mM Tris-HCl, 0.1 mM EDTA, pH 8.0, Teknova) were used as provided by the manufacturer. Acrydite-modified DNA strand A, acrydite-modified strand B, and “LinkerAdap” were prepared as 5 mM solutions in DNA suspension buffer. Different volumes of strand A, strand B, and “LinkerAdap” solutions, as well as DNA suspension buffer, were first added to a centrifuge tube, and then, after 2 min for the three DNA strands to combine, a fixed volume of 40% w/v acrylamide and different volumes of 0.25% w/v bis-acrylamide solutions were added to the tube to achieve a constant monomer concentration of 1.4 mol L−1, varying the physical and chemical cross-linker concentrations, as summarized in Table 1. Nitrogen was bubbled through the solutions for 5 min to remove dissolved oxygen prior to centrifugation at ≈103g for 2 min to collect the liquid transferred to the tube wall during degassing. In the pre-gel solution, base pairs form between strand A and “LinkerAdap” and between strand B and “LinkerAdap”, thus forming “DNA crosslinkers”, which, similarly to bis-acrylamide cross-linkers, are tetrafunctional, but with a significantly higher molecular weight. To distinguish the samples, we adopt a nomenclature BxDy, where x is the ratio of the N,N′-methylene(bis)acrylamide cross-linker concentration to the acrylamide concentration (ratio as mmol mol−1) in the pre-gel solution and y is the ratio of the DNA-crossC

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Figure 2. Top left: mid-point slope P (left axis) and gelation half-time θ (right axis) versus cross-linker ratio for bis- (circles) and DNA cross-linked (squares) gels: ω = 1 rad s−1, T = 21 °C. Top right: P for dual cross-linked gels with a fixed total cross-linker ratio equal to that for sample B0D0.8. Bottom left: network-formation rate versus cross-linker ratio for bis cross-linked gels (circles), DNA cross-linked gels (squares), bis cross-linked gels with a higher TEMED concentration (triangles), DNA cross-linked gels with a higher TEMED concentration (diamonds), and bis cross-linked gels with monomer concentration 1.3 mol L−1 (asterisk): ω = 1 rad s−1, T = 21 °C. Bottom right: The network-formation rate for dual cross-linked gels with a fixed total cross-linker ratio equal to that for DNA cross-linked sample B0D0.8.

The dual cross-linked gels (Figure S2) have a fixed total cross-linker ratio. The storage moduli increase systematically with the DNA-cross-linker ratio and are somewhat higher than those for DNA cross-linked gels with the same DNA-crosslinker ratio. Thus, the bis- and DNA-cross-linking contributions to the storage moduli are qualitatively additive, as elaborated upon below. The loss moduli for DNA- and dual cross-linked gels are all very similar, with the exception of the DNA cross-linked gel with the highest DNA concentration (sample B0D0.8) and ostensibly higher loss modulus. Despite the storage and loss moduli all exhibiting a slow relaxation, their ratio, reported as loss-tangent time series, establishes clear steady-state values. Storage-modulus time series are well characterized by the empirical formula47,48 ′ G′(t ) = G∞

tn t n + θn

vertical lines). The maximum values are followed by a slow relaxation toward an equilibrium value. We assume that the short-time dynamics captured by eq 1 are principally due to the gelation kinetics and that the subsequent decrease in G′ is due to the release of chains that are trapped by entanglements during the initial, rapid network formation. The mid-point slope P is plotted in the top panels of Figure 2 versus various measures of gel composition. The top-left panel compares P and θ for DNA cross-linked gels with those for bis cross-linked gels having the same acrylamide monomer concentration. For both types of gels, P increases linearly with the cross-linker concentration. As highlighted in the bottom′ for bis cross-linked gels left panel, the characteristic rates P/Gm (circles, asterisks, and triangles) are practically independent of the cross-linker ratio. Also shown are data from several bis cross-linked gels that we synthesized using a higher concentration of TEMED in the pre-gel solution (triangles). These produced very similar results (with higher TEMED increasing the reaction rate), as did a series of bis cross-linked gels with a slightly lower monomer concentration (asterisks). ′ indicates that the rate at which The constant value of P/Gm elastically active partial chains form is proportional to the concentration of bis-cross-linking centers. This affirms that elastically active partial chains are principally formed by inactive chains (with concentration of reactive ends proportional to the monomer concentration) attaching to network chains (with concentration proportional to the cross-linker concentration). For DNA cross-linked gels (squares), P/G′m increases somewhat with the DNA-cross-linker ratio, possibly reflecting the larger influence that cross-linking might have on

(1)

where G′∞ is the storage modulus (according to the model) when t → ∞, θ is the time at which G′(t) = G′∞/2, and n is a fitting exponent. The mid-point slope P=

dG′ dt

= t=θ

′ nG∞ 4θ

(2)

is customarily adopted to quantify the gelation kinetics.47 Due to the slow relaxation of G′, which is characteristic for these very weakly cross-linked gels, we fit eq 1 at times for which it is compared to data in the top-right panels of Figures S1 and S2. Thus, the fitting parameter G∞ ′ approximates the maximum values of G′ (shown in the left-hand panels with D

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Figure 3. G′ (circles) and G″ (squares) spectra for DNA cross-linked gels following TTS with reference temperature 21 °C (T = 21−56 °C, increasing from blue to red). Lines are power laws with indicated exponent.

Flory exponent. It follows that self-termination would be unhindered when

the self-termination of chains attached to DNA-cross-linking centers. We ascribe the higher cross-linking efficiency for DNA crosslinking to the larger cross-linker size, decreasing the probability for forming self-terminating loops. A mechanistic scaling argument is proposed as follows. If chain ends growing from cross-linking centers are assumed to undergo a random walk, then the time to self-terminate in the absence of steric hindrance would be the O(τa2c /l2) diffusion time, where ac is the cross-linker size, l is the monomer size, and τ is the reciprocal polymerization rate (proportional to the monomer concentration, nm). However, the time for growing polymer chains in the pre-gel solution to form a semidilute solution that would hinder the foregoing self-termination is O[τ(nml3)1/(1−3ν)], where ν ≈ 0.6 is the

ac /l ≲ (nml 3)1/(2 − 6ν) ∼ 10

(3)

−1

which (using nm = 1.4 mol L and l = 3 Å) is much easier to justify for the pair of reactive sites in bis-cross-linking centers than for their counterparts (two acrydite strands) in DNAcross-linking centers. Thus, considering the proximities of the four reactive groups on each cross-linking center, the rate of self-termination might reasonably be expected to be 3 times higher for bis- than for DNA-cross-linking centers. For dual cross-linked gels, the top-right panel in Figure 2 shows P versus the DNA-cross-linker mole fraction (with a fixed total cross-linker concentration of 1.12 mmol L−1). The weak, negative departure of the quadratic variation of P E

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Figure 4. The same as Figure 3 but for dual cross-linked gels.

ω = 0.1−100 rad s−1) are shown in the right panels of Figures 3 and 4. The temperature dependence is much stronger than for bis cross-linked polyacrylamide gels with comparable crosslinking densities46 and can therefore be attributed to the dynamics of the DNA cross-links. Here, vertical and horizontal shifts to the spectra were appliedusing the time−temperature superposition (TTS) function of TA Instruments Trios softwareto overlap the spectra at low frequencies. Accordingly, the horizontal shift factor aT and vertical shift factor bT furnish

compared to a straight line between the limits for pure bis and DNA cross-linking suggests a weak interaction of the two cross-linking species. Below (see Figure 6), an even weaker negative departure from perfect additivity is evident in the plateau moduli and cross-linking efficiency. This suggests that the interactions between the two cross-linkers manifest principally in the reaction cross-sections, which can reasonably be assumed to be influenced by the contrasting microscale geometries of the clusters formed by the different cross-linking centers. The bottom-right panel reveals an approximately linear, weak variation in P/Gm ′ with respect to the mixing of DNA and bis cross-linkers. Dynamic Modulus Spectra and Time−Temperature Superposition. Dynamic modulus spectra for DNA- and dual cross-linked gels at various temperatures (T = 21−56 °C with

bTG*(ω , T ) = G*(ωa T , T0)

where G*(ωaT, T0) denotes the modulus at the reference temperature and shifted frequency ωaT.49 The temperature dependence of the relaxation time is captured by ωaT,50 and bT F

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Figure 5. Schematic representations of TTS dynamic spectra for DNA- (top left) and dual (bottom left) cross-linked polyacrylamide gels, defining τc = 2π/ωc (cross-over time), τX = 2π/ωX (network-relaxation time43), and entanglement plateau modulus G0N (from the minimum in G″) (plotted in Figure 7). Middle panels are time−concentration superposed spectra for bis cross-linked polyacrylamide gels with (i) nbis/na ≈ 25−46 mmol mol−1 (above the gel point) and na ≈ 0.42 mol L−1 (top, adapted from Adibnia and Hill58) and (ii) nbis/na ≈ 0.1−0.8 mmol mol−1 and na ≈ 1.4 mol L−1 (bottom, adapted from Du and Hill46). Right panels are the well-known Rouse and Doi−Edwards (ω < 1/τe) models with Rouse and reptation times, τR ∼ 1/ωR and τd ∼ 1/ωd, respectively.

Figure 6. Left: Plateau modulus (left axis) and cross-linking efficiency (right axis) at T = 21 °C versus cross-linker ratio for bis- (circles) and DNA cross-linked (squares) gels. Right: Plateau modulus (left axis) and cross-linking efficiency (right axis) at T = 21 °C versus DNA-cross-linker mole fraction for dual cross-linked gels with a fixed total cross-linker ratio equal to that for the DNA cross-linked sample B0D0.8.

has been related to the density ρ(T) of elastomers and polymer melts as bT = ρ0T0/(ρT), where ρ0 = ρ(T0).49,51 For hydrogels, we interpret ρ(T) as an effective cross-link number density, N/ V, furnishing

the G″ upturn at each temperature according to the temperature dependence of the solvent viscosity. Plateau Moduli. For DNA cross-linked gels, a rubbery plateau is present at high frequencies. As shown in Figure 5, we take the entanglement plateau modulus G0N to be the value of G′ at the frequency where G″ (at T = 21 °C) has a local minimum.57 Note that bis cross-linked gels do not have a local minimum in G″, so we take G0N for bis cross-linked samples to be the value of G′ at the frequency for which G0N is defined for its DNA cross-linked counterpart (having the same cross-linker concentration). Figure 6 shows that G0N for bis- and DNA cross-linked gels increases linearly with the cross-linker ratio but with distinctly different cross-linking efficiencies. As the scaling argument above supports, the much higher efficiency achieved by DNA cross-linking can be attributed to the larger cross-linking centers hindering the formation of self-terminating loops. Note that G0N for bis cross-linked gels vanishes when cbis/ca ≈ 0.16 mmol mol−1, which we adopt to approximate the critical percolation threshold. The cross-linking efficiency, as measured by the fit

N 1 VT0 = N0 bT V0T

where N0 = N(T0) and V/V0 ≈ 1 + β(T − T0) (with β the linear thermal expansion of water). Note that the sample volume is attributed entirely to that of water (an approximation based on the low polymer concentration). Master curves with the reference temperature T0 = 21 °C are plotted in the left panels of Figures 3 and 4. The systematic upturns in G′ and G″ that appear at higher frequencies following TTS might be attributed, in part, to the acrydite and four extra bases connecting strands A and B to polyacrylamide acting as polymer branches, increasing the relaxation time. A similar upturn has also been observed in the rheological spectra of reversible gels following TTS. 52−55 Noro et al. 56 demonstrated that the deviation can be interpreted by shifting G

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Figure 7. Left: Network-relaxation time τX = 2π/ωX (circles) and cross-over time τc = 2π/ωc (squares) from TTS spectra for DNA cross-linked gels at 21 °C. Middle: τX for DNA- (filled with lines) and dual- (open) cross-linked gels (linear ordinate). Right: Power-law exponents from G″: ωn1 (blue), ωn2 (green), and ωn3 (red) (defined in Figure 5) for DNA- (filled with lines) and dual- (open) cross-linked gels. Note that two samples (B0.4D0.4 and B0.1D0.4) have DNA-cross-linker ratio equal to 0.4 mmol mol−1.

GN0 /GN0 ideal ≈ 0.32 − 5.1 × 10−5cc /cbis

exponents are plotted in Figure 7 versus the DNA-cross-linker ratio, for DNA- and dual cross-linked gels. All of the viscoelastic spectra for DNA cross-linked gels in Figure 3 have a crossing of the storage and loss moduli. Thus, in striking contrast to the dual cross-linked gels in Figure 4, DNA cross-linked gels are readily classified as viscoelastic liquids (G′ < G″). The permanent cross-linking in the dual cross-linked gels clearly imparts a viscoelastic solid character. As shown in the left panel of Figure 7 (squares), the cross-over time τc increases significantly and systematically with the DNA-cross-link concentration. If, according to Piest et al.,59 we take the average cross-link lifetime to be τc ≈ 2π/ωc, where ωc is the cross-over angular frequency, then the cross-link lifetime must be considered to increase with the DNA concentration. Below, we will show that this can be attributed to a cooperative DNA-dissociation rate that decreases with increasing DNAcross-linker concentration (with a constant DNA-association rate). Also interesting to note is that the network-relaxation time τX, which is available for DNA- and dual cross-linked gels (compared in the middle panel of Figure 7), varies only with the DNA-cross-linker concentration and so is independent of the bis cross-linking. For bis cross-linked polyacrylamide gels with similar monomer and cross-linker concentrations, we have previously shown that the scaling exponent n1 ≈ 0.3146 (see Figure 5). The low-frequency exponents n1 for dual cross-linked samples B0.2D0.6, B0.4D0.4, and B0.6D0.2 are very close to this value, affirming that permanent cross-links dominate the lowfrequency dynamics. The low-frequency relaxations for DNA cross-linked samples in Figure 3 have frequency-dependent exponents (i.e., nonpower-law scaling) that are often notably smaller than predicted by a single-relaxation Maxwell-type mode for which G′ ∼ ω2 and G″ ∼ ω1 in the terminal regime (e.g., Rouse and reptation models in Figure 5). The maximum values of the power-law scaling exponents at low frequency are tabulated as SI. These vary with the composition, decreasing in magnitude from close to the Maxwell values at the lowest DNA-cross-linker ratio toward 0.5 as the cross-over region shifts toward the low-frequency instrumental limit with increasing DNA-cross-linker concentration. Only the DNA cross-linked sample with the lowest DNA concentration furnishes compelling terminal power-law relaxations in the instrumental range.

where G0Nideal = 2(nDNA + nbis)kBT (ideal affine network) with nDNA + nbis the cross-linker number density, increases from zero (at the percolation threshold) to ≈26% when cbis/ca ≈ 0.8 mmol mol−1. Despite this measure of efficiency vanishing when approaching the percolation threshold, the linear contribution to G0N with respect to cbis indicates that ≈32% of the bisacrylamide cross-linker in the pre-gel solution produces elastically active partial chains (due to cross-linking and entanglements). For DNA cross-linked gels, G0N vanishes when cDNA/ca ≈ 0.12 mmol mol−1 and the cross-linking efficiency, as measured by the fit GN0 /GN0 ideal ≈ 0.63 − 7.4 × 10−5ca /c DNA

increases from zero (at the percolation threshold) to ≈54% when cDNA/ca ≈ 0.8 mmol mol−1. The linear contribution to G0N with respect to cDNA indicates that ≈63% of the DNA crosslinker in the pre-gel solution produces elastically active partial chains (again due to cross-linking and entanglements). The right panel in Figure 6 shows the plateau modulus of dual cross-linked gels (and the cross-linking efficiency) versus the DNA-cross-linker mole fraction (with a fixed total crosslinker concentration 1.12 mmol L−1). The transition from the pure bis- to pure DNA-limits deviates very weakly from perfect additivity. The slight negative departure suggests that the mixing interactions are weak and decrease the overall crosslinking and entanglement efficiency. Other metrics for DNA- and dual cross-linked gels is tabulated as SI. These quantify how the cross-linker concentrations influence the molecular weight of the polymer between effective cross-links (in the plateau region), also reporting the effective mesh size ξ = (2kBT/G0N)1/3 (∼20−40 nm when assuming and ideal affine network) and the rootmean-squared end-to-end distance Re of effective partial chains (∼30−150 nm). For example, ξ/Re increases weakly, but systematically, with the cross-linker concentration, from ≈0.3 to 0.5. Relaxation Times and Scaling Exponents. General features of the dynamic spectra for DNA- and dual cross-linked gels are highlighted in Figure 5. These include the definitions of several characteristic time scales/reciprocal frequencies and power-law scaling regimes. The relaxation times and scaling H

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unambiguously exhibit hallmarks of entanglement and reptation at frequencies high enough for DNA association and dissociation dynamics to be neglected, i.e., when ω ≳ ωX, with tube-length fluctuations (|n2| < 1/2) manifesting at the lower cross-linker concentrations, as expected when chain ends contribute a larger fraction to the effective chain length. For sample B0.1D0.4, which has the largest ratio cDNA/cbis, the power-law exponents for G′ and G″ at lower frequencies may be interpreted from two perspectives. From the associative Rouse model, the power-law exponents are close to the model scaling: G′ ∼ G″ ∼ ω1/2 when 2π/τA ≪ ω ≪ 2π/τX. This is because τA for sample B0.1D0.4 is infinite due to bis crosslinking, whereas τX ≈ 200 s. Unlike DNA cross-linked gels, the permanent cross-linking in sample B0.1D0.4 imparts a significant disparity between 2π/τA and 2π/τX, but unlike other dual cross-linked gels, the bis-cross-linker ratio brings this sample into the proximity of a critical state. From the perspective of universal gelation dynamics,62−65 the cross-linker concentration in the bis cross-linked sample B0.1D0 is below the percolation threshold,46 whereas sample B0.1D0.4 is slightly above the percolation threshold. This seems to explain why G′ and G″ for sample B0.1D0.4 have almost the same low-frequency power-law exponent (as expected for critical gels). Critical exponents have been reported for chemically crosslinked networks in the range 0.19−0.92.50 As shown in Figure 5, master spectra (from time−concentration superposition) for bis cross-linked gels having a relatively low monomer concentration furnish a distinct terminal plateau modulus, universal scaling (G′ ∼ G″ ∼ ω0.7) at high frequency, and a power-law loss modulus. On the other hand, bis cross-linked gels with a low cross-linker ratio (equal to that in the present study) also exhibit a terminal plateau (albeit at much lower frequencies), power-law scaling of the loss modulus (with a much lower power-law exponent ≈0.3), but no crossing of the storage and loss moduli. Note that the spectra reproduced here are exclusively from gels that are above the percolation threshold. The apparent critical exponent, n1, for sample B0.1D0.4 is close to the value ≈0.38 established by Du and Hill46 for very weakly cross-linked bis-acrylamide gels. The smaller magnitude of this exponent, as compared to 0.7 from Adibnia and Hill,58 is consistent with the high degree of entanglement increasing the elasticity of the critical gel.50 Interestingly, the power-law exponents n3 are practically indistinguishable for DNA- and dual cross-linked gels. Moreover, as shown in the right panel of Figure 7, these approach practically the same value of n1 ≈ 0.31 for G″ in the terminal region for bis cross-linked and dual cross-linked gels. The upturn in G″ in the entanglement plateau regime has been associated with Rouse relaxation within a primitive-path step.50 Note that the reptation model also predicts an upturn in the storage modulus at frequencies above the reciprocal time for segmental displacements to become comparable to the step length of the primitive path, τe, furnishing G′ ∼ ω1/2.66 The loss-tangent tan δ spectra for each DNA- and dual cross-linked gel are available as SI. For the DNA cross-linked gels, increasing the DNA-cross-linker ratio produces an increasingly solidlike response. At low frequencies, increasing the frequency brings tan δ from >1 to 1/τR(2 M̅ ). Thus, with τX ∼ c−1.83 and τA ∼ τc ∼ c1.49 for T = 56 °C (from the right panel in Figure 11), we find either 1.7

α∼c ,β∼c

1.0

⇒ N̅ ∼ c

1.7

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CONCLUSIONS Polyacrylamide hydrogels were synthesized using complementary DNA strands as a physical cross-linker and N,N′methylene(bis)acrylamide as a chemical cross-linker. Using rheometry, gelation by DNA cross-linking was found to be faster and more efficient than bis cross-linking. We proposed a mechanistic scaling argument to quantify the role of crosslinker size on sterically hindering the formation of selfterminating loops, thus influencing the overall cross-linking efficiencies. Time−temperature superposition was applied to the rheological spectra of DNA- and dual cross-linked gels. The master spectra exhibit distinct characteristics from the application of vertical and horizontal shifts. DNA-only crosslinked gels were demonstrated to be viscoelastic liquids, exhibiting qualitative hallmarks of entangled polymer networks: including a distinct crossing of the storage and loss moduli and terminal and entanglement plateau regimes. Dual cross-linked gels have distinctly different rheological signatures, reflecting DNA and bis cross-linking: including low-frequency, terminal plateau modulus and no crossing of the storage and loss moduli. Thus, bis cross-linking imparts a viscoelastic solid character. At high frequencies, the dynamic spectra of DNAand dual cross-linked gels are similar, affirming that these dynamics reflect the relaxation of subchains on time scales that are short compared to the DNA association lifetime. A rheological determination of the apparent activation energy for the dissociation of DNA cross-links furnished ≈318 kJ mol−1, consistent with thermodynamic estimates for 12 base pairs (at T ≈ 21 °C). The temperature dependence of the dynamic moduli is principally attributed to the DNA crosslinking and is reversible. In contrast to N,N′-methylene(bis)acrylamide cross-linked gels, the activation energy is temperature-independent at low temperatures when the gels are solidbehaving but decreases significantly and systematically with increasing temperature (and varying cross-linker composition) when the gels are liquid-behaving. We interpreted the varying activation energyrelative to the low-temperature limitas a measure of the degree of DNA-cross-linker association. Together, the temperature and composition dependencies of the apparent activation energy (from horizontal shift factors) and the effective cross-link number density (from vertical shift factors) suggest a cooperative relationship between the DNAcross-linker disengagement and network connectivity.

with m = 2, (Rouse)

or α ∼ c 0 , β ∼ c −0.7 ⇒ N̅ ∼ c1.7 with m = 3. (reptation)

Recall, our interpretation of the apparent activation energy and cross-linking efficiency requires N̅ to increase with c, so both possibilities are compatible. However, only the reptation possibility is compatible with the DNA-association rate being practically independent of the DNA-cross-linker concentration (|a| ≪ 1) and the DNA-dissociation rate decreasing with increasing the DNA-cross-linker ratio (b < 0), as required by the apparent activation energy for DNA dissociation increasing with the DNA-cross-linker concentration. Thus, our data and model support the foregoing “associative reptation” hypothesis. Applying the formulas above to the scalings of Narita et al.24 for borate-cross-linked PVA solutions yields α ∼ c−6.6 and β ∼ c−6.6 for associative Rouse and α ∼ c−7.6 and β ∼ c−7.6 for associative reptation, both with N̅ ∼ c1, where c is the borate ion concentration. It is not clear how such large negative exponents can be justified from a physical perspective (e.g., Narita et al.24 argued that the association rate increases with the free-borate ion concentration, but this is contrary to the scaling required for their relaxation times to be compatible with the associative Rouse model), perhaps casting doubt on whether the associative Rouse model is appropriate for the ionbinding cross-linking mechanism. Note, however, that their association of the longest relaxation time τA with a chain diffusion coefficient that scales with the PVA radius of gyration may be questionable if entanglements are active (friction is proportional to the chain length for reptation, not the coil size). Finally, we consider the low-temperature relaxation times, both of which increase with c ∼ γ (similarly to Narita et al.24) but with the longest relaxation time growing superexponentially with c. Our analysis of the apparent activation energy suggests a high degree of DNA association at T = 21 °C, and the resulting relaxation times are extremely large. The superexponential growth is suggestive of the entanglement of branched polymers, for which the arm relaxation time scales as τarm ≈ (Na /Ne)5/2 eγ′ Na /(2Ne) M

DOI: 10.1021/acs.macromol.9b01338 Macromolecules XXXX, XXX, XXX−XXX

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Finally, we examined in detail the cross-linker concentration dependence of the relaxation times from DNA cross-linked samples at low and high temperature. At high temperature (56 °C), we proposed an “associative reptation” modelbased on the associative Rouse model of Indei and Takimoto for associative polymer solutionsthat captures, in a physically consistent and quantitative manner, how the network and longest relaxation times, τX and τc, depend on the association and dissociation rates α and β. A reptational relaxation of subchains spanning cross-linking junctions is necessary to furnish an association rate that is independent of the crosslinker ratio and a dissociation rate that varies according to the cross-linker ratio (consistent with the apparent activation energies furnished by TTS). At low temperature (21 °C), the samples have a longest relaxation time that grows superexponentially with the cross-linker concentration. This regime bears many similarities to the relaxation of star-polymer melts, indicating branching with ≈2−20 entanglements per arm.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b01338.

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Storage modulus, least-squares fit of equation 1, loss modulus, and loss tangent for DNA cross-linked samples and dual cross-linked gels; loss-tangent spectra for DNAcross-linked gels and dual cross-linked gels; sequence of scaling calculations; and analyses of gel samples (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Reghan J. Hill: 0000-0001-9735-0389 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from NSERC Discovery and NSERC Research Tools and Instruments programs is gratefully acknowledged. This work was also supported, in part, by the NSERC Sentinel Bioactive Paper Network.

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DOI: 10.1021/acs.macromol.9b01338 Macromolecules XXXX, XXX, XXX−XXX