Photoreconfigurable Physically Cross-Linked Triblock Copolymer

Feb 20, 2015 - †Department of Materials Science and Engineering and ‡Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh,...
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Photoreconfigurable Physically Cross-Linked Triblock Copolymer Hydrogels: Photodisintegration Kinetics and Structure−Property Relationships Congcong Zhu† and Christopher J. Bettinger*,†,‡,§ †

Department of Materials Science and Engineering and ‡Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States § McGowan Institute of Regenerative Medicine, 450 Technology Drive, Suite 300, Pittsburgh, Pennsylvania 15219, United States S Supporting Information *

ABSTRACT: Photoreconfigurable physically cross-linked hydrogel networks are prepared by self-assembly from amphiphilic ABA triblock polymers with photolabile poly(onitrobenzyl methacrylate) (PNBMA) A blocks and poly(ethylene glycol) (PEG) B blocks. Generalizable structure− property relationships of this class of photosensitive compounds have yet to be reported. Here, a library of amphiphilic linear PNBMA-b-PEG-b-PNBMA triblock copolymers is synthesized, and the physical properties of subsequent hydrogel networks are characterized across two parameters: the degree of polymerization of PNBMA segments and the concentration of PNBMA-b-PEG-b-PNBMA in precursor solutions. The storage modulus, photodisintegration kinetics, and swelling ratio are reported. A quantitative model to correlate molecular scale photolysis of NBMA groups with macroscopic mechanical properties is proposed and validated. Hydrogel network parameters including cross-link density and mesh size are also included and compared to covalently cross-linked PEG-diacrylate analogues. The concept of reduced swelling ratio is introduced to map the physical properties of self-assembled physically cross-linked photolabile networks with covalently crosslinked hydrogels. This revised parameter permits direct comparisons of macroscopic network properties between PEG-based gels with either physical or covalent cross-links.

1. INTRODUCTION

undergo programmable disintegration using extracorporeal illumination. These prospective applications require a detailed understanding of the kinetics that governs light-induced network disintegration. Mapping molecular-scale uncaging to the temporal evolution in macroscopic properties is a strong function of the bond topology of photolabile bonds. The kinetics of network disintegration will vary significantly between covalently cross-linked photolabile networks and physically cross-linked ABA hydrogels because the evolution of macromolecular structures and bond topology during uncaging will evoke differential temporal dynamics on the macroscopic properties of each network. The structure− property relationships that underpin the anticipated departure in behavior are presently unknown. Herein, the kinetics of lightinduced disintegration for a library of physically cross-linked hydrogel networks composed of photolabile ABA triblock copolymers is measured. A framework to describe relevant macroscopic physical parameters of these networks is also presented. The behaviors of physically cross-linked networks

Photoreconfigurable hydrogels are a class of photofunctional polymers with a wide range of potential applications as a smart polymeric biomaterial. Light-sensitive hydrogels can serve as programmable matrices for controlled release,1,2 substrates for biomolecular patterning,3−6 or dynamic scaffolds for elucidating cell−biomaterials interactions.7,8 Photoreconfigurable hydrogels are typically composed of covalently cross-linked networks with photolabile components that are integrated into the backbone of active chains.8−10 This bond topology affords characteristic dynamics in the evolution of network properties upon photolysis in response to irradiation.8 Physically cross-linked photolabile hydrogel networks can also be prepared from ABA triblock copolymers.11,12 Hydrophobic photolabile A blocks aggregate into physical cross-links that are covalently coupled through hydrophilic B blocks. Light-induced uncaging of pendant photolabile groups in A blocks converts this condensed temporary hydrophobic phase into a hydrophilic domain that destabilizes physical cross-links and ultimately promotes disintegration of the network. Physically cross-linked photolabile hydrogels can self-assemble in aqueous environments.13 This processing capability is advantageous because hydrogel networks can be formed in situ by injection and can © XXXX American Chemical Society

Received: December 1, 2014 Revised: February 11, 2015

A

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formation (DPAblock = 24). Rhodamine B-loaded hydrogels were equilibrated in ddH2O for 18 h before charged with fresh water (1 mL). Aqueous solutions were retrieved every 5 min during light exposure (λmax = 365 nm, 10 mW cm−2, Blak-Ray, Upland, CA), and UV−vis spectra were recorded (Shimadzu 2600, Columbia, MD). Absorbance intensities at λ = 540 nm I(t) were normalized against the absorbance value after the initial 5 min exposure I(t=5). Hydrogels incubated in the dark were used as control samples.

and covalently cross-linked networks are compared across relevant properties including light-induced disintegration kinetics and equilibrium swelling ratios.

2. EXPERIMENTAL SECTION 2.1. Synthesis of Triblock Copolymer Bearing o-Nitrobenzyl Functional Groups. Photolabile triblock copolymers were synthesized according to a previously reported method.12 Briefly, poly(methacrylic acid)-b-poly(ethylene glycol)-b-poly(methacrylic acid) (PMAA-b-PEG-b-PMAA) ABA triblock copolymers were synthesized using atom transfer radical polymerization (ATRP) of tert-butyl methacrylate followed by acid hydrolysis. PEG macroinitiator (Mn = 20 000 g/mol) was selected as the B block. The degree of polymerization of A blocks was varied by adjusting the feed stream of the monomers. The degree of polymerization of A blocks (DPAblock) was measured by comparing 1H NMR integrals of the peaks assigned to tert-butyl groups at 1.45 ppm with those assigned to methylene groups in PEG blocks at 3.65 ppm. Light-sensitive linear amphiphilic ABA triblock copolymers were synthesized via esterification reaction between PMAA-b-PEG-b-PMAA and photolabile protecting groups of o-nitrobenzyl bromide. The degree of esterification was calculated by comparing 1H NMR integrals of the peaks assigned to aromatic groups at 8.02, 7.62, and 7.5 ppm of o-nitrobenzyl-bearing monomers with those at 3.65 ppm within −CH2− groups of PEG monomers in B blocks. The weight fraction of photolabile A blocks was calculated by comparing the molecular weight of PNBMA segments with PNBMAb-PEG-b-PNBMA triblock copolymers. 2.2. Preparation of Self-Assembled Hydrogel Networks. Physically cross-linked hydrogel networks were prepared by precipitation in aqueous reservoirs. Briefly, PNBMA-b-PEG-bPNBMA triblock copolymers were dissolved in a mixture of DMSO/methanol (1:1 by weight) at the following polymer concentrations: 10, 15, 20, and 25% (w/w). Polymer solutions (∼200 μL) were injected into a ddH2O bath at 25 °C over a time period between 3 and 5 s. Hydrogels with spherical macroscopic form factors form on the surface of water instantaneously. Hydrogels were incubated in ddH2O baths (∼15 mL) for >18 h to permit solvent exchange and equilibrate swollen hydrogel networks. 2.3. Characterization of Physical Properties of Hydrogel Networks. The mechanical properties of physically cross-linked hydrogels were measured using a rheometer (HR-2, TA Instruments, New Castle, DE) equipped with a UV exposure accessory (λ = 320− 500 nm; 30 mW cm−2; Lumen Dynamics, Mississauga, Ontario, Canada). This instrument permits continuous time-dependent rheological measurements of samples exposed to UV. Rheological measurements were conducted using a strain amplitude of γ = 0.5%, which lies within the linear viscoelastic regime for hydrogel samples used in this study. The time-varying normalized storage modulus G′(t) is defined via the relationship G′(t ) =

G′(t ) G′(t0)

3. RESULTS AND DISCUSSION The macromolecular architecture and bond topology of covalently cross-linked photolabile hydrogel networks are different compared to physically cross-linked networks composed of photolabile triblock copolymers. The cross-link density of active networks in covalent gels can be calculated using the storage modulus via modified rubber elasticity theory14,15 or from the swelling ratio via the Peppas−Merrill equation.16,17 The former relationship is presented here18 ρ=

Ws − Wd Wd

(3)

where ρ represents the cross-link density in units of moles of active network per m3, G′ represents the storage modulus in the linear elastic regime, Q represents the dimensionless swelling ratio, and RT is a product of the gas constant and temperature in kelvin.19 Structure−property relationships in covalently cross-linked hydrogels have been well characterized.20,21 Covalently cross-linked photolabile hydrogels contain a homogeneous distribution of photolabile groups that are integrated into the polymer backbone such that photolysis of a single molecule can cleave an elastically effective chain element.8 Equation 3 suggests that the bond topology in covalent photolabile networks will produce an immediate and rapid reduction in the number of active chains as measured by storage modulus during photolysis.22 These parameters are also intimately linked to other important properties such as the number-average molecular weight between cross-links Mc and mesh size ξ.21,23 Physically cross-linked hydrogels formed from ABA triblock copolymers can be considered as swollen networks with micellar structures.24,25 The size and spacing of micellar phases can be measured using scattering techniques.26−29 Furthermore, the macromolecular architecture determines the physical properties of the hydrogel. Among all the possible macromolecular structures that can be prepared into physical hydrogels, ABA triblock copolymers with hydrophobic A segments and a hydrophilic B segment are of particular interest because they self-assemble into physically cross-linked aggregates that are covalently linked by B segments.30−32 The composition of ABA triblock copolymers facilitates the correlation of macromolecular architecture with physical properties. The distance between physical cross-links is constant and is determined by the end-to-end distance of the PEG chain in the B block. The size of the A block can be varied systematically and precisely through synthesis via ATRP.33 B blocks composed of PEG with Mn = 20 000 g/mol produce transparent hydrogels with mesh sizes and swelling ratios that permit homogeneous spatial distributions of light intensity during irradiation. Networks formed using ABA triblocks with B segments of Mn = 4000 g/mol result in translucent solid bulk films with limited hydration.11 The DP of PNBMA A blocks are 10, 24, 35, and 50 as measured by 1H NMR. A summary of the composition of the family of photolabile triblock copolymers

(1)

where G′(t0) and G′(t) represent the initial storage modulus and storage modulus at time t, respectively. Swelling ratios were calculated by measuring the mass of fully swollen hydrogels (n = 3) after removing excess water. Hydrogels were dehydrated under vacuum oven at 40 °C for 48 h before the dry mass was recorded. The swelling ratio Q for hydrogel networks is defined as

Q=

G′ RTQ−1/3

(2)

where Ws and Wd are the masses of the hydrogel network in swollen and dehydrated states, respectively. 2.4. Photodisintegration Kinetics of Cross-Links Using Secondary Reporters. Rhodamine B was chosen as a secondary reporter to measure composition-dependent degradation rates of physical cross-links. Rhodamine B was dissolved in DMSO (0.3 mg/ mL) and incorporated into physical cross-links during hydrogel B

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active PEG cross-links increases as the length of hydrophobic A blocks increases within ABA triblock copolymers.36 These observations are consistent with other physically cross-linked networks composed of amphiphilic ABA triblock copolymers.37,38 The concentration-dependent storage modulus is governed by the probability of overlap between adjacent physical cross-links.34 This trend is also observed in other physically cross-linked hydrogels.39,40 Structure−property relationships in photolabile physically cross-linked networks will first be analyzed with respect to composition of A blocks. The kinetics of light-induced disintegration of physically cross-linked hydrogels as measured by G′ vs t is shown in Figure 2. The disintegration rate of physical cross-links, as inferred from rheological data, is a strong function of the concentration of polymer in precursor solutions cpre. Networks formed using NB10 at cpre = 15% (w/w) exhibit the most rapid degradation rate during UV irradiation with G′ = 0.2 after 200 s. Networks prepared from NB10 at cpre = 25% (w/w) require 500 s to achieve G′ = 0.2. The inverse relationship between network disintegration rate and precursor concentration is consistent for all values of DPAblock in this study. The disintegration rate of physical cross-links is also a strong function of DPAblock (Figure 2d). These results are consistent with the proposed mechanism for light-induced network disintegration. Hydrogels prepared from precursor solutions with either relatively higher values of cpre or DPAblock require more irradiation time to achieve a given value of G′. The disintegration profiles exhibit three discrete phases during light-induced disintegration, each of which exhibits a different value for |dG′(t)/dt|. The initial disintegration rate in the first phase is relatively slow but accelerates for values of G′(t) between 0.95 and 0.8. The second phase exhibits the maximum rate of |dG′(t)/dt|, which is followed by deceleration in the rate of disintegration at values of G′(t) between 0.3 and 0.2. The

synthesized in this study is shown in Table 1. Stable hydrogel networks require a DOE >90% as determined from empirical Table 1. Relevant Properties of Triblock Copolymers Including Composition, Molecular Weight, and Mass Fraction of Poly(o-nitrobenzyl methacrylate) A Blocks abbrev

DP of A blocka

DOE of onitrobenzylb (%)

Mn (g/mol)

mass fraction of A block (%)

NB10 NB24 NB35 NB50

10 24 35 50

100 99 92 94

24400 30560 34596 41196

18 34 42 51

a

Degree of polymerization calculated from 1 H NMR (see Experimental Section). bDegree of esterification calculated from 1H NMR (see Experimental Section).

observations. Photolabile ABA triblock copolymers with pendant o-nitrobenzyl derivatives were chosen as model compounds to characterize structure−property relationships. Physically cross-linked hydrogels prepared from PNBMA-bPEG-b-PNBMA triblock copolymers exhibit frequency-independent storage moduli and sufficiently small loss moduli (Figure 1a). These data indicate that all hydrogels exhibit linear elastic solidlike behavior. The dynamic storage modulus G′ at 10 rad/s of physically cross-linked PNBMA-b-PEG-b-PNBMA networks ranges from 82 ± 16 to 4772 ± 380 Pa as measured by rheology. The value of G′ is directly proportional to the volumetric density of active chains within the network ρ.34,35 The primary driver of ρ is the total concentration of NBMA groups in the network, which is governed by both the DP of the A block DPAblock and the concentration of polymer in the precursor solution cpre (Figure 1b,c). Observed values of G′ increase by approximately 10-fold as the DPAblock increases from 10 to 50 for a given polymer concentration. The number of

Figure 1. Rheological data of physically cross-linked PNBMA-b-PEG-b-PNBMA triblock copolymer networks. (a) Frequency sweeps for the (a, i) storage modulus and (a, ii) loss modulus are shown for gels prepared using 20% (w/w) precursor solutions across a range of DP for A blocks in ABA triblock copolymers. (b) Values of storage modulus at 10 rad/s are shown as a function of DPAblock for various concentrations of precursor solution cpre. (c) Storage modulus at 10 rad/s is shown as a function of copolymer concentrations for A segments of NB10, NB24, NB35, and NB50. C

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Figure 2. Plots of G′(t) as a function of DPAblock and precursor concentration cpre. The rate of decrease of G′ is a strong function of DPAblock and cpre. Plots of G′(t) versus time are shown for the following compositions of A blocks: (a) NB10, (b) NB24, and (c) NB35. (d) The role of A block size on the rate of light-induced disintegration is also shown for various values of DPAblock for cpre = 10% (w/w).

Scheme 1. Molecular Structure and Schematic Illustration of (a) Covalently Cross-Linked Hydrogels That Use Photolabile Monomers in the Polymer Backbone8 and (b) Physical Hydrogels Formed by ABA Triblock Copolymersa

a Photolabile o-nitrobenzyl groups are denoted as rectangles that are distributed homogeneously in covalent hydrogels and heterogeneously in selfassembled physically cross-linked phase-segregated photolabile hydrogels.

chains. The combination of strong π−π interactions and block copolymer topology suggests that a critical amount of NBMA groups must be converted into methacrylic acids to destabilize the gel and accelerate disintegration.41 The value of |dG′(t)/dt| becomes smaller in the third and final phase for G′(t) < 0.2

first phase of disintegration may be associated with uncaging of NBMA groups in A blocks incorporated within active crosslinks, which yield a gradual but immediate reduction in G′(t). The next phase corresponds to liberation of a critical number of physically cross-linked triblock copolymers with active PEG D

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Scheme 2. Schematic Illustration of Light-Induced Disintegration Process of Photolabile (a) Covalently Cross-Linked and (b) Physically Cross-Linked PEG Hydrogel Networksa

a

Photolysis of NBMA groups in covalently cross-linked hydrogels results in instantaneous decrease of cross-link density. Uncaging of photolabile groups in physical hydrogels requires a critical fraction of uncaged NBMA to convert amphiphilic ABA triblock copolymers into water-soluble chains that lead to network disintegration.

intensities (20 mW cm−2). These trends indicate that homogeneous distributions of photolabile groups permit immediate and complete disintegration of cross-links. The critical fraction fc of uncaged NBMA for converting amphiphilic ABA triblock copolymer into uniformly hydrophilic chains is an important parameter that links molecular-scale photolysis with macroscopic properties. This critical value is estimated by using empirical relationships between the Hansen solubility parameters (δd, δp, and δh) of PNBMA, PMAA, and water (Table 2).43 The solubility parameters of PNBMA is estimated from polystyrene based on the mutual presence of aromatic groups.43 The solubility parameter of a random copolymer composed of NBMA and MAA is estimated as the intermediate between δNBMA and δMAA in the 3D Hansen solubility coordinate space.44 The molar ratio between NBMA and MAA is varied so that the Hansen parameters of water lies within the solubility sphere of the copolymer.43 A value of fc > 0.34 implies that >34% of NBMA groups in A blocks need to be uncaged to dissociate physical cross-links. Next, a histogram of the DPAblock distribution of triblock copolymers is

because of the evolution of water-insoluble o-nitrosobenzaldehyde groups. Furthermore, newly formed benzaldehyde derivatives have an extinction coefficient that is larger than NBMA groups.42 These groups attenuate the intensity of incident light within physical cross-links and reduce the rate of light-induced disintegration. This phenomenon is most evident for gels prepared from PNBMA-b-PEG-b-PNBMA of NB50 (10% w/w). The value of G′(t) is >0.75 throughout these measurements (Figure 2d). The temporal evolution of G′(t) in physically cross-linked networks composed of photolabile ABA triblock copolymers differs from the progression of G′(t) for covalently cross-linked networks. A schematic illustration of each network is shown in Schemes 1 and 2. Reconfigurable hydrogels with photolabile covalent main chains exhibit an exponential decrease in G′(t) with time.8 The value of |d2G′(t)/ dt2| > 0 for all times t because homogeneously distributed photolabile groups are uniformly susceptible to light-induced uncaging at UV wavelengths. Furthermore, the value of G′(t) monotonically and steadily approaches zero during time periods on the order of 300 s for comparable UV light E

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Macromolecules Table 2. Hansen Solubility Parameters (δd, δp, and δh in MPa0.5) and Interaction Radius (R0 in MPa0.5) of PNBMA, PMAA, and Watera,43 material

δd

δp

δh

R0

PNBMA PMAA H2O

21.3 25.6 18.1

5.8 11.2 17.1

4.3 19.6 16.9

12.7 20.3 13.0

to 75% (Figure S2b). At a given step, the value of keff at fc = 25% drops 2−4 times compared with the keff at fc = 75%. This model is extended to hydrogels with DPAblock of 10 and 35 (Figure S3). [NBMA] = exp( −keff t ) [NBMA]0

(4)

The value of keff is a strong function of polymer concentration cpre. The dependence of keff on cpre was verified by measuring the release of a reporter molecule from physically cross-linked aggregates. The normalized absorbance of released Rhodamine B in aqueous solution increases with exposure time compared to control samples (Figure S4). These data suggest that the release is controlled by light-induced hydrogel disintegration. The release kinetics of Rhodamine B, as inferred by the slope of the curves, is a function of polymer concentration cpre. Hydrogels with cpre = 10% (w/w) exhibit the most rapid rates of Rhodamine B release and network disintegration for a given illumination intensity. This trend is consistent with the photodegradation kinetics of hydrogels measured by rheology (Figure 2b). The release rate of noncovalently coupled Rhodamine B from physical cross-links is likely associated with the geometry of the aggregates. Physical cross-links formed using relatively small values of cpre will likely have relatively low aggregation numbers with A blocks that are more susceptible to NBMA uncaging. Physical cross-links with relatively low aggregation numbers will also facilitate Rhodamine B release because of the larger surface area-to-volume ratio. Taken together, these results suggest that the intrinsic rate of NBMA uncaging in physical cross-links is a strong function of cpre. The equilibrium swelling ratios Q of a network is governed by the end-to-end distance of B blocks (Figure 4). Values of Q vary inversely with both the DPAblock and cpre. The cross-link density of hydrogels is related to Q and G′ via eq 3 (Figure 5). This expression considers cross-linked domains as zero-volume elements, an assumption that is valid for covalently cross-linked hydrogels. ABA networks require additional considerations. First, physical cross-links composed of PNBMA exhibit a composition-dependent non-negligible volume that scales with the DP of the A block. Second, the mean distance between physical cross-links is determined by the average end-to-end distance of B blocks composed of 20 000 g/mol PEG. The end-

a

The solubility parameters associated with PNBMA are estimated from values with polystyrene due to structural homology.

constructed from GPC measurements (Figure S2a). The distribution of DPAblock provides a baseline to establish a quantitative model for simulating photolysis kinetics, as inferred by reduced values of G′. The phase angle δ as determined by tan δ = G″/G′ is restricted below 10° in subsequent calculations to ensure the hydrogel remains within the linear elastic regime during the analysis. A representative fit between experimental and calculated results for hydrogels with DPAblock = 24 is shown in Figure 3a. An exponential function of ∑nn=0t on the step number n gives an optimal fitting.45 This model indicates that the reduction of G′ at initial stages of irradiation are governed by triblock copolymer chains that have a relatively low DPAblock since fewer photolytic steps are required to reach fc compared to polymers with higher DPAblock. This model also explains the accelerated reduction in G′ during the second phase of light-induced network disintegration. This observed trend in G′ likely arises due to the onset chain instability in polymers with DPAblock within the mode of the molecular weight distribution of A blocks. The uncaging kinetics of NBMA in physical cross-linked hydrogels can be described as a first-order reaction rate (eq 4).45 The amount of uncaged NBMA during every step number, as denoted by [NBMA], and the associated time t can be calculated from the fitting model. Therefore, the effective uncaging rate coefficient keff can be calculated for each step (Figure 3b). Values of keff generally exhibit a gradual decrease with irradiation time. This trend in keff is attributed to accumulation of o-nitrosobenzaldehyde byproducts which have an extinction coefficient 2−4 times larger than that of NBMA groups for wavelengths 320−500 nm.46 The value of keff also depends on the value of fc. A sensitivity analysis of keff versus fc is conducted by varying the critical fraction from 25%

Figure 3. (a) Comparison of the experimental and predicted profiles of hydrogel disintegration with DPAblock = 24 and cpre = 10%, 15%, 20%, and 25%. The normalized storage modulus where the phase angle δ below 10° is used in calculation to ensure that the materials are in the linearly elastic regime. The model is described in detail in the Supporting Information. (b) Plot of the uncaging rate coefficient keff of NBMA in physically crosslinked hydrogels as a function of step number. The decrease of keff with n is due to the attenuated light intensity caused by accumulation of onitrosobenzaldehyde byproducts. F

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Figure 4. Swelling ratio of physically cross-linked hydrogels is plotted as a function of (a) polymer concentration in precursor solutions cpre and (b) DP of A blocks DPAblock.

hypothetical physically cross-linked network model with an infinitesimally small A segment by assuming that the hydrophobic PNBMA-rich domains contain no water. Qr is plotted as a function of cpre and DPAblock (Figure 6). Qr values become

Figure 5. Calculated cross-link density of photolabile ABA hydrogels as a function of the degree of polymerization (DP) of A blocks and the concentration of polymer in the precursor solution. Values are calculated using eq 3 (see text). Figure 6. Reduced swelling ratio Qr as a function of both DPAblock and cpre. The calculated value of Qr uses several assumptions to isolate the contribution of PEG chains to water uptake of physically cross-linked hydrogel networks (see text). The value of Qr for DPAblock = 60 was set to Qr = 0 to indicate the inability for this formulation to form a coherent swollen network.

to-end distances of a PEG chain (Mn = 20 000 g/mol) in a good solvent and PNBMA in a poor solvent are estimated using eq 5 and summarized in Table 3. r0 = bN v1

(5)

The Kuhn length bPNBMA of PNBMA segments is estimated from polystyrene monomers,47 while the Kuhn length of PEG bPEG has been previously reported.48 The swelling ratio of physically cross-linked hydrogels is governed by the ratio of the average end-to-end distance of PEG in the swollen and relaxed states. The reduced swelling ratio Qr is defined as the mass of the swollen hydrogel less the gravimetric contribution of the PNBMA phase divided by the dry mass of PEG B blocks. W − WPNBMA Qr = s WPEG (6)

smaller as DPAblock increases beyond 50. This trend reflects the transition from a hydrogel to a condensed phase with limited hydration. Qr can be extrapolated to DPAblock → 0 to predict the swelling ratio of a network with physical cross-links of negligible volume. The mesh size of hydrogels based on the extrapolated reduced swelling ratio is estimated using Peppas− Merrill theory via the following equations:49

In this equation, Ws is the mass of hydrated network while WPNBMA and WPEG represent the total dry mass of the PNBMA A blocks and PEG B blocks, respectively. Qr describes a

( r0̅ 2)1/2 = l(3M̅ c /M r)1/2 Cn1/2

(7)

ξ = υ2,s−1/3( r0̅ 2)1/2

(8)

The number-average molecular weight between cross-links Mc is fixed at 20 000 g/mol. Values are assigned to the following

Table 3. Estimated End-To-End Distance in Water for Mn = 20 000 g/mol PEG and PNBMA with DP = 10, 24, 35, and 50; Value of N for Each Block Was Calculated from the Relative 1H NMR Signals from PEG and NBMA Groups polymer

PEG20000

PNBMA10

PNBMA24

PNBMA35

PNBMA50

b (nm) N r0 (nm) r0(PNBMA)/r0(PEG)

0.6 454 23.5

0.67 10 1.4 0.06

0.67 24 1.9 0.08

0.67 35 2.2 0.09

0.67 50 2.5 0.11

G

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Macromolecules relevant parameters: Cn is the characteristic ratio of PEG in water of 4.0;50 l is the average bond length of 1.48 Å;51 Mr is the molecular weight of repeat unit = 44 g/mol; υ2,s ≈ 1/Qr is the polymer volume fraction of hydrogels after swelling assuming a polymer density of ∼1 g/cm3. The results of these calculations are summarized in Table 4.

water. The calculated mesh sizes of physically cross-linked hydrogels are approximately 6 nm larger than that of PEGDAbased hydrogel analogues. The difference may be due to the assumption that physical cross-links in enriched A blocks are completely anhydrous. In reality, hydrophilic functional groups in PNBMA blocks and DOE < 1 promote hydration of physically cross-linked aggregates. The mesh sizes in physical cross-linked hydrogels are predicted using Peppas−Merrill theory from values of Qr as DPAblock approaches zero. This excluded volume model describes swelling behavior more accurately in other physically cross-linked hydrogel systems that have A segments with increased hydrophobicity and uniformity.

Table 4. Comparison of Mesh Sizes Calculated Using Peppas−Merrill Theory between Physically Cross-Linked Hydrogels from Photolabile Triblock Copolymers with Reduced Swelling Ratio and Photopolymerized PEG Covalent Gels with Comparable Values of Swelling Ratio mesh size,b ξ (nm) swelling ratio (Q, Qr)

a

32.3 ± 0.3 26.2 ± 0.9 23 ± 0.8

physically cross-linked hydrogels

covalently cross-linked hydrogels

34.8 ± 0.1 32.4 ± 0.4 31.1 ± 0.4

28.4 ± 0.1 26.4 ± 0.3 25.2 ± 0.3

4. CONCLUSION This work establishes structure−property relationship of physically cross-linked photolabile hydrogels formed by selfassembly of ABA triblock copolymers. Composition-dependent physical properties and light-induced disintegration rates are measured. Detailed knowledge of this class of hydrogels composition and topology provides an important framework when designing application specific materials for potential use in biomedical applications. Two additional parameters are introduced to map the properties of physically cross-linked photolabile networks to covalently cross-linked networks. A discretized uncaging/stability model and reduced swelling ratios can predict the static and dynamic evolution of physically cross-linked networks by establishing quantitative relationships with covalently cross-linked PEG-based hydrogel analogues. These additional considerations establish informative relationships between molecular scale photolysis events with macroscopic properties. This model could potentially describe structure−property relationships in other types of photolabile physically cross-linked hydrogel networks.

a

Swelling ratios refer to either Qr or Q for physically cross-linked ABA triblock copolymer hydrogels or covalently cross-linked PEG hydrogels, respectively. bMesh sizes calculated via Peppas−Merrill theory via eqs 7, 8, and 9.

Covalently cross-linked PEG hydrogels serve as model networks to validate the mesh size calculations of physically cross-linked hydrogels that utilize the reduced swelling ratio parameter. PEG networks also serve as models to quantify the deviation between physical and chemical gels from the Peppas− Merrill theory. Hydrogels photopolymerized using PEGDA with molecular weight 20 000 g/mol exhibit molecular and topological homology to PNBMA-b-PEG-b-PNBMA triblock copolymers. The mesh size of PEGDA gels is calculated using eqs 7 and 8 with the value of Mc calculated first from eq 9. Other relevant parameters are as follows: υ̅ is the specific volume of PEG = 0.861 cm3/g;51 V1 is the molar volume of water = 18 cm3/mol; υ2,r is the volume fraction of the hydrogel prior to swelling. (υ ̅ /V1)[ln(1 − υ2,s) + υ2,s + χυ2,s 2] 1 2 = − ⎡ υ 1/3 ⎤ M̅ c M̅ n 1 υ υ2,r ⎢ υ2,s − 2 υ2,s ⎥ 2,r ⎦ ⎣ 2,r

( )

( )

■

Figures S1−S5. This material is available free of charge via the Internet at http://pubs.acs.org.

■

⎛ ξ ⎞b ⎜ ⎟ ⎝a⎠

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (C.J.B.). (9)

Notes

The authors declare no competing financial interest.

The relationship between Q and ξ for PEGDA networks is presented in Figure S5. The data are fit using a power law relationship (eq 10), which is in agreement with theoretical predictions via eq 8. Q=

ASSOCIATED CONTENT

S Supporting Information *

■

ACKNOWLEDGMENTS Funding was provided by the following organizations: the Berkman Foundation; the American Chemical Society Petroleum Research Fund (ACS PRF #51980-DNI7); the American Heart Association Scientist Development Grant (12SDG12050297); the Carnegie Mellon University School of Engineering; and the National Institutes of Health (NIBIB R21RB015165). NMR instrumentation at CMU was partially supported by National Science Foundation (CHE-0130903 and CHE-1039870).

(10)

The parameters of best fit occur for a = 8.15 ± 0.2 nm and b = 2.78 ± 0.05. These values are comparable to previously described theoretical relationship between these parameters (eq 8). The slight departure of b from the anticipated value of three may be attributed to experimental error in determining Q. The calculated mesh sizes of both physically cross-linked hydrogels formed by triblock copolymers with values of Qr and PEG gels with a comparable value of Q are summarized in Table 4. Physically cross-linked hydrogels and the covalently crosslinked PEGDA hydrogels exhibit an identical swelling ratio. Therefore, the mesh size of both gels should be equal since this parameter depends upon the conformation of PEG chains in

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