Biomacromolecules 2005, 6, 2857-2865
`
`2857
`
`Rheological Characterization of in Situ Cross-Linkable
`Hyaluronan Hydrogels
`
`Kaustabh Ghosh,† Xiao Zheng Shu,‡ Robert Mou,§ Jack Lombardi,§ Glenn D. Prestwich,‡
`Miriam H. Rafailovich,| and Richard A. F. Clark*,†,^
`DepartmentsofBiomedicalEngineering,MaterialScienceandEngineering,DermatologyandMedicine,
`StateUniversityofNewYorkatStonyBrook,StonyBrook,NewYork11794-8165,Departmentof
`MedicinalChemistry,TheUniversityofUtah,419WakaraWay,Suite205,SaltLakeCity,Utah
`84108-1257,andPhysicalChemistryLaboratory,EsteeLauderResearch,Melville,NewYork11747
`
`ReceivedMay26,2005;RevisedManuscriptReceivedJune10,2005
`
`This report investigates the rheological properties of cross-linked, thiol-functionalized HA (HA-DTPH)
`hydrogels prepared by varying the concentration and molecular weight (MW) of the cross-linker, poly-
`(ethylene glycol) diacrylate (PEGDA). Hydrogels were subsequently cured for either short-term (hours) or
`long-term (days) and subjected to oscillatory shear rheometry (OSR). OSR allows the evaluation and
`comparison of the shear storage moduli (G¢), an index of the total number of effective cross-links formed
`in the hydrogels. While the oscillatory time sweep monitored the evolution of G¢ during in situ gelation, the
`stress and frequency sweeps measured the G¢ of preformed and subsequently cured hydrogels. From stress
`sweeps, we found that, for the hydrogels, G¢ scaled linearly with PEGDA concentration and was independent
`of its MW. Upon comparison with the classical Flory’s theory of elasticity, stress sweep tests on short-term
`cured hydrogels revealed the simultaneous, but gradual, formation of spontaneous disulfide cross-links in
`the hydrogels. Results from time and frequency sweeps suggested that the formation of a stable, three-
`dimensional network depended strictly on PEGDA concentration. Results from the equilibrium swelling of
`hydrogels concurred with those obtained from oscillatory stress sweeps. Such a detailed rheological
`characterization of our HA-DTPH-PEGDA hydrogels will aid in the design of biomaterials targeted for
`biomedical or pharmaceutical purposes, especially in applications involving functional tissue engineering.
`
`Introduction
`
`Hyaluronan (HA) is a linear, nonsulfated glycosaminogly-
`can found ubiquitously in the extracellular matrix (ECM) of
`virtually all mammalian connective tissues.1 This polyanionic
`biopolymer is composed of repeating disaccharide units of
`(cid:226)-1,4-D-glucuronic acid and (cid:226)-1,3-N-acetyl-D-glucosamine.2
`Previously, HA in tissues was believed to act only as an
`inert lubricating substance; however, important biological
`functions of HA are now widely reported in the literature.1,3
`HA occurs naturally in a wide range of molecular weights
`(MWs; 0.1-10 million) and concentrations4 and is stabilized
`by association with a number of link proteins. These
`attributes impart HA with its unique rheological properties
`that allow it to fulfill diverse physicochemical functions in
`different locations in the body. This property of native HA
`has been exploited therapeutically in viscosupplementation
`and viscosurgery.5 However, pure native HA has found
`limited clinical application, largely due to its poor bio-
`
`* Corresponding author: phone 631-444-7519; fax 631-444-3844; e-mail
`rclark@notes.cc.sunysb.edu.
`† Department of Biomedical Engineering, SUNY at Stony Brook.
`‡ The University of Utah.
`§ Estee Lauder Research.
`| Department of Material Science and Engineering, SUNY at Stony
`Brook.
`^ Department of Dermatology and Medicine, SUNY at Stony Brook.
`
`mechanical properties and rapid degradation in vivo. To
`address this problem, several chemical modifications have
`been successfully employed to significantly improve the
`biomechanical properties of HA and, thereby, its ease of
`handling and residence time in vivo.6-9
`One such novel chemical modification involving the
`synthesis of thiol-functionalized HA (HA-DTPH) has been
`previously reported6 (Figure 1A). By virtue of their ability
`to form spontaneous disulfide bonds upon exposure to air,
`the free thiols on HA backbone act as latent cross-linking
`agents (Figure 1B). Since the formation of disulfide bonds
`is slow, Michael-type addition between free thiols and
`acrylates of poly(ethylene glycol) (PEG) has been utilized
`to rapidly cross-link HA-DTPH. This chemistry, first
`reported by Lutolf et al.10 and suitably modified for HA-
`DTPH,11 uses homobifunctional PEG diacrylate (PEGDA)
`to produce an in situ cross-linkable hydrogel in approximately
`10 min (Figure 1C). Importantly, the cross-linking reaction
`between free thiols and PEGDA occurs at physiological pH
`and room temperature, which ensures complete biocompat-
`ibility during cell encapsulation or incorporation of biologi-
`cally active ligands.11,13 The disulfide and PEGDA cross-
`linked HA-DTPH biomaterials (denoted hereafter by HA-
`S-S-HA and HA-PEGDA-HA, respectively) and their
`functional derivatives have great potential in drug delivery
`and tissue engineering applications.6,11-13
`
`© 2005 American Chemical Society
`10.1021/bm050361c CCC: $30.25
`Published on Web 07/20/2005
`
`ALL 2027
`PROLLENIUM V. ALLERGAN
`IPR2019-01505 et al.
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`2858 Biomacromolecules,Vol.6,No.5,2005
`
`Ghosh et al.
`
`Figure 1. Schematic showing (A) synthesis of thiol-functionalized HA (HA-DTPH),6 (B) spontaneous cross-linking forming HA-S-S-HA linkages,
`and (C) exogenous PEGDA-mediated cross-linking forming HA-PEGDA-HA linkages (adapted and modified from Shu et al.6).
`
`the rheological
`Previous published data indicate that
`properties of most polymeric biomaterials, including HA-
`based biomaterials, depend not only on the MW and
`concentration of the macromer but also on the nature and
`density of effective cross-links.11,14 Furthermore, the rheo-
`logical properties of biomaterials can modulate their thera-
`peutic utility. For example, rheological modifications of
`PLGA film-based implants affect drug release profiles.15 The
`cross-linking density influences the stiffness of PEG hydro-
`gels and thereby the synthesis and distribution of extracellular
`matrix produced by the seeded chondrocytes.16 Lee et al.17
`reported the effect of multifunctional cross-linking on in vitro
`
`degradation of the resulting hydrogels. The viscoelasticity
`of cross-linked HA has been shown to affect their therapeutic
`potential in viscosupplementation,18 in significant reduction
`of postsurgical adhesions,19 and in soft-tissue augmentation.20
`These findings underscore the importance of rheological
`properties of biomaterials.
`This study, therefore, characterizes the rheological proper-
`ties of the recently reported HA-PEGDA-HA hydrogels.11
`Oscillatory shear rheometry, operated in time, stress, and
`frequency sweep modes, was used to evaluate the shear
`storage moduli (G¢) of the hydrogels as a function of
`concentration and MW of the PEGDA cross-linker. Since
`
`

`

`Rheology of Cross-Linked HA Hydrogels
`the slow HA-S-S-HA and the rapid HA-PEGDA-HA
`cross-linking reactions proceed at very different rates,11 we
`also monitored G¢ as a function of short-term (hours) and
`long-term (days) curing times. Effects of PEGDA concentra-
`tion and MW on the levels of equilibrium swelling of the
`various hydrogels were also evaluated.
`
`Materials and Methods
`
`Materials. Fermentation-derived hyaluronan (HA, sodium
`salt, Mw 1 500 000) was provided by Clear Solutions Bio-
`technology, Inc. (Stony Brook, NY). 1-Ethyl-3-[3-(dimethyl-
`amino)propyl]carbodiimide (EDCI) and poly(ethylene glycol)
`diacrylate (PEGDA, MW 700, purity 95%) were purchased
`from Aldrich Chemical Co. (Milwaukee, WI). PEGDA (MW
`3400, purity 98%) was purchased from Nektar Therapeutics
`(Huntsville, AL). Dulbecco’s modified Eagle’s medium
`(DMEM) was obtained from Sigma Chemical Co. (St. Louis,
`MO). Dithiothreitol (DTT) was purchased from Diagnostic
`Chemical Limited (Oxford, CT). 5,5¢ -Dithiobis(2-nitroben-
`zoic acid) (DTNB) was purchased from Acros (Houston,
`TX). 3,3¢ -Dithiobis(propanoic dihydrazide) (DTP) was syn-
`thesized as previously described.6 Distilled phosphate-
`buffered saline (1(cid:2) dPBS, pH 7.4) was prepared in the lab
`according to a standard protocol.
`Synthesis of Thiol-Functionalized HA. Thiol-function-
`alized HA, or 3,3¢ -dithiobis(propanoic dihydrazide)-modified
`HA (HA-DTPH), was synthesized according to a previously
`reported procedure.6 In principle, the native carboxylic groups
`on HA disaccharide units were replaced by thiol-containing
`DTPH groups. The degree of substitution (% SD), defined
`as the number of DTPH groups per 100 disaccharide units
`on the HA molecule, was determined by 1H NMR.6 The free
`thiol content (percent), defined as the number of free thiols
`per 100 disaccharide units, was measured in parallel by a
`modified Ellman method.6,21,22 Both % SD and the free thiol
`content were found to be approximately 42%, indicating that
`the remaining 58% of the HA disaccharide units contained
`the native carboxylic acid group. The pKa of thiols in HA-
`DTPH was 8.87 as determined spectrophotometrically on the
`basis of UV absorption of thiolates. The MW was determined
`by calibrated gel-permeation chromatography (GPC) to be
`Mw 158 000 and Mn 78 000 (polydispersity index 2.03).
`Specimen Preparation: Hydrogels. A 1.25% (w/v) HA-
`DTPH solution was prepared by dissolving HA-DTPH in
`serum-free DMEM supplemented with 1% (v/v) penicillin,
`streptomycin, and glutamine (antibiotic mix). The HA-
`DTPH solution was first pH-adjusted to 7.4 (by addition of
`1.0 M NaOH) and then sterilized by filtration through a 0.22
`(cid:237)m filter. A 4.5% (w/v) PEGDA (MW 3400) stock solution
`was prepared by dissolving PEGDA powder in 1(cid:2) dPBS.
`Four volumes of 1.25% HA-DTPH solution were then
`mixed with one volume of PEGDA solution of varying
`concentrations (4.5%, 3.0%, 2.25%, 1.5%, and 0.75%) to
`obtain HA-PEGDA-HA hydrogels of different cross-
`linking densities (defined in this report as the molar ratio of
`thiols on HA-DTPH:acrylate groups on PEGDA) of 2:1,
`3:1, 4:1, 6:1, and 12:1, respectively. To determine if MW
`of PEGDA had an influence on the physicochemical proper-
`
`Biomacromolecules,Vol.6,No.5,2005 2859
`ties, HA-PEGDA-HA hydrogels with a cross-linking
`density of 2:1 were also prepared from PEGDA MW 700.
`The final concentration of HA-DTPH in the hydrogels was
`always 1% (w/v). As previously reported,11 gelation time
`was found to be inversely proportional to PEGDA concen-
`tration. A 1% HA-DTPH solution was also prepared without
`addition of any PEGDA. All hydrogels were plated in regular
`35 mm tissue culture dishes. Serum-free DMEM was added
`to the surface of all hydrogels to allow for equilibrium
`swelling prior to oscillatory shear rheometry.
`Regardless of the cross-linking densities used in this study,
`all HA-PEGDA-HA hydrogels ideally contain excess free
`thiols. We, therefore, investigated the extent of net effective
`cross-linking in these hydrogels arising from both HA-S-
`S-HA and HA-PEGDA-HA cross-links as a function of
`curing time. For this study, all HA-PEGDA-HA hydrogels
`were plated simultaneously (at t ) 0); at the end of each
`experimental time point, an 11 mM iodoacetamide solution
`in 1(cid:2) dPBS was added to the hydrogel surface to block
`residual free thiols and thereby prevent any additional HA-
`S-S-HA or HA-PEGDA-HA cross-links.
`Rheological Characterization: Oscillatory Shear Rhe-
`ometry of Hydrogels. An AR2000 rheometer (TA Instru-
`ments Inc.) with a standard steel parallel-plate geometry of
`20 mm diameter was used for the rheological characterization
`of all hydrogel samples. The test methods employed were
`oscillatory time sweep, stress sweep, and frequency sweep.
`The time sweep was performed to monitor, within a given
`time frame, the in situ gelation of the 2:1, 6:1, and 12:1 HA-
`PEGDA-HA hydrogel solutions. The strain was maintained
`at 5% during time sweeps by adjusting the stress amplitude.
`The test, which was operated at 1 Hz and terminated after
`30 min, recorded the temporal evolution of G¢ and the shear
`loss modulus, G¢¢ .
`The stress sweep was performed on hydrogels to determine
`and compare their G¢ under the same physical condition. The
`stress sweep was set up by holding the temperature (25 (cid:176) C)
`and frequency (1 Hz) constant while increasing the stress
`level from 50 to 70 Pa. The applied range of 50-70 Pa was
`found to be safe-for-use from a prior experiment where we
`determined the linear viscoelastic region (LVR) profiles of
`the 2:1, 6:1, and 12:1 hydrogels by shearing them until
`structure breakdown. In the stress sweep (or “controlled
`stress”) tests, the stress was locally controlled in every cycle
`and the strain (and the corresponding G¢ ) was measured,
`while globally speaking, the hydrogels were subjected to a
`steady stress ramp. A constant normal compressional force
`of (cid:24)4g was applied to all samples throughout the stress
`sweep regime. Both the time and stress sweeps provide G¢
`and G¢¢
`information on the structural integrity of the cross-
`linked network, but at two different physical settings.
`We also subjected the 2:1, 6:1, and 12:1 hydrogels to a
`frequency sweep at 50% of their respective ultimate stress
`levels (corresponding to the point of dip on the LVR profile).
`At this fixed shear stress and temperature (25 (cid:176) C), the
`oscillatory frequency was increased from 0.1 to 100 Hz and
`the G¢ was recorded. To avoid dislocation during each test
`method, all 35 mm dishes containing the hydrogels were
`fixed to the bottom plate with stable, double-sided tape. The
`
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`2860 Biomacromolecules,Vol.6,No.5,2005
`plots of G¢ versus shear stress, reaction time, or frequency
`from the three sweep tests were obtained directly from the
`software controlling the rheometer. All samples were done
`in triplicate.
`FTIR Analysis. A Nicolet Magna-IR 760 optical bench
`spectrometer (Thermo Electron Corp.) was used to obtain
`Fourier transform infrared (FTIR) spectra of pure HA-
`DTPH, pure PEGDA, and 8-h cured HA-DTPH-PEGDA
`hydrogel on calcium fluoride disks. A normalized spectrum
`was obtained by subtracting the HA-DTPH spectrum from
`the hydrogel spectrum, which was then compared with that
`of pure PEGDA. The peaks at 1634 and 1410 cm-1
`(corresponding to -CdC- bond stretching and scissoring,
`respectively) were used to follow the consumption of
`PEGDA in the HA-PEGDA-HA hydrogel.
`Equilibrium Swelling of Hydrogels. Identical volumes
`of hydrogel samples were plated in wells of a 24-well plate.
`All hydrogel samples were allowed to sit at room temperature
`for about 2 h before weighing them; this allowed the weakly
`cross-linked 12:1 hydrogels to set well before the start of
`the experiment. After the initial weights (Wi) were recorded,
`all hydrogels were gently transferred to weigh boats filled
`with distilled, deionized water. To obtain equilibrium swell-
`ing, all samples were allowed to swell at room temperature
`for 48 h. The equilibrium swollen mass (Ws) was then
`recorded by gently blotting excess water from each sample.
`The hydrogel samples were subsequently dried for 48 h in a
`desiccator at room temperature and their dry weights (Wd)
`were measured. The equilibrium swelling ratio (Q) was
`defined as the ratio of Ws to Wd.
`
`Results and Discussion
`Thiol-functionalized HA, or HA-DTPH, is synthesized
`by substituting the native carboxylic group on HA molecule
`with free and active thiol groups. Upon exposure to air, the
`thiols on HA-DTPH are oxidized to form a spontaneous,
`albeit slow (within 4-6 h), HA-S-S-HA cross-linked
`network. These HA-S-S-HA cross-links are reversible in
`nature since addition of DTT (a reducing agent) results in
`the dissolution of the networked structure.6 However, to
`enhance the rate of cross-linking, Michael-type addition
`reaction is employed where, by use of homobifunctional
`PEGDA, a HA-DTPH solution is cross-linked to form a
`stable hydrogel within approximately 10 min.11 This rapid
`gelation, also occurring at physiological pH and room
`temperature, advocates its proposed injectable in vivo use.
`In the first published report describing the formation of
`HA-PEGDA-HA hydrogels,11 Shu et al. showed an in-
`crease in both cross-linking efficiency of PEGDA (i.e.,
`double-end anchorage, from 76.2% to 100%) and the
`observed gelation time (from 5 to 19 min) with decreasing
`PEGDA concentration [from 9% to 3% (w/v)]. On the basis
`of these data, PEGDA concentration of 4.5% (corresponding
`to a cross-linking density of 2:1) was found to be optimum
`for use both in vitro and in vivo.11,13 Importantly, after these
`optimally cross-linked hydrogels have been formed, about
`half the original number of thiol groups is still freely
`available that may potentially form additional HA-S-S-
`
`Ghosh et al.
`
`HA cross-links. Both the extent and rate of formation of these
`disulfide links are likely to alter the microlevel network
`structure and thereby the rheological and physicochemical
`properties of these HA-PEGDA-HA hydrogels. Altering
`the molar concentration and MW of PEGDA can also
`produce such effects. A similar trend was observed in HA-
`ADH-PEG dialdehyde hydrogels where changes in PEG
`dialdehyde (cross-linker) concentration altered the network
`structure and the inherent physicochemical properties.23
`These issues have, however, never been addressed before
`for the HA-PEGDA-HA hydrogels. Therefore, in this study
`we aimed to determine the effect of the above-mentioned
`parameters on the rheological behavior and levels of equi-
`librium swelling of the resulting HA-PEGDA-HA hydro-
`gels. On the basis of these data, we propose plausible
`schemes of cross-linking occurring in these hydrogels.
`Rheological Characterization of HA-DTPH Hydrogels.
`(A) Oscillatory Time Sweep. Oscillatory time sweeps were
`performed to monitor the in situ gelation of HA-PEGDA-
`HA solutions prepared from PEGDA MW 3400, the MW
`shown to be optimal for use both in vitro and in vivo.11 Figure
`2 shows the time sweep profiles of G¢ and G¢¢
`for the 2:1,
`6:1, and 12:1 HA-PEGDA-HA hydrogel networks (panels
`A, B, and C, respectively). Initially, G¢¢
`is larger than G¢,
`which is expected since the samples are still in liquid state
`where viscous properties dominate, and therefore most (if
`not all) of the energy is lost as viscous heat. As the solutions
`begin to gel and a cross-linked network is formed, both G¢
`and G¢¢ begin to increase; however, the rate of increase of
`G¢
`is much higher than that of G¢¢
`since now the elastic
`properties of the gelling hydrogel begin to dominate.
`Consequently, there is a crossover point where G¢ becomes
`larger than G¢¢. The time required for this crossover to occur
`is sometimes referred to as the gelation time for the
`solution.24 Although the apparent gelation times observed
`by the “test tube inverting” method were greater than those
`observed in these profiles, they were proportionate for all
`three cross-linking densities. Furthermore, from Figure 2 we
`see that with increased PEGDA concentration the crossover
`point appears sooner, indicating that PEGDA cross-linking
`of HA-DTPH is the rate-limiting reaction during this early
`phase of gelation. Although the plot of G¢¢ plateaus with time,
`it never decreases to 0, suggesting the viscoelastic nature of
`these hydrogels under the applied physical conditions. The
`slightly erratic nature of G¢¢ observed during the time sweep
`tests is attributed to grip-slip caused by the release of water
`from the hydrogels as they undergo shear stress.
`(B) Oscillatory Stress Sweep. Oscillatory stress sweep
`allows determination of G¢ of the hydrogels as a function of
`PEGDA concentration and MW. The effect of curing time
`on G¢ can also be similarly evaluated. The data obtained can
`be further used to predict and compare the rate and extent
`of formation of effective cross-links in various hydrogels.
`In compliance with the principle of small deformation
`rheology,24 the hydrogels must be tested within their respec-
`tive linear viscoelastic ranges, the length of which determines
`the structural stability. We, therefore, first determined the
`LVR profiles of the 2:1, 6:1, and 12:1 HA-PEGDA-HA
`hydrogels by subjecting them to a stress sweep until structure
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`Rheology of Cross-Linked HA Hydrogels
`
`Biomacromolecules,Vol.6,No.5,2005 2861
`
`Figure 3. Determination of the linear viscoelastic region (LVR) of
`the 8-h cured 12:1, 6:1, and 2:1 cross-linked HA-PEGDA-HA
`hydrogels (PEGDA MW 3400). Frequency of the applied oscillatory
`shear stress was 1 Hz.
`
`Figure 4. Comparison of G¢ of HA-PEGDA-HA hydrogels prepared
`from PEGDA of MW 3400 and 700. Oscillatory shear stress was
`performed at 1 Hz.
`
`verified to be lying in the LVR of even the least (2 h) cured
`hydrogels (data not shown).
`We next looked at the effect of PEGDA MW on the
`storage moduli of the hydrogels. PEGDA MW 700 and 3400
`were used to prepare 2:1, 6:1, and 12:1 HA-PEGDA-HA
`hydrogels. These hydrogels were subsequently cured for 8
`h before being subjected to stress sweep. Figure 4 illustrates
`that G¢ of HA-PEGDA-HA hydrogels was almost entirely
`independent of PEGDA MW; G¢ was, however, strongly
`dependent on the number of cross-links formed, which was
`controlled by PEGDA concentration. We inferred that, in a
`hydrated state, water molecules act as the most flexible
`component and therefore the hydrogel stiffness becomes
`insensitive to the flexibility imparted by the length (or MW)
`of the PEGDA molecule. As a result, all subsequent
`oscillatory stress sweeps were performed on hydrogels
`prepared from PEGDA MW 3400 only.
`Next, hydrogels of varying cross-linking densities were
`formed and allowed to cure for 2, 4, 8, 10, and 24 h. Existing
`theories and numerous published reports have earlier sug-
`gested a strong correlation between the measured G¢ and the
`number of effective intermolecular cross-links formed in a
`hydrogel network.14,15,17,25,26 We, therefore, monitored and
`compared the evolution of G¢ as a function of cross-linking
`density and curing time to assess the extent of effective
`intermolecular cross-links formed in the various hydrogel
`networks. Two additional cross-linking densities of 3:1 and
`
`Figure 2. Evolution of shear storage moduli, G¢ (]), and shear loss
`moduli, G¢¢
`(4), as a function of time during the pregelation and early
`gelation phases of (A) 2:1, (B) 6:1, and (C) 12:1 HA-PEGDA-HA
`hydrogels (PEGDA MW 3400).
`breakdown. Since the HA-PEGDA-HA and HA-S-S-
`HA cross-links, and the corresponding rheological properties,
`are expected to develop over varying time scales (minutes
`to hours to days),11 it becomes impractical
`to perform
`rheological tests at all time points. Therefore, rheological
`properties such as the LVR profile and frequency response
`of G¢ (in the following section) were determined at a fixed
`curing time of 8 h. The choice of this curing time point was
`justified from previous studies on a similar system (HA-
`PEG monoacrylate conjugation)11 that intuitively suggest that
`HA-PEGDA-HA cross-links might more or less reach
`completion within this period. Figure 3 represents the LVR
`profile of the 8-h cured HA-PEGDA-HA hydrogels,
`showing clearly that, with increasing cross-linking density,
`the structure breakdown occurred at higher shear stress levels.
`On the basis of these data, a stress range of 50-70 Pa was
`chosen for comparing various hydrogel samples, which was
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`2862 Biomacromolecules,Vol.6,No.5,2005
`
`Ghosh et al.
`
`Figure 5. Evolution of G¢ of HA-PEGDA-HA hydrogels as a function
`of short-term curing time (PEGDA MW 3400).
`
`4:1 were introduced in this study in order to obtain enough
`data points to allow comparison of our results with those
`predicted by the classical elasticity theories. From the results
`of the stress sweep test shown in Figure 5, the development
`of G¢ appears to be solely governed by the cross-linking
`density (or PEGDA concentration). Additionally, these data
`also suggests that within the small time frame of this test,
`the HA-S-S-HA cross-links do not contribute significantly
`to the network structure properties. This was further con-
`firmed by measuring the G¢ of HA-S-S-HA hydrogels
`(no PEGDA added) at 24 h postcuring. Not so surprisingly,
`the value was much smaller (13 Pa) that is, about 1/7 the
`value for the most weakly cross-linked 12:1 HA-PEGDA-
`HA hydrogels (Figure 5).
`A thorough understanding of the structure of underlying
`molecular networks requires evaluating differentially the
`extent and rate of formation of both HA-PEGDA-HA and
`HA-S-S-HA cross-links. One must, therefore, be able to
`tell approximately (a) when the HA-PEGDA-HA cross-
`links become saturated and (b) when and to what extent the
`HA-S-S-HA cross-links contribute to the overall G¢ -
`network structure relationship. The classical Flory’s rubber
`elastic theory,27 widely used by investigators to validate
`experimental assumptions and data,24,28 was consequently
`used as a standard reference to find plausible explanations.
`Since the rate of conjugation between acrylate and thiol
`groups is much faster than that between two thiol groups,
`we looked at both short-term and long-term curing effects
`on the evolution of G¢ .
`Short-Term Curing. When G¢ was plotted against PEGDA
`molar concentration, a linear relationship was obtained
`initially at the end of the 30-min time sweep (Figure 6A),
`characterized by high R2 and low ł2 values for the linear fit
`(Table 1). This linear relationship is representative of the
`classical Flory’s rubber elasticity theory27 that assumes the
`cross-linking reaction to be solely cross-linker (PEGDA)
`governed. As shown in Figure 6B, with increasing curing
`time (up to 24 h), however, we observed an increasing
`deviation from the typical first-order linearity to a power
`law, with R2 decreasing and ł2 increasing for the linear fit
`and vice versa for the power fit, indicating that the cross-
`linking reaction was no longer entirely PEGDA governed.
`This can be attributed to the gradual formation of HA-S-
`S-HA cross-links occurring secondary to HA-PEGDA-
`
`Figure 6. Correlation of experimental G¢ values, obtained at (A) 30
`min and (B) 24 h postcuring with those predicted from the classical
`Flory’s rubber elasticity theory. Shown are the linear and power fits,
`with the solid line indicating the better fit.
`Table 1. Comparing G¢ Values Obtained for Short-Term Cured
`Hydrogels with Those Expected from Flory’s Elasticity Theory
`ł2
`R2
`short-term curing time linear fita power fitb linear fita power fitb
`30 min
`0.9945
`0.9583
`3.684
`95.216
`4 h
`0.9905
`0.9835
`37.782
`25.162
`8 h
`0.9851
`0.9816
`41.238
`32.602
`24 h
`0.9733
`0.9948
`94.557
`2.507
`
`a As predicted by Flory’s elasticity theory. b Deviation from Flory’s
`prediction.
`
`HA cross-links. It is also plausible that intramolecular cross-
`links are occurring. These would, however, not contribute
`to the increase in G¢ and may in fact interfere with formation
`of intermolecular cross-links.
`Also from Figure 5, we see that for almost all hydrogel
`samples the G¢ values plateau between 10 and 24 h, with
`about 90% or more of the final (24 h) value attained in just
`about 8 h. This, we assumed, was due to the rapid quenching
`of all available PEGDA molecules that result in the formation
`of effective double-end-anchored HA-PEGDA-HA cross-
`links in the network. To verify analytically, we used FTIR
`to follow the addition reaction between PEGDA and HA-
`DTPH in the 2:1 cross-linked HA-PEGDA-HA hydrogels.
`Figure 7 shows the normalized spectrum obtained by
`subtracting the HA-DTPH spectrum from that of the
`hydrogel, which was used at 8 h postcuring. The arrows
`indicate the disappearance of the absorbance peaks at 1634
`and 1410 cm-1 in the normalized spectrum that correspond
`to the stretching and scissoring of -CdC- bonds in
`PEGDA, respectively. This suggests that 90% or more of
`PEGDA is used up in the reaction with HA-DTPH within
`8 h, a finding that correlates well with those obtained from
`other chemical analyses of these HA-PEGDA-HA hydro-
`gels. By use of GPC and the modified Ellman method, it
`
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`Rheology of Cross-Linked HA Hydrogels
`
`Biomacromolecules,Vol.6,No.5,2005 2863
`
`from the quenching of all PEGDA molecules, which is shown
`in detail in Figure 5. This suggests that a further increase in
`G¢ and the corresponding second plateau arises from the
`formation of HA-S-S-HA cross-links. Since the tendency
`to form HA-S-S-HA cross-links should be identical in
`all samples (owing to identical thiol content of HA-DTPH
`in all samples), data from Figure 8 suggest that PEGDA,
`besides creating HA-PEGDA-HA cross-links, also strongly
`facilitates the formation of HA-S-S-HA cross-links that
`otherwise form at a very slow rate (Figure 5). This concept
`can be explained as follows.
`The large segmental fluctuations and the entropic barrier
`inhibit spontaneous formation of HA-S-S-HA cross-links.
`This barrier may be overcome if the enthalpy of the cross-
`linking reaction is highly favorable, as is the case when
`PEGDA is present. We believe that due to its high concen-
`tration in the 2:1 hydrogels, PEGDA potentially creates a
`“zipping” effect where, during cross-linking, it brings the
`HA-DTPH chains and, as a result, the pendant free thiol
`groups in close proximity to each other, thereby facilitating
`the formation of additional HA-S-S-HA linkages. In this
`way, PEGDA helps the HA-DTPH chains overcome the
`entropic barrier that would otherwise preclude the formation
`of such HA-S-S-HA cross-links. In 6:1 and 12:1 hydro-
`gels, the lower concentration of PEGDA fails to produce
`this effect to the same extent and hence the rate of formation
`of spontaneous HA-S-S-HA linkages is much slower.
`Alternate reasoning comes from the fact that the probability
`of bond formation between different chains is proportional
`to the probability of those chains lying in the same small
`volumetric unit.29 Along this line of reasoning, HA-
`PEGDA-HA cross-links restrict the random flexibility of
`the HA-DTPH chains, thereby increasing their density per
`unit volume. This effect may also produce nonuniformities
`in the cross-linking density since areas of relatively higher
`density may “nucleate” around regions where the HA-
`PEGDA-HA cross-links occur. A detailed understanding of
`this effect is relevant to the characterization of this bio-
`material since this effect is also responsible for deviations
`from linearity of the modulus with cross-linking density.
`More importantly, this may affect the cross-linking density
`in the near-surface region, which is relevant for cell/substrate
`interactions. This effect will be studied in the future by finite
`element analysis and the digital image speckle correlation
`methods,30-32 which can map the modulus across the sample
`with submicrometer resolution.
`(C) Oscillatory Frequency Sweep. Frequency sweep tests
`are widely used to obtain information about the stability of
`three-dimensional cross-linked networks.14,24,25,33 Conse-
`quently, we subjected our 8-h cured 2:1, 6:1, and 12:1 HA-
`PEGDA-HA hydrogels to a frequency sweep from 0.1 to
`100 Hz (100 Hz being the highest operable frequency on
`the AR2000 rheometer). The shear stresses applied to
`hydrogels were 50% of their respective ultimate stress levels.
`Shown in Figure 9 is the plot between G¢ and oscillatory
`frequency (top panel), where the data obtained for 2:1
`hydrogels are characterized by G¢ exhibiting a plateau in the
`range 0.1-10 Hz that is indicative of a stable, cross-linked
`network. The G¢ -frequency profile for 6:1 and 12:1 hydro-
`
`Figure 7. Changing FTIR spectrum of PEGDA during Michael-type
`addition with HA-DTPH. Arrows indicate the disappearance of
`absorbance peaks at 1634 cm-1 (-CdC- stretching) and 1410 cm-1
`(-CdC- scissoring) in the normalized spectrum. HA-PEGDA-HA
`hydrogels were cured for 8 h.
`
`Figure 8. Evolution of G¢ of HA-PEGDA-HA hydrogels as a function
`of long-term curing time (PEGDA MW 3400).
`
`has previously been shown11 that 94% of the bifunctional
`PEGDA molecules get effectively incorporated (double-end-
`anchored) into the HA-PEGDA-HA network within a
`similar time frame. The same study also showed that, at a
`lower cross-linking density of 3:1, all PEGDA molecules
`were completely used up in the addition reaction. It is
`therefore likely that, at lower cross-linking densities of 6:1
`and 12:1, all PEGDA become incorporated within the
`hydrogel network.
`Long-Term Curing. Since even the most densely cross-
`linked 2:1 hydrogel should stoichiometrically contain half
`the original number of free thiol groups, we investigated the
`extent of formation of additional HA-S-S-HA cross-links
`as a function of long-term curing. The 12:1, 6:1, and 2:1
`hydrogels were chosen for this study where the hydrogels
`were cured over a period of 1, 3, 6, or 9 days (instead of
`hours as in short-term curing) and later subjected to oscil-
`latory stress sweep. Figure 8 shows a plot of G¢ versus curing
`time, where G¢ of all the HA-PEGDA-HA hydrogels was
`found to plateau twice, once between 10 and 24 h and again
`several days l