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As featured in:

See Surita R. Bhatia et al., Soft Matter, 2014, 10, 1905.

Highlighting collaborative work of the Bhatia lab, Stony

Brook University and Brookhaven National Laboratory;

and the Tew lab, University of Massachusetts Polymer

Science and Engineering.

Title: SANS study of highly resilient poly(ethylene glycol)

hydrogels

PEG hydrogels were synthesized with a tetra-functional

crosslinking chemistry, leading to networks with a nearly

ideal structure. These structural studies, together with

previously reported rheological data, provide insight

into the impact of network defects on gel elasticity.

Soft Matter

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aDepartment of Chemical Engineering, Un

01003, USA. E-mail: surita.bhatia@stonybrbDepartment of Polymer Science and En

Amherst, MA 01003, USAcDepartment of Chemistry, Stony Brook UnivdCenter for Functional Nanomaterials, Broo

11793, USA

Cite this: Soft Matter, 2014, 10, 1905

Received 10th September 2013Accepted 6th January 2014

DOI: 10.1039/c3sm52395k

www.rsc.org/softmatter

This journal is © The Royal Society of C

SANS study of highly resilient poly(ethylene glycol)hydrogels

Erika M. Saffer,a Melissa A. Lackey,b David M. Griffin,a Suhasini Kishore,a

Gregory N. Tewb and Surita R. Bhatia*acd

Polymer networks are critically important for numerous applications including soft biomaterials, adhesives,

coatings, elastomers, and gel-based materials for energy storage. One long-standing challenge these materials

present lies in understanding the role of network defects, such as dangling ends and loops, developed during

cross-linking. These defects can negatively impact the physical, mechanical, and transport properties of the gel.

Here we report chemically cross-linked poly(ethylene glycol) (PEG) gels formed through a unique cross-linking

scheme designed to minimize defects in the network. The highly resilient mechanical properties of these

systems (discussed in a previous publication) [J. Cui, M. A. Lackey, A. E. Madkour, E. M. Saffer, D. M. Griffin, S. R.

Bhatia, A. J. Crosby and G. N. Tew, Biomacromolecules, 2012, 13, 584–588], suggests that this cross-linking

technique yields more homogeneous network structures. Four series of gels were formed based on chains of

35 000 g mol�1, (35k), 12 000 g mol�1 (12k) g mol�1, 8000 g mol�1 (8k) and 4000 g mol�1 (4k) PEG. Gels

were synthesized at five initial polymer concentrations ranging from 0.077 g mL�1 to 0.50 g mL�1. Small-angle

neutron scattering (SANS) was utilized to investigate the network structures of gels in both D2O and d-DMF.

SANS results show the resulting network structure is dependent on PEG length, transitioning from a more

homogeneous network structure at high molecular weight PEG to a two phase structure at the lowest

molecular weight PEG. Further investigation of the transport properties inherent to these systems, such as

diffusion, will aid to further confirm the network structures.

Introduction

Polymer networks, in their many forms, remain critically impor-tant materials from both a fundamental and technological view-point. Industrially important adhesives, high temperatureepoxides,2 and so hydrogels3,4 found in biomaterials andconsumer products demonstrate the wide application andimportance of networked materials. Many biological materials,both naturally-occurring (e.g., tissues)5–7 and synthetic,8 arecomposed of so material networks. Despite signicant progressin understanding the basic structure–property relationships ofnetworks, much remains to be learned about how the founda-tional macromolecular building blocks transmit properties acrossthe length-scales to the macroscopic sample. Fundamental grandchallenges include understanding the relationship betweennetwork structure, dynamics, and mechanical properties.

The ability to manipulate and predict the structure andresulting physical properties of a polymer network by changing

iversity of Massachusetts, Amherst, MA

ook.edu

gineering, University of Massachusetts,

ersity, Stony Brook, NY 11794, USA

khaven National Laboratory, Upton, NY

hemistry 2014

specic variables (i.e. polymer molecular weight, polymerconcentration, cross-linking time), is advantageous for industrialand academic applications of a given material. One key step todeveloping structure–property relationships of polymer networksis the reduction of network defects (i.e. highly cross-linkedjunctions, looping chains, dangling ends). These defects typicallyform in an unpredictable manner and can impact the resultingphysical properties of the network. For example, highly cross-linked network junctions found in some hydrogels developed forin vivo applications result in difficulty when predicting physicalproperties such as the degradation rate or drug release proles.9

Looping chains and dangling ends detract from the elasticproperties and resilience of a network. Polymer networks withminimal defects are also of interest for applications in energystorage. For example, poly(ethylene glycol) (PEG)-basednetworks are currently being investigated for energy storageapplication due to their ability to conduct lithium ions. PEGachieves lithium ion conductance through chain relaxation,however, energy storage applications require materials withrobust mechanical properties. Therefore, the optimization ofion transport in PEG-based networks is achieved by balancingthe mechanical properties with ion conductivity.10,11 As networkdefects detract from the mechanical properties of the hydrogel,efficient cross-linking techniques designed to reduce defectformation are highly desired.12,13

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The need for more homogeneous polymer networks haslead to the development of cross-linking techniques that allowfor greater control over the resulting network microstructure.One of the most basic chemical cross-linking techniques is thephotopolymerization of end-functionalized, or telechelic,polymers. While this technique allows for some control overthe cross-link density of the network,14 it does not denecross-link functionality and commonly results in the forma-tion of cross-linked clusters in the network (i.e. high func-tionality cross-links).15,16 A more recent approach utilizes clickchemistry to control cross-linking in networks.17,18 Clickreactions are highly efficient, have high functional grouptolerance, and are highly active in water making them ideal foruse as a hydrogel cross-linking strategy.18,19 Hydrogels formedthrough click chemistry have demonstrated high elasticmoduli, suggesting that this cross-linking strategy can reducethe formation of defects in the network.17,20 Greater controlover the cross-link functionality was obtained through thedevelopment of multifunctional cross-linkers designed toreact with a specic number of telechelic polymer chains.Small angle neutron scattering (SANS) studies have revealedthat defects are still present in these networks uponswelling.21–27 A recent approach by Sakai and coworkers28

utilized 4-arm star-shaped polymers to reduce network defectsand form highly elastic, remarkably homogeneous hydro-gels.29 They achieved this through the use of tetra-arm PEGmacromers that cross-link through activated-ester chemistry.The resulting gels, referred to as tetra-PEG gels, were found tohave a remarkably homogeneous network structure throughsmall-angle neutron scattering (SANS)30 and static-light scat-tering (SLS) studies.31

Tew and coworkers1 recently developed a novel cross-link-ing technique that utilizes thiol-norbornene chemistry to formPEG-based hydrogel networks with minimal defects, or inho-mogeneities (Fig. 1). Also referred to as a “click reaction”,thiol-ene reactions are simple, highly efficient, do not produceside products, and rapidly achieve high yield. Thiol-ene chemistry has been used to form several different typesof materials, including nearly ideal, uniform polymer

Fig. 1 Synthesis of tetra-functional PEG hydrogels. Image of hydrogelin tension was obtained from Cui et al.1

1906 | Soft Matter, 2014, 10, 1905–1916

networks.32,33 The synthesis technique developed by the Tewgroup utilizes norbonene functionalized PEG macromers anda tetra-functional thiol cross-linker to produce PEG-basednetworks with well-dened cross-link functionalities andminimal defects. The resulting hydrogels are optically clearand have displayed high toughness and resilience. Resilienceis a measure of a material's ability to deform reversibly (elas-tically) without loss of energy. A recent publication demon-strates that tetra-functional PEG hydrogels with anequilibrium water content greater than 95% have a resilience$97% at strains of up to 300%.1 As network defects typicallycontribute to viscous losses in mechanical behavior, the highresilience values suggest that these materials may have arelatively low level of defects.

Here, we have employed small-angle neutron scattering(SANS) to investigate the network microstructure and relativehomogeneity of these tetra-functional PEG networks. Fourseries of gels were created by varying the initial polymerconcentration of 35 000 g mol�1 PEG, 12 000 g mol�1 PEG,8000 g mol�1 PEG and 4000 g mol�1 PEG. These systems willbe referred to as 35k, 12k, 8k and 4k tetra-functional PEGhydrogels, respectively. Analysis of the SANS data revealedthat resulting network structure was dependent on the lengthof the PEG macromer. We nd that the network structure inD2O transitions from a homogeneous network to a two-phasenetwork as the length of the PEG macromer is decreased. Thiseffect decreased signicantly for gels swollen with deuteratedN,N-dimethylformamide (d-DMF), suggesting that clusteringof hydrophobic chain ends and crosslinker occurs in the lowermolecular weight gels; however, it did not disappearcompletely in d-DMF, indicating that there may also be morenetwork defects at lower molecular weights that become“locked in” to the network structure during cross-linking ind-DMF. We have validated this through tting of empiricalmodels to the data sets. Additionally, the model ts revealedthat the mesh size of the networks were tunable within eachmolecular weight series, varying inversely with initial polymerconcentration as expected.

Experimental section

Poly(ethylene glycol) (PEG) (Mn ¼ 35 kDa, 12 kDa, 8 kDa, 4 kDa),exo-5-norbornenecarboxylic acid, triphenylphosphine, diisopropylazodicarboxylate (DIAD), pentaerythritol tetrakis(3-mercapto-propionate) (PETMP), 2-hydroxy-40-(2-hydroxyethoxy)-2-meth-ylpropiophenone (PI), and N,N-dimethylformamide (DMF) anddeuterated N,N-dimethylformamide (d-DMF) were purchased fromAlfa Aesar, Sigma Aldrich, Acros Organics, or Fisher and usedwithout further purication.

GPC characterization

Gel permeation chromatography (GPC) was conducted with aPolymer Laboratories PC-GPC50 with two 5 mm mixed-Dcolumns, a 5 mm guard column, and a RI detector (HP1047A),with polystyrene standards and THF as the eluent at a ow rateof 1.0 mL min�1. The polydispersity index (PDI) of the resulting

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35k, 12k, 8k and 4k PEGmacromers were found to be 1.07, 1.07,1.04, and 1.06 respectively.

Hydrogel preparation

The norbornene end-functionalized PEG (n-PEG-n) precursorswere prepared by the Mitsunobu reaction according to theprocedure described previously.1 The desired amount of n-PEG-n (0.077 g, 0.10 g, 0.14 g, 0.25 g, 0.33 g, or 0.50 g) was dissolvedin DMF (1 mL) to form a clear solution. The tetra-functionalcross-linker, PETMP, and the PI (0.5 wt% with respect to thepolymer) were added to form the precursor solution. The molarratio of the polymer (n-PEG-n) to the cross-linker (PETMP) was 2to 1, so the molar ratio of norbornene to thiol groups was 1 to 1.Aer thorough mixing, the precursor solution was transferredto the desired mold (a customized Teon or syringe mold)and exposed to ultraviolet light with a wavelength of 365 nm for45–60 min. The cross-linked gel was removed from the moldand washed with excess DMF, which was replaced three times,to remove unreacted materials. The gel then was immersed indeionized water, which was replaced daily until equilibriumswelling was reached.

Small-angle neutron scattering

Samples for small-angle neutron scattering (SANS) wereprepared as described above, except the immersion andequilibration steps were performed in D2O. SANS measure-ments were conducted on the 30 m small angle neutron scat-tering instrument on the NG-7 beamline at the NationalInstitute of Standards and Technology (NIST) Center forNeutron Research, Gaithersburg, MD.34 Spectra were obtainedat room temperature in quartz sample cells with a path lengthof 2 mm. Gels were synthesized prior to placement in thesample cells according to the procedure listed above. Greatcare was taken to produce gels with a thickness of 2 mm anddiameter of 0.750 0 in order to ll the sample cell. Once thesample was in place, excess D2O was added to the cell tomaintain equilibrium swollen conditions and prevent anysolvent evaporation during scattering. Spectra were collectedfor 105 minutes per sample. The sample to detector distancevaried from 1.0 to 13 m, resulting in q-range for these experi-ments of 0.003 A�1 < q < 0.5 A�1. Data reduction andnormalization were performed using standard techniques.35

Model tting to the rst sample run for the 12k tetra-func-tional hydrogel at an initial polymer concentration of 0.14 gmL�1 gave non-physical results, so the values reported here arefrom a second, rehydrated sample.

Results and discussionQualitative analysis

SANS experiments were carried out on tetra-functional PEGhydrogels formed from norbornene-functionalized 4k, 8k,12k and 35k PEG. The initial polymer concentration wasvaried from 0.077 g mL�1 to 0.50 g mL�1 to form a series ofhydrogels at each molecular weight. Due to its high molecularweight, cross-linking reactions done with 35k PEG had

This journal is © The Royal Society of Chemistry 2014

consistently lower yields than the other three PEG chainlengths. This is most likely due to the lower concentration offunctional groups, especially at very low concentrations forthis system.36 Therefore, the lowest initial polymer concen-tration used for that series was 0.10 g mL�1. An additionalhydrogel was formed at an initial polymer concentration of0.33 g mL�1 for the 35k series. Fig. 2 contains spectra fromhydrogels with varying PEG length at initial polymerconcentrations of 0.077 g mL�1, 0.10 g mL�1, 0.143 g mL�1,0.25 g mL�1 and 0.50 g mL�1.

These SANS experiments probed network structures between180 nm and 2 nm. As the size of polymer chains used to formthese networks range from 4.9 nm to 14.5 nm, the size rangeprobed by SANS would provide structural information on theconformation of single polymer chains as well as multiple cross-linking sites (i.e. nano-scale network structure). Network defectsthat occur on length scales larger than 180 nm would not becaptured in this SANS experiment, however, an upturn in thespectra at low q would indicate their presence. The spectraplotted in Fig. 2 qualitatively demonstrate that a change innetwork structure occurs with changes in the length of the PEGmacromer. While all spectra contain a broad shoulder andupturn at low q, the shoulder becomes more pronounced as thelength of the PEG is decreased. Structural differences are moststriking at the highest initial polymer concentration, 0.50 gmL�1, where a distinct peak forms in the spectra of the 4khydrogel. The other three gels exhibit a broad shoulder thatshis towards lower q as the molecular weight of PEG isincreased.

The presence of a peak is commonly found in scatteringspectra from networks with high junction functionality.15,16,37

These types of networks have a higher density of polymer nearthe junctions, resulting in the junction points serving asscattering centers. Due to the cross-linking chemistry used toform the tetra-functional PEG networks, we would expect thesesystems to have a uniform junction functionality of 4 andwould therefore not expect to see a peak in the scatteringspectra. For the 35k and 12k gels, the absence of a maximumin the spectra conrm this low junction functionality. Thepresence of a broad shoulder indicates that the mesh size isfairly uniform. Similar behavior has been observed in SANSstudies of poly(dimethylsiloxane) (PDMS) and polystyrene (PS)networks with low cross-link functionalities.22,38 Spectraobtained from these studies lack a correlation peak as thecross-link junctions are small in comparison to the rest of thenetwork, preventing them from acting as distinct scatteringcenters.15,22,38

While the SANS results for the 35k and 12k systems indicatea relatively homogeneous structure for the majority of the qrange probed, the upturn at low q suggests the presence ofstructural heterogeneities on larger length scales. The shape ofthe scattering curves from the 35k and 12k tetra-functionalPEG systems are notably similar to those obtained for PEGsolutions.39 Scattering spectra from PEG solutions have alsoshown an upturn at low q which has been attributed to clus-tering of the chains in solution. Several groups have comparedscattering from a semi-dilute polymer solution to that of the

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Fig. 2 Scattering spectra from tetra-functional PEG hydrogels formed with 4k, 8k, 12k, and 35k MW PEG with varying initial polymerconcentrations between 0.077 g mL�1 and 0.50 g mL�1. Spectra have been shifted for clarity.

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cross-linked gel in order to investigate network homoge-neity.22,30,31,40 For many of these systems, the scattering fromthe unswollen (or as-prepared) gel was similar to scatteringfrom the semi-dilute precursor solution. However, at higherdegrees of swelling, scattering from the gel began to deviatefrom that of the semi-dilute solution. In these instances, thehigh q scattering from both systems remained similar, while atlow q, the gel exhibited scattering at a higher intensity than thesolution scattering.22,40 The excess in scattering was attributedto concentration uctuations in the network that result inregions of inhomogeneity due to the formation of “hard-to-swell” zones.22,41

We have qualitatively compared the scattering from the 35kand 12k tetra-functional PEG hydrogels to scattering from linear

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PEO chains in solution (Mw¼ 100k at 90 �C, 10 wt%) reported byHammouda and coworkers.39 For both systems, the upturn atlow q is slight but still present. Matsunaga and coworkers31

observed a similar upturn in SANS from as-prepared tetra-PEGhydrogels, which were also compared to scattering from PEG insolution (102k PEO at 10 �C reported by Hammouda andcoworkers).31,42

The spectra obtained for the 8k and 4k series are noticeablydifferent than those obtained for the higher MW series.Hydrogels formed at initial polymer concentrations of 0.077 gmL�1 and 0.10 g mL�1 have two broad shoulders in theirspectra, one at low q and one at high q. As the initial polymerconcentration increases from 0.10 g mL�1 to 0.14 g mL�1, thehigh q shoulder becomes more pronounced, decreasing in

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broadness and increasing in intensity. At the highest initialpolymer concentration (0.50 g mL�1), the high q shoulderbecomes more pronounced for the 8k series, and for the 4ktetra-functional hydrogel the shoulder becomes a peak. Similarspectra were obtained from SANS studies of randomly cross-linked PEG hydrogels.15,16 The presence of a peak in the scat-tering spectra for these systems indicates the presence of scat-tering centers, and is a common feature in scattering fromhighly branched gels and end-cross-linked gels with high endgroup functionality.37 For these systems, a peak indicates clus-ters or highly cross-linked regions within the network. A studyby Lin-Gibson and coworkers16 investigated the structure ofrandomly cross-linked 1k, 2k, 4k, and 8k PEG-dimethacrylatehydrogels through SANS. They concluded that it was reasonableto assume a network structure of cross-linked clusters in asolution like matrix. The absence of a dened peak occurred atlow polymer concentrations when the polymer was too diffuseto form uniform clusters, resulting in large defects in thenetwork. Waters and co-workers15 investigated the scatteringfrom randomly cross-linked 3.4k, 4.6k, and 8k PEG-diacrylateand PEG-diacrylamide hydrogels. They also observed a denedpeak in the scattering spectra of these systems, and related it tothe average spacing between dense cross-linked junctionregions in the network.

For the tetra-functional PEG systems discussed in this paper,it is unlikely that the correlation peak seen in the spectra is duesolely to network defects, as is the case in the randomly cross-linked PEG networks discussed above. The cross-linking tech-nique used to form the tetra-functional PEG systems shouldresult in junctions of low functionality regardless of the lengthof PEG macromer used. Additionally, both the 4k and 8ksystems demonstrate highly resilient mechanical propertiessimilar to the 12k and 35k systems.36 This supports the idea thatthe structure seen in the 4k and 8k systems does not primarilyarise from network defects, but rather from clustering orsegregation of the hydrophobic end-groups and crosslinkerwithin the gels, which we expect to be more signicant as PEGlength decreases. Therefore, we believe that these structuraldifferences between different molecular weight tetra-functionalPEG hydrogels are mainly due to the formation of domains richin the hydrophobic components of the network (norborneneend-groups and tetra-thiol cross-linker) upon swelling in water.It is important to note here that all hydrogels are synthesized inDMF, and that both the hydrophilic PEG with the norborneneend-groups and the hydrophobic cross-linker are readily solublein DMF. The cross-linked gels are then washed with DMF toremove any unreacted material that is not connected to thenetwork.

As the length of the PEG macromer is decreased, the ratio ofhydrophobic material (norbornene end-groups and tetra-thiolcross-linker) to hydrophilic material (PEG chains) in thenetwork increases. At the same polymer concentration, therewill be more low molecular weight chains present in solutionwhich will result in a higher cross-link density (i.e. morehydrophobic norbornene end-groups and tetra-thiol cross-linker are contained in the gel). The reduction in PEG lengthalso results in less hydrophilic units between the hydrophobic

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norbornene end-groups which could result in clustering dueto end effects43 when the network is swollen with water. Asdiscussed further below, there is also evidence of a higherincidence of defects in lower molecular weight samples,which also contributes to the development of a shoulder andlow q scattering in the spectra. However, the structuraldifferences observed as molecular weight decreases appearsto be mainly due to a microphase separation of chain endsand crosslinker.

Effect of solvent on hydrogel structure

In order to investigate these structural differences further, weconducted a SANS experiment on tetra-functional PEG networksswollen in deuterated N,N-dimethylformamide (d-DMF).Results were obtained for the following hydrogels: 35k at 0.33 gmL�1, 12k at 0.50 g mL�1, 8k at 0.10 g mL�1, and 4k at 0.10 gmL�1 (Fig. 3). The intensity of background scattering wasdetermined with a high q scaling approximation (eqn (1)),where n is a high-q Porod exponent and B is incoherentbackground.

IðqÞ ¼ A

qnþ B (1)

A plot of qn I(q) vs. qn at high q yields a linear plot that has aslope, B, and intercept A.42 The value for background deter-mined from these plots was subtracted from the original scat-tering spectra. Spectra for hydrogels swollen in D2O have beenshied up so both spectra can be seen clearly as they wouldotherwise overlap.

The effect of solvent on network structure is most clearlyseen for the 4k, 8k, and 12k hydrogels. Swelling these systems ind-DMF appears to result in a more homogeneous networkstructure for all systems, which is indicated by the reducedpresence of high q features that are prominent in spectra fromtheir D2O-swollen counterparts. Additionally, the slope of theupturn at low q that is present for the 12k system is greatlyreduced when swollen in d-DMF. These results support thetheory that the networks undergo phase separation whenswollen in D2O. The only system that remains relatively unaf-fected by the change in solvent is the 35k system, which wouldhave the highest ratio of hydrophilic to hydrophobic compo-nents due to the high MW of the PEG macromer used. There-fore, this system would be less likely to undergo a large degreeof phase separation in D2O even at the highest initial polymerconcentration as the hydrophobic content of the network ismuch less than the hydrophilic content. However, both D2O andd-DMF swollen networks display an upturn at low q, suggestingthat the large scale inhomogeneities in these systems formindependently of solvent and could possibly be the result ofchain entanglements that become locked into place aer cross-linking.

It is interesting to note that, while spectra from all d-DMF gelsshow a more homogenous structure than is obtained in D2O, the8k and 4k samples in d-DMF still exhibit a small upturn at low qand development of a small shoulder. These indicate that there issome presence of clusters or inhomogeneity in the polymer

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Fig. 3 Spectra from hydrogels swollen in D2O and d-DMF with background scattering subtracted.

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segment density for these lower molecular weights, even ind-DMF. Thus, the inhomogeneity in network structure thatbegins to appear for shorter length PEG cannot completelybe attributed to phase separation. We believe there may besome structural defects in the network, such as loops ordangling ends, that become locked into place as the gels arecross-linked in d-DMF, and that these are more signicantfor the lower molecular weight samples. Results fromswelling studies conrm that there is some deviation fromideal network behavior for lower molecular weight hydrogelsin d-DMF.36

These differences can be seen more clearly by replotting thedata in a Kratky plot. A Kratky plot is used to highlight scat-tering at high q, and has been used to investigate the structureof hydrogel networks.44–48 The shape of the Kratky plot indicatesthe conformation of the scattering unit. For a rod at high q, I(q)z 1/q. Therefore, a Kratky plot of scattering from a rod-likeobject would become linear at high q as q2I(q) ¼ A + Bq. Scat-tering from Gaussian chains at high q approximates to I(q)z 1/q2, while scattering from a three-dimensional object at high qapproximates to I(q) z 1/q4. Therefore, Kratky plots of scat-tering from Gaussian chains would increase monotonically withq and would reach a plateau at high q, while that for a threedimensional object should have a peak and would thendecrease as 1/q2 at high q.

A large peak at low q is commonly observed in the Kratkyplots of polymer gels and indicates the presence of frozeninhomogeneities in the gel network.45 Shinohara andcoworkers44 and Karino and coworkers45 recently used theKratky plot to provide further evidence that their cross-linking

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technique, which forms cross-links that can move position bysliding along polymer chains in the network, could be used toreduce inhomogeneities in the networks of their hydrogels.Kratky plots of the SANS data from tetra-functional gels swollenin D2O and d-DMF are shown in Fig. 4.

Kratky plots of scattering from networks swollen ind-DMF vs. D2O provide further insight into solvent-basedstructural changes (Fig. 4). For all systems, the high qbehavior of the Kratky plots indicate that the polymer chainsin the network become more swollen in d-DMF. The mostdrastic change occurs for the 4k system, and is seen in theelimination of the peak when the network is swollen ind-DMF.

Model fittingResults for 35k and 12k tetra-functional hydrogels

More insight into the nano-scale structure of these networkscan be obtained by tting the SANS data with an empiricalmodel. The scattering spectra for the 35k and 12k PEG tetra-functional hydrogel series were successfully t with the corre-lation length model through a nonlinear, least squares t(Fig. 5).35

This model was developed by Hammouda and coworkers39

and has been used to analyze the scattering spectra of polymersolutions as well as scattering from other hydrogelsystems.31,49–51 Scattering intensity is modeled by eqn (2):

IðqÞ ¼ A

qnþ C

1þ ðqxLÞmþ Bkg (2)

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Fig. 4 Kratky plots for 35k, 12k, 8k and 4k tetra-functional hydrogels in D2O and d-DMF. Background has been subtracted through the samemethod discussed in a previous section.

Fig. 5 Scattering spectra for 35k and 12k tetra-functional hydrogel series. Symbols indicate scattering data, while solid lines indicate the fit of thecorrelation length model to the data is indicated by the solid line. Spectra have been shifted for clarity.

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where I(q) is the scattering intensity, q is the scattering vector,and Bkg is scattering from background. Parameters n, m, andxL are the Porod exponent, the Lorentzian exponent, and theLorentzian screening length, respectively. The Porod expo-nent characterizes the fractal structure of the gel, while theLorentzian exponent characterizes the polymer–solventinteractions and therefore describes the thermodynamics ofthe system. The Lorentzian screening length, xL, is thecorrelation length for polymer chains39 and in the case of agel network gives an indication of the gel mesh size. Resultsof the t of this model to the 35k and 12k SANS spectra areshown in Table 1.

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The reduced c2 values for all the ts were equal to orless than 2.6, indicating a good agreement between themodel and the data. All of the gels are mass fractal, indi-cated by a Porod exponent, n, of 2 or greater, with theexception of the 35k and 12k tetra-functional gels with aninitial polymer concentrations of 0.33 g mL�1 and 0.143 gmL�1 respectively. A Porod exponent, n, of 2 or greatersuggests that the 35k and 12k tetra-functional PEG hydro-gels are a one-phase system.31 The correlation length modelwas also used to t master curves of SANS from as-preparedtetra-PEG hydrogel systems by Matsunaga et al.,31 Similar toour results, they obtained a Porod exponent of 2, which they

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Table 1 Results from correlation length model fit to 35k and 12k PEG hydrogels

Parameters 35k PEG

C0 (g mL�1) 0.10 0.143 0.25 0.33 0.50

n 2.5 � 0.08 2.1 � 0.05 1.9 � 0.04 1.4 � 0.03 2.2 � 0.02xL (nm) 13.0 � 0.8 7.3 � 0.2 4.8 � 0.1 2.9 � 0.1 3.7 � 0.1m 1.7 � 0.01 1.7 � 0.01 1.8 � 0.01 1.8 � 0.02 1.7 � 0.01Bkg (cm�1) 0.07 � 8 � 10�5 0.08 � 1 � 10�4 0.07 � 1 � 10�4 0.09 � 2 � 10�4 0.09 � 2 � 10�4

Parameters 12k PEG

C0 (g mL�1) 0.077 0.10 0.143 0.25 0.50

n 2.4 � 0.09 3.0 � 0.10 1.1 � 0.004 2.2 � 0.05 2.3 � 0.02xL (nm) 6.3 � 0.1 5.8 � 0.1 2.8 � 0.4 2.9 � 0.02 2.1 � 0.01m 1.8 � 0.004 1.7 � 0.01 2.4 � 0.04 1.9 � 0.02 2.0 � 0.005Bkg (cm�1) 0.08 � 9 � 10�5 0.13 � 2 � 10�4 0.09 � 5 � 10�4 0.09 � 4 � 10�4 0.11 � 2 � 10�4

Fig. 6 Representation of 35k and 12k tetra-functional hydrogelnetworks, mesh-like network structures with minimal defects. xLindicates the Lorentzian screening length.

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argued suggested homogeneity of their hydrogel networkstructure.31

The Lorentzian exponent, m, for all of 35k and 12k tetra-functional PEG hydrogels was less than or equal to 2, indicatingthat the polymer chains in the system are behaving as though ina good solvent. The 12k hydrogel with an initial polymerconcentration of 0.143 g mL�1 is again an outlier, with a Lor-entzian exponent slightly greater than 2 indicating a statebetween theta and bad solvent. The outlying values obtained forboth the 12k and 35k systems at a single concentration aredifficult to understand. Qualitatively, the spectra from thesegels do not appear signicantly different than the rest of thegels in the series. Also, mechanical and swelling data supportthe fact that these systems are very reproducible.36 However,these tting results could indicate slight variations betweensamples on a level that would not be detected in a study of themacroscopic properties of these systems.

The Lorentzian screening length, or gel mesh size, decreasedwith increasing initial polymer concentration as expected, andwith values of 3.7 nm# xL # 13.0 nm and 2.1 nm# xL # 6.3 nmrespectively for 35k and 12k. We can compare this mesh size tothe end-to-end distance of 35k and 12k PEG chains. Assuming arandom walk Gaussian chain conrmation, the end-to-enddistance can be calculated as:

r0 ¼ bNV1 (3)

where ro is the end-to-end distance, b is the Kuhn length for PEG(0.76 nm), N is the number of Kuhn segments,52 and v1 is thescaling exponent (equal to 0.5 for an ideal Gaussian chainmodeled as a randomwalk).53Using eqn (3), we estimate ro¼ 14.5nm and ro ¼ 8.5 nm for a 35k and 12k PEG chain, respectively, inan ideal Gaussian chain conformation. The correlation lengthfound through the model t is similar to the estimated ro at lowconcentrations and decreases with increasing polymer concen-tration, as we would expect. We speculate that the chains are in anenvironment similar to a semi-dilute solution. Classic work by deGennes54 supports the idea that the correlation length, xL, inhomogeneous gels should be equal to or less than size of theaverage mesh, and should not differ signicantly from the

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correlation length of a polymer solution at the same concentra-tion.40 A schematic of the 35k and 12k tetra-functional PEGnetwork structure is shown in Fig. 6.

Results for 8k and 4k tetra-functional hydrogels

Scattering spectra from both the 8k and 4k tetra-functionalhydrogels contain an additional broad shoulder that becomesmore well-dened at higher concentrations, and therefore thecorrelation length model could not be used to t the entirescattering specta. We hypothesize that at low concentrations thepresence of two shoulders indicates two correlation lengths; therst corresponding to the formation of relatively hydrophobicdomains of cross-linker and chain ends dispersed in a hydro-philic gel matrix. As the polymer concentration is increased, thesecond shoulder becomes more pronounced. In the case of the4k system, this shoulder transitions into a well-dened peak.This indicates the presence of a sharp boundary betweendomains that corresponds to a specic d-spacing.

To elicit more information about these structural changes,we chose to t the shoulder that appears at low q for all spectrawith the correlation length model (Fig. 7). The background

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Fig. 7 8k and 4k tetra-functional PEG hydrogels at varying initial polymer concentrations. Symbols indicate scattering data, while solid linesindicate the fit of the correlation length model the data. The dashed lines indicate the portion of the model that was not fit to the data. Spectrahave been shifted for clarity.

Table 2 Results of the fit of the correlation length model to 8k and 4k PEG tetra-functional hydrogels

Parameters 8k PEG

C0 (g mL�1) 0.077 0.10 0.143 0.25 0.50

n 2.6 � 0.08 2.5 � 0.13 2.6 � 0.09 2.6 � 0.10 2.3 � 0.10xL (nm) 4.0 � 0.10 3.4 � 0.09 3.0 � 0.08 2.8 � 0.11 2.6 � 0.20m 1.9 � 0.05 1.9 � 0.12 1.7 � 0.12 1.6 � 0.17 1.5 � 0.33Bkg (cm�1)* 0.08 0.08 0.08 0.08 0.10Peak Position (A�1) — — — 0.051 0.055d-Spacing (nm) — — — 12.3 11.4

Parameters 4k PEG

C0 (g mL�1) 0.077 0.10 0.143 0.25 0.50

n 2.9 � 0.1 2.6 � 0.12 2.9 � 0.05 2.4 � 0.18 2.2 � 0.10xL (nm) 3.2 � 0.03 2.6 � 0.03 1.9 � 0.01 1.4 � 0.34 1.4 � 0.18m 2.0 � 0.03 2.0 � 0.05 2.1 � 0.08 2.1 � 0.75 2.2 � 0.52Bkg (cm�1)* 0.08 0.07 0.08 0.08 0.09Peak Position (A�1) — — 0.068 0.070 0.074d-Spacing (nm) — — 9.2 9.0 8.5

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(calculated from eqn (1)), was held constant during the ttingprocess for consistency. In spectra that contain a well denedpeak, the position of the peak maxima was determined andrelated to a d-spacing according to the relation d ¼ 2p/q. Thevalues obtained from the model t and d-spacing analysis canbe seen in Table 2.

As expected, the Lorentzian screening length, xL, decreasedwith increasing initial polymer concentration and ranged from2.6 nm # xL # 4.0 nm for the 8k series and 1.4 nm # xL # 3.2nm for the 4k series. These values were also consistently smallerthe end-to-end distance of 8k and 4k PEG chains assuming arandom walk Gaussian chain conrmation (4k PEG ¼ 4.9 nm,8k PEG ¼ 7.0 nm). The Lorentzian exponents indicate goodsolvent for the 8k system and theta to poor solvent for the 4ksystem. This further supports our hypothesis that the featuresseen at low q describe the structure of the swollen gel network ofthese systems.

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The d-spacing found for both systems decreased as theinitial polymer concentration increased, ranging from 12.3 to11.4 nm in the 8k system and 9.2 to 8.5 nm in the 4k system.This supports our theory that these structural changes are dueto phase separation. The increase in polymer concentrationcorresponds to an increase in the hydrophobic content (e.g.norbornene end-groups and cross-linker). Therefore, it isexpected that these hydrophobic domains would grow in sizeand the distance between them would decrease as theconcentration of polymer in the system is increased. The d-spacings are smallest in the 4k systems, likely due to thehigher ratio of hydrophobic to hydrophilic contact in thesenetworks. This is also supported by the well-dened peakpresent in these spectra, which suggests a sharp transitionbetween hydrophobic domains and hydrophilic gel matrix. Adepiction of the resulting network structures of these systemsis shown in Fig. 8.

Soft Matter, 2014, 10, 1905–1916 | 1913

Fig. 9 Correlation length model fits to tetra-functional PEG networksswollen with d-DMF. Open symbols represent the scattering spectra,while the model fit is indicated by the solid line. Spectra have beenshifted for clarity.

Table 3 Results of correlation length model fits to tetra-functionalPEG networks swollen in D2O and d-DMF

Parameter D2O d-DMF

35k Tetra-functional PEG Gel, C0 ¼ 0.33 g mL�1

n 1.4 � 0.03 1.7 � 0.04xL (nm) 2.9 � 0.1 4.5 � 0.2m 1.8 � 0.02 1.5 � 0.01Bkg (cm�1) 0.09 � 2 � 10�4 0.32 � 4 � 10�4

12k Tetra-functional PEG Gel, C0 ¼ 0.50 g mL�1

n 2.3 � 0.02 2.2 � 0.5xL (nm) 2.1 � 0.01 4.0 � 0.06m 2.0 � 0.005 1.6 � 0.01Bkg (cm�1) 0.11 � 2 � 10�4 0.27 � 3 � 10�4

8k Tetra-functional PEG Gel, C0 ¼ 0.10 g mL�1

n 2.5 � 0.13 3.3 � 0.2xL (nm) 3.4 � 0.09 4.7 � 0.05m 1.9 � 0.12 1.6 � 0.01Bkg (cm�1) 0.08 0.27 � 2 � 10�4

4k Tetra-functional PEG Gel, C0 ¼ 0.10 g mL�1

n 2.6 � 0.12 4.5 � 0.8xL (nm) 2.6 � 0.03 3.7 � 0.03m 2.0 � 0.05 1.7 � 0.01Bkg (cm�1) 0.07 0.28 � 2 � 10�4

Table 4 Comparison of mesh size (Lorentzian screening length) fortetra-functional PEG hydrogels in D2O and d-DMF, and comparison tocalculated length of PEG macromer assuming a random walkconfirmation

Mesh size (nm)

Solvent4k C0 ¼0.10 g mL�1

8k C0 ¼0.10 g mL�1

12k C0 ¼0.50 g mL�1

35k C0 ¼0.33 g mL�1

D2O 2.9 3.6 2.1 2.9d-DMF 3.7 4.7 4.0 4.5Random walklength (nm)

4.9 7.0 8.5 14.5

Fig. 8 Representation of the 4k and 8k tetra-functional hydrogelnetwork in D2O. The two-phase, net-likemesh structure that occurs inthe water swollen network contains phase-separated regions (indi-cated by the circles) separated by a characteristic length scale, d. Themesh size in these networks is denoted by xL.

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Results for tetra-functional PEGhydrogels swollen with deuteratedN,N-dimethylformamide

The spectra obtained for hydrogels swollen with deuterated N,N-dimethylformamide (d-DMF) were all t with the correlationlength model, which yields a mesh size and information aboutchain conformation. Results of these ts are shown in Fig. 9 andTable 3. There was a good agreement between the model t andthe data for all d-DMF networks, which was indicated by reducedc2 values of 2.2 or less. However, the model t to the 4k systemdoes not capture the shoulder in the low q region even though thereduced c2 value of 2.0 indicates a good agreement.

A comparison of the model t results for networks swollen inD2O and d-DMF is shown in Table 3. The effect of solvent quality

1914 | Soft Matter, 2014, 10, 1905–1916

on network structure can most clearly be seen in the change inmesh size, xL. As expected, all systems demonstrated anincrease in mesh size in d-DMF when compared to D2O. TheLorentzian exponent for gels swollen in d-DMF is less than forgels swollen in D2O, indicating that d-DMF is a better solvent forthe network.

However, the resulting d-DMF mesh sizes are still less thanthe predicted length of the same length PEG polymer in arandom walk conguration (Table 4) even though they arethermodynamically behaving as though in a good solvent(indicated by a Lorentzian exponent, m, less than 2). This, inconjunction with the persistence of the upturn at low q for allspectra, indicates that there are still some inhomogeneitiespresent in these networks.

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Conclusions

Tetra-functional chemically cross-linked 35k, 12k, 8k and 4kpoly(ethylene glycol) (PEG) hydrogels with well-dened networkstructures were synthesized via photo-initiated thio-norbornenechemistry. A previous publication has discussed the highlyresilient mechanical properties of these hydrogels, whichsuggest that they have more homogeneous network structures.1

Through qualitative analysis and model-tting of SANS data, wehave shown that the 35k and 12k tetra-functional PEG hydrogelshave a remarkably homogeneous network structure with lowjunction functionality. SANS results from the 8k and 4k tetra-functional PEG hydrogels suggests a deviation from thehomogeneous network structure seen in the 35k and 12ksystems that we believe is primarily due to some segregation ofthe hydrophobic chain ends and cross-linker upon swelling thenetwork in water. This effect becomes more signicant as PEGchain length decreases and is supported by spectra of gelsswollen in d-DMF, which show a much more homogeneousstructure than the gels in D2O. However, there are still somesmall indications of inhomogeneity for the 8k and 4k networkseven in d-DMF, suggesting a higher level of defect formationduring cross-linking for these systems. Future investigations ofthe physical properties inherent to systems, such as diffusion,will aid to further conrm the network structures.

Acknowledgements

This work utilized facilities partially supported by the NationalScience Foundation under agreement no. DMR-0944772. Weacknowledge the support of the National Institute of Standardsand Technology, U.S. Department of Commerce, in providingthe neutron research facilities used in this work. Support forEMS was provided by the NSF-funded IGERT in Cellular Engi-neering (DGE-0654128), support for DMG was provided by theNSF-funded IGERT program in Nanotechnology Innovation(DGE-0504485) and an NIH-sponsored Chemistry–BiologyInterface Training Grant (National Research Service Award T32GM08515), and support for SK was provided by NSF CBET0853551. Partial support was also provided by NSF PIRE (NSF-0730243), NSF DMR-0820506, NSF CMMI-0531171, AROW911NF-09-1-0373, and ONR N00014-10-1-0348.

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