Mechanical Spectroscopy and Relaxometry on ... - ACS Publications

Annalucia Stanisci , Olav A. Aarstad , Anne Tøndervik , Håvard Sletta , Lene B. Dypås , Gudmund Skjåk-Bræk , Finn L. Aachmann. Carbohydrate Polymers 2...
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Mechanical Spectroscopy and Relaxometry on Alginate Hydrogels: A Comparative Analysis for Structural Characterization and Network Mesh Size Determination Gianluca Turco,† Ivan Donati,*,† Mario Grassi,‡ Giulia Marchioli,† Romano Lapasin,‡ and Sergio Paoletti† † ‡

Department of Life Sciences, University of Trieste, Via Licio Giorgieri 1, 34127 Trieste, Italy Department of Industrial Engineering and Information Technology, University of Trieste, via Valerio 10, 34127 Trieste, Italy

bS Supporting Information ABSTRACT: The structure of calcium-saturated alginate hydrogels has been studied by combining rheological determinations and relaxometry measurements. The mechanical spectroscopy analyses performed on alginate gel cylinders at different polysaccharide concentration allowed estimating their main structural features such as the average mesh size. The calculation was based on the introduction of a front factor in the classical rubber elasticity approach which was correlated to the average length of the Guluronic acid blocks along the polysaccharide chain. Transverse relaxation time (T2) determinations performed on the cylinders revealed the presence of two relaxation rates of the water entrapped within the hydrogel network. The cross-correlation of the latter data with the rheological measurements allowed estimating the mesh size distribution of the hydrogel network. The results obtained for the hydrogel cylinders were found to be consistent with the relaxometric analysis performed on the alginate microbeads where, however, only one type of water bound into the network structure was detected. A good correlation was found in the average mesh size determined by means of relaxometric measurements on alginate microbeads and by a statistical analysis performed on TEM micrographs. Finally, the addition of a solution containing calcium ions allowed investigating further the different water relaxation modes within alginate hydrogels.

1. INTRODUCTION The term alginate refers to a family of unbranched polysaccharides isolated from brown seaweeds. They are composed of 1-4-linked β-D-mannuronic acid (M) and R-L-guluronic acid (G) arranged in a block-wise pattern with homopolymeric regions of M (M-blocks) and G (G-blocks) residues interspersed by regions of alternating structure (MG-blocks). The polysaccharide has been known since 18811,2 and its structure has been elucidated around 1965.3-6 Alginate has largely been used in biotechnological and industrial applications for its gel forming properties, which were described in detail around the '70s by Rees7,8 and Smidsrød9 based on X-ray diffraction data.10,11 The model proposed was indicated as “egg-box” and describes junctions as composed by two opposing G-blocks which form a cavity that can accommodate divalent cations such as Ca2þ and Ba2þ. Different authors over the years have tackled this model by means of several physical techniques, that is, circular dichroism,8,9 small-angle X-ray scattering,12 AFM,13 X-ray crystallography,14 and of theoretical15-17 and computations methods.18 The renovated interest in the elucidation of the structure-properties relationships in alginate has been boosted mainly by two aspects. First, the study of the biosynthetic pathways of alginate production by bacteria allowed identifying and producing, by means of recombinant technologies, large amounts of mannuronan C-5 r 2011 American Chemical Society

epimerases. At least seven different alginate epimerases, named from AlgE1 to AlgE7, have been recognized to catalyze the postpolymerization reaction of C-5 inversion on M residues within the alginate chain. The different epimerases are able to introduce G sequences in a specific pattern along the chain. For example, AlgE4 introduces G residues in a strictly alternating sequence. The availability of the latter enzyme allowed to (partially) revise the existing knowledge on the ion binding properties of alginate chains and, to some extent, explain peculiar features of its hydrogels.19-23 The second aspect on the importance of the physical properties of alginate is closely connected with its use in the field of biomaterials. The development of novel materials for biomedical applications has emerged in the recent years as a reliable approach to tackle the organ donor shortage. Alginate-based hydrogels have been largely proposed for bioencapsulation of cells for the preparation of implantable bioreactors for the treatment of type I diabetes or of brain tumors. Alginate-based scaffolds have shown marked resemblance with the trabecular structure of bone inducing positive effects on bone cell Received: December 23, 2010 Revised: February 8, 2011 Published: March 07, 2011 1272

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Biomacromolecules proliferation.24 Moreover, the introduction of specific biologically active signals, such as galactose moieties and RGD peptides has emerged as a reliable technique to impart specific bioactive features to the otherwise nonbioadhesive polysaccharide. The relevance of the interactions between cells and alginate hydrogel has been underlined in several reports. At variance, the importance of the mechanical properties of this soft material, especially in the large deformation range, has not been extensively considered until recently. This is basically correlated with the difficulty of defining, in an unambiguous way, fundamental parameters such as the fracture energy for the hydrogel.25 Moreover, limited attention has been devoted to the effect on mechanical properties of the exposure of the alginate hydrogels to conditions simulating the biological environment. These two considerations point on the critical role of the properties of alginate hydrogels and scaffolds to be used in biomedical field. These have been tackled by means of several different technical approaches spanning from rheological determinations to analyses of the mechanical performances19,25-28 and of viscoelastic properties29-31 to name a few. In addition, some authors attempted to unveil the characteristics of alginate hydrogels by focusing on the properties of the solvent it is mainly composed of. This elucidation was tackled by means of transverse relaxometry with 1H NMR. The latter is a nondestructive technique whose physical information is related to the environment that water molecules experience and that affects their rate of relaxation. The extended analyses of these results led to the evaluation of the mesh-size distribution in the sample. This concept has been exploited in several fields, from biopolymer hydrogels to cortical bone characterization.32 The present work aims to perform a screening on alginate calcium cylindrical hydrogels and microbeads at different polysaccharide concentration. A comprehensive overview of the hydrogel properties has been achieved focusing on the response of both the polysaccharide network and the water largely comprising the soft system by means of mechanical spectroscopy and transverse relaxation time (T2) determinations, respectively.

2. MATERIALS AND METHODS Sodium alginate isolated from Laminaria hyperborea stipe was provided by FMC Biopolymer (Norway). The weight average molecular mass was found to be 1.3  105 (polydispersity index = 2.2), as determined by SEC-MALLS-VISC.33 The composition of this alginate sample was determined by means of 1H NMR34,35 and resulted to be FG = 0.69, FGG = 0.56, FGM,MG = 0.12, FGGG = 0.49, FMGM = 0.07, FGGM, MGG = 0.04. The average length of the G blocks, NG>1 = (FG - FMGM)/ FGGM was found to be 14.36 CaCO3 (mean particle size 10 μm) and glucono-δ-lactone (GDL) were purchased from Sigma Chemical Co (St. Louis, MO). 2.1. Preparation of Alginate Solutions. Solutions were prepared by dissolving the polysaccharide powder in deionized water by means of magnetic stirring at final alginate concentration of 8, 6, 4, and 2 w/v %. The water solution was diluted with an equal volume of NaCl 0.3M, Hepes 20 mM (pH 7.4). 2.2. Preparation of Cylindrical Alginate Hydrogels. Homogeneous saturated calcium gels were prepared by blending the alginate solution prepared as reported in 2.1 with an inactivated form of Ca2þ (CaCO3, 20 mM) followed by the addition of the slowly hydrolyzing Dglucono-δ-lactone (GDL), maintaining a ratio [GDL]/[Ca2þ] = 2. The suspension was degassed prior to the addition of GDL to avoid bubble formation. The Ca-polymer gelling solutions were cured in a Petri dish for 24 h to get cylindrically shaped hydrogels. The hydrogels were

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removed and immersed in 800 mL of a saturating solution containing CaCl2 50 mM, NaCl 0.15 M, and Hepes 10 mM (pH 7.4). The hydrogels were cured for 48 h prior to rheological measurements. The final dimensions of the hydrogels used for rheological determination were 3 mm height and 20 mm in diameter.

2.3. Preparation of Spherical Alginate Hydrogels: Microbeads. Alginate solutions prepared as reported in section 2.1 were dropped into a gelling bath containing CaCl2 50 mM or 200 mM in the same saline buffer. The droplet size was controlled by use of a highvoltage electrostatic bead generator37 (7 kV, 10 mL/h, steel needle with 0.7 mm outer diameter, 1.7 cm distance from the needle to the gelling solution). The alginate gel microbeads were aged for 24 h in the gelling solution prior to analysis. The average diameter of the beads was 450 ((90), 730 ((45), 786 ((39), and 854 μm ((58 μm) for the alginate concentration of 1, 2, 3, and 4 w/v %, respectively. 2.4. Cross-Linking Kinetics of Alginate Hydrogel. To study the kinetics of the gelation process, a 2% (w/V) solution of alginate in NaCl 0.15 M, Hepes 10 mM (pH 7.4) was mixed with CaCO3 (final concentration 20 mM) and the solution was degassed. GDL was added maintaining a ratio [GDL]/[Ca2þ] = 2. The suspension was poured into the NMR tube and its transverse relaxation time T2 was recorded at specific time intervals. 2.5. Mechanical Spectroscopy. Rheological characterization of cylindrical alginate hydrogels was performed by means of a controlled stress rheometer Haake Rheo-Stress RS150, using, as measuring device, a shagreened plate and plate apparatus (HPP20 profiliert: diameter = 20 mm) and operating at 25 °C. To avoid water evaporation from the gel, the measurements were led in a water saturated environment realized by using a glass bell (solvent trap) containing a wet cloth. In addition, to prevent both the wall-slippage38 and the excessive gel squeezing (reflecting in the alterations of polymeric network properties), the gap between plates was determined, for each sample, by executing a series of short stress sweep tests (f = 1 Hz; stress range 2-5 Pa; maximum deformation < 0.02%) characterized by a reducing gap.39 The selected gap was that maximizing the value of the elastic modulus G0 (used gaps ranged between 2 and 4 mm). For each hydrogel, the linear viscoelastic range was determined by means of a stress sweep test consisting in measuring elastic (G0 ) and viscous (G00 ) moduli variation with increasing shear stress (1 Pa < τ < 104 Pa) being the solicitation frequency f = 1 Hz (ω = 2πf = 6.28 rad/s). The hydrogel mechanical spectrum was determined according to a frequency sweep test consisting in the measurement of elastic (G0 ) and viscous (G00 ) moduli variation with decreasing pulsation ω at constant shear stress τ = 4 Pa (well within the linear viscoelastic range that, for all samples, spans up to at least 30 Pa). All tests (stress and frequency sweep) were performed in triplicate. 2.6. Low Field NMR Relaxometry. Low field NMR characterization on alginate hydrogels was performed by means of a Bruker Minispec mq20 (0.47 T). Transverse relaxation time (T2) measurements were made according to CPMG (Carr-Purcell-Meiboom-Gill) sequence with a 90-180° pulse separation of 1 ms (number of scans 4; delay 5 s), T = 25 °C. The T2 discrete distribution was determined by fitting the experimental time (t) decay of the signal (I), related to the extinction of the x-y component of the magnetization vector (Mxy) by a sum of m exponential functions: m

I ¼

ð ∑ Ak e k:1

-t T2k Þ

m

with

∑ Ak ¼ 100 k:1

ð1Þ

where T2k is the transverse relaxation time associated with the kth relaxation mode and Ak is its weight. The number of different spin-spin relaxation times (m) was that minimizing the product χ2Np, where χ2 is data fitting chi-square, while Np is the number of model parameters used (Np = 2m. Each exponential function considered involves two parameters: the pre-exponential factor, Ak and relaxation time T2k). 1273

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Figure 1. (a) G0 (full symbols) and G00 (open symbols) for cylindrical alginate hydrogels at a total polymer concentration of 1% (squares), 2% (circles), and 4% (triangles). Lines represent the fitting of the experimental data according to eqs 3 and 4. (b) Spring constants (Gi) of the Maxwell elements used to fit the experimental mechanical spectra of the hydrogels with the respective relaxation times (λi). Symbols as in (a). Inset: storage modulus of the purely elastic spring used in the Maxwell model (Ge) as a function of alginate concentration. The continuous relaxation time distribution was determined supposing that each point of the discrete distribution (T2k, Ak) corresponds to a Weibull distribution whose peak falls exactly in T2k. Accordingly, I(t) can be expressed by Z IðtÞ ¼

T2max T2min

m

∑ Bi δi i¼1 ε i



T2 - T2min εi

ðδi - 1Þ

  !  ! T2 - T2min δi t exp dT2 exp T2 εi  δi ð1=δi Þ εi ¼ ðT2 - T2min Þ δi - 1

ð2Þ



ð2'Þ

where T2max (=2200 ms) and T2 min (=0 ms) indicate, respectively, the lower and upper range of the continuous T2 distribution, while Bi, δi, and εi are Weibull equations parameters, eq 2, descending from imposing the Weibull distributions peaks in T2k for all k, reduces to two the number of fitting parameters for each Weibull distribution. Eq 2, was numerically evaluated subdividing the relaxation spectrum wideness (T2max - T2min) into 400 parts. This way of determining the continuous T2 distribution led to very similar results to those obtained from a previously reported approach.40 Alginate cylinders and microbeads were gently dried prior to the analysis. In the rehydration experiments led on microbeads, different volumes of gelling solution (100, 200, and 300 μL) were progressively added in the NMR tube prior to the transverse relaxation determination. Each relaxation test is the mean of nine replicates. 2.7. Image Analysis. Image analysis was performed on microbeads coming from 2% alginate aqueous solution. Five microbeads were embedded in Epon resin and ultrathin sections were conventionally contrasted using Pb3(C6H5O7)2 and UO2(CH3COO)2. Visual analysis and image record were performed using a CM12 Philips STEM Transmission Electron Microscope. Six images were randomly collected at the magnification factor of 22000x (which was selected as more representative for the image analysis investigation). From the acquired images, four 1024  1024 regions of interest (ROI) were identified. Therefore, a total of 24 images were subjected to the analysis. The TEM images produced were affected by a small impulsive noise and a median filter with square kernel size of two was applied to each image to enhance image quality. The particle analysis was performed by means of the ImageJ 1.43u software. Once the median filter was applied, the original image underwent to an automatic threshold based on the Otsu’s

method.41 Then, the particles, related to the voids present on the image, were quantitatively analyzed.42

3. RESULTS AND DISCUSSION 3.1. Cylindrical Alginate Hydrogels. Cylindrical alginate gels at different polysaccharide concentration, namely, 1, 2, and 4% (w/v), have been prepared in calcium-saturated conditions and their mechanical spectra recorded (Figure 1a). In all the cases considered, the storage (G0 ) modulus is higher than the loss modulus (G00 ) and basically stable in three decades of the frequency, thus, describing the systems under consideration as strong hydrogels. The frequency sweep test were interpreted in terms of the generalized Maxwell model composed of a sequence of elements in parallel (spring and dashpot) to which an additional spring has been added. The storage and loss moduli can be modeled as a function of the pulsation ω according to the following equations (eqs 3 and 4):

G0 ¼ Ge þ

n

2

ðλi ωÞ ηi ∑ Gi 2 ; Gi ¼ λ i¼1 1 þ ðλ ωÞ

00

G ¼

ð3Þ

i

i

n

λi ω ηi ∑ Gi 2 ; Gi ¼ λ i¼1 1 þ ðλ ωÞ i

ð4Þ

i

where n is the number of Maxwell elements considered, Gi, ηi, and λi represent the spring constant, the dashpot viscosity, and the relaxation time of the ith Maxwell element, respectively. Ge is the spring constant of the last Maxwell element which is supposed to be purely elastic.38 The fitting of the experimental data was performed assuming that relaxation times are not independent each other but they are scaled by a factor 10. Hence, the parameters of the model are Ge, ηi, and λ1. The number of the Maxwell elements was selected, based on a statistical procedure, to minimize the product χ2*Np, where χ2 is the sum of the squared errors, while Np (= 2 þ n) indicates the number of fitting parameters. The experimental data were efficiently fitted by the generalized Maxwell model, as reported in Figure 1a and supported by the statistical F test (F1%(5, 36, 0.95) < 112, F2%(5, 36, 0.95) < 32, F4%(6, 37, 0.95) < 3458). Figure 1b reports the relaxation spectra of the different alginate samples studied; alginate hydrogels with a total polymer concentration of 1 and 2% were fitted adequately by means of 1274

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Figure 2. Dependence of the shear modulus (G) from the polymer concentration for cylindrical alginate hydrogels. The dashed line represents the linear fit of the experimental data (R2 = 0.98). Inset: dependence of the average mesh size, ξ, from the alginate concentration in the calcium saturated hydrogels (Cp) with λ = 1 (open symbols) and λ = 14 (full symbols).

Figure 3. Dependence of the relaxation time T2 from the concentration of the alginate in solution as obtained in the present work (9) and from Degrassi et al.61 (O). Dashed lines represents the best fit of the experimental results with the function y = xb. Inset. Dependence of the relaxation rate (1/T2) from the alginate concentration in solution. Lines represent the linear fit of the experimental data.

four Maxwell elements while in the case of the highest alginate concentration considered, namely, 4%, five spring-dashpot elements were required. Figure 1b shows that, regardless of the relaxation time (λi), the values of all the spring components of the Maxwell model increase with the concentration of alginate in the hydrogel. The same conclusion can be drawn looking at the purely elastic spring included in the model (Ge; see inset in Figure 1b). The use of the generalized Maxwell model to describe the alginate system allows determining the shear modulus, G as (eq 5):

where R is the universal gas constant and T is the absolute temperature. Biopolymer hydrogels display junction zones rather than the cross-linking points described in the original version of the rubber elasticity theory. Hence, in these cases, F from eq 6 is overestimated. To take this into account, a front factor, λ, is included which, in the case of ideal rubbers, equals 1 (eq 7).46-49

n

G ¼ Ge þ

∑ Gi

i¼1

ð5Þ

This modulus was found to scale with the total polymer concentration (Cp) in an approximately linear manner (G µ Cp0.97, Figure 2). This is in very good agreement with previous findings by Mooney and co-workers26 in calcium-limited conditions. The shear modulus of the alginate cylinders was interpreted in terms of the rubber elasticity theory, originally developed by Flory.43 The use of this theory for biopolymer gels, whose macromolecular characteristics, such as flexibility, are far from those exhibited by rubbers, has been repeatedly questioned. However, recent results have shown that very stiff biopolymers might give rise to networks which are suitably described by a purely entropic approach.44 This holds when small deformations are considered, that is, under linear stress-strain relationship (linear viscoelastic region). An enthalpic contribution needs to be taken into account upon exceeding this point to capture all the physics of the system. Indeed, a purely entropic approach has also been recently used to calculate the mesh size for alginate hydrogels.19,45 As the mechanical characterization performed in the present paper was led in the linear viscoelsatic region, the entropic contribution prevails in the description of the alginate network. In view of these considerations, the number (per unit volume) of elastically active chains, F, can be calculated, according to the rubber elasticity theory, simply using eq 6: G ¼ FRT

ð6Þ

G ¼ λFRT

ð7Þ

The average network mesh size, ξh, can be easily calculated by means of eq 8:29,50 sffiffiffiffiffiffiffiffiffiffiffiffi 6 3 6λRT with F ¼ ξ ¼ ð8Þ 3 πNA G ξ πNA Specifically, ξh represents the diameter of the collection of spheres that composes an ideal network with a regular mesh. It resulted to be 5.1, 4.1, and 3.3 nm when alginate hydrogels at total polysaccharide concentration of 1, 2, and 4%, respectively, were considered as ideal rubbers (i.e., λ = 1). These values of the average network mesh size are in good agreement with previous reports.45 This estimation, although realistic in terms of absolute order of magnitude of ξh, lacks of a specific macromolecular insight on the features of the alginate gels. Indeed, junctions formed among the G-blocks can hardly be “compressed” in point-like cross-links to mirror the theory originally proposed by Flory. To consider this aspect, a different value of λ was evaluated taking the move from a previously proposed approach.48,51,52 The egg-box structures composing the junctions of the real gel are subdivided to form independent cross-links in the idealized network. The elastically active chain is then equally split among the single egg boxes. As reported in the Supporting Information, this is equal to say that the front factor coincides with the number of egg-box structures within the junction in the alginate hydrogel. In the present case, the alginate hydrogels have been formed in saturated conditions. It can then be assumed that all the possible G-blocks are involved in cross-linking the calcium ions and all junctions are formed at their maximum length. With these points in mind, it was 1275

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Figure 4. (a) Variation of the short (T21, 9) and long (T22, 0) relaxation time during the hydrogel formation (alginate concentration =2%). (b) Variation of the spin density of the signal referred to the short (A21, 9) and long (A22, 0) relaxation times. Lines are drawn to guide the eye.

considered that the average length of the junctions equals the average length of the G-block in the alginate chain as calculated from 1H NMR, NG>1, which in turn becomes the front factor in eq 8. A value of λ = 14, which is of the same order of magnitude of previously reported values,19 stresses the difference of the present biopolymer based hydrogel from a perfect rubber. Under this assumption, on the calculation of the front factor λ, the average network mesh size ξh resulted to be 12.4, 9.8, and 7.8 nm for cylindrical alginate gels with a polymer concentration of 1, 2, and 4%, respectively. These values are in good agreement with previous reports53-55 and with mesh dimensions estimated from diffusion data.56 As approximate as this approach might be, it provides a rational methodology, allowing a more realistic evaluation of the network mesh size; all in all, it reduces the discrepancy between the calculated ξh and its (very few) experimental evaluation, that is, from TEM analysis.57 Regardless, the value of λ used for the calculation in eq 8, it was found that the average mesh size scales with Cp as ξh µ Cp-0.32(0.01 (Figure 2, inset). To get further information on the structure of the alginate hydrogel, a low field NMR analysis was carried out. In particular, the relaxation was investigated of the proton nucleus of the water molecules within the hydrogels. In the case of alginate solutions, the decay of the magnetization vector (Mxy) was nicely fitted by using just one exponential term. The T2 was found to scale with the polymer concentration according to the following equation T2 µ Cp-0.62 (Figure 3). This is equal to state that there is a linear relation between the transverse relaxation rate (1/T2) and the alginate concentration in solution (Figure 3, inset). These results are in line with those previously reported,58-61 although in the present case a slightly higher dependence of the transverse relaxation time from the alginate concentration was noticed with respect to ref 61. Low field NMR has been used to follow the kinetics of calcium-alginate hydrogel formation (Figure 4). A calcium limited alginate hydrogel has been prepared by using the in situ release induced by the slowly hydrolyzing lactone GDL. The I time decay was recorded at different intervals. A oneexponential equation fitted satisfactorily the experimental decay of the magnetization vector up to approximately 60 min from the addition of the GDL. Hence, it can be concluded that during this time the amount of calcium ions released from the inorganic salt is very limited and not sufficient to induce a chain-chain association on large scale. However, after that, two different transverse relaxation times, a short one (T21) and a long one (T22), become evident in the fitting of the experimental decay

Table 1. Relaxation Time, T2x, and Spin Density, A2x, for Saturated Cylindrical Alginate Hydrogels at Different Polymer Concentration, Cp relaxation time (ms) Cp (%)

T21

T22

T23

area of the relaxation mode (%) A21

A22

A23

1

47 ( 5

112 ( 4 714 ( 33 24 ( 5

70 ( 5

6 ( 0.4

2

64 ( 5

116 ( 10 865 ( 16 56 ( 11

37 ( 12

6 ( 0.2

4

58 ( 0.4

761 ( 30 94 ( 0.4

6 ( 0.2

(Figure 4a). This can be interpreted as the initial setting of the hydrogel58 and indicates that water molecules experience two microenvironments characterized by different mobility. After the gelation point, both long and short transverse relaxation decrease with time. After approximately 1500 min, T21 reaches a steady value of approximately 220 ms while T22 oscillates from 410 to 550 nm. A closer insight into the characteristics of the alginate hydrogel can be obtained from the analysis of the spin densities associated with the short and long relaxation times, that is, A21 and A22, respectively (Figure 4b). Once the gel formation has started, the two relaxation times are very differently populated. In fact, the short relaxation time accounts for approximately 80% (or more) of all the water molecules of the hydrogel. At variance, the long time, T22, is associated with the relaxation rate of only 20% (or even less) of all the water molecules. From this analysis, it seems safe to conclude that T21 is associated with the relaxation of the water molecules entrapped within the alginate hydrogel meshes.60,62 At variance, T22 seems to be associated with a minor amount of water, which experiences a higher mobility with a relaxation that, however, is still strongly influenced by the presence of alginate. Relaxometric investigation was performed on calcium saturated cylindrical alginate hydrogels at different polysaccharide concentration. The hydrogels were sliced, externally dried and introduced in the NMR sampling tube. The time decay of the signal (I) related to the extinction of Mxy was adequately fitted by means of a three-exponentials function in the case of 1 and 2%, while in the case of 4% alginate hydrogel, two relaxation times were sufficient (Table 1). The interpretation of these data was not straightforward. Due to their low values and high % weight (see Table 1), it can be safely stated that the shorter relaxation times, that is, T21 and T22, are associated with relaxation of water in close contact with the hydrogel network. Relaxometry is able to distinguish among two relaxation times of internal (entrapped) 1276

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Table 2. Relaxation Time, T2x, and Spin Density, A2x, for Alginate Microbeads at Different Polymer Concentration, Cp, Prepared in the Presence of NaCl 0.15 M, Hepes 10 mM (pH 7.4), and CaCl2 50 mM relaxation time (ms)

area of the relaxation mode (%)

Cp (%)

T21

1 107 ( 1

Figure 5. Occurrence probability of the mesh size (ξ) referring to the saturated cylindrical alginate hydrogels at total polymer concentration Cp of 1% (solid thin line), 2% (solid thick line), and 4% (dashed line).

water, namely, T21 and T22, when the alginate concentration in the hydrogel is 1 and 2%. This observation stresses the high sensitivity of the relaxometric technique in determining the structural features of soft materials and the uneven distribution of network structure on molecular scale within an overall macroscopically homogeneous system. When the alginate concentration in the hydrogel is increased to 4%, the distribution of the junctions within the hydrogel is more uniform and the two relaxation times of internal water are averaged out to a single value. The longer relaxation time, T23, seems to be, in all the cases analyzed, too long to be associated with internal water molecules and it appears to have a very low spin density, equal to 6% in all cases. Still, the comparison with the relaxation times of water molecules in alginate solutions does not lead to conclude that T23 is correlated with bulk water. In the light of the above discussion, the relaxation times T21 and T22 were set proportional to the dimension of the hydrogel network mesh, ξ, via a constant (k), which depends on the pore geometry and inner surface properties.63,64 The evaluation of k is based on the relation existing between the average transverse _ relaxation time (T 2) and the average network mesh hξ (eqs 9-11):40 R T2max _ IðT2 Þ 3 T2 3 dT2 T 2 ¼ TR2min ð9Þ T2max T2min Ix ðT2 Þ 3 dT2 assuming T2 ¼ kξ

ð10Þ

it follows that sffiffiffiffiffiffiffiffiffiffiffiffi R kξ2max _ k2 kξ2min IðξÞ 3 ξ 3 dξ 6 3 T 2 ¼ R kξ ¼ kξ ¼ k 2max πNA F k kξ2min IðξÞ 3 dξ

ð11Þ

were I(T2) is peak local intensity, T2max and T2 min indicate peak extension in terms of transverse relaxation time (on the basis of T21 and T22 values, we set T2min = 1 ms and T2max = 2200 ms). The T2max was set equal to the relaxation time of the gelling solution (free water, 25 °C), while T2min was determined by the sensitivity of the equipment used. It follows that (eq 12): _ T2 ð12Þ k ¼ rffiffiffiffiffiffiffiffiffiffiffiffi 6 3 πNA F

T22

T23

A21

A22

A23

359 ( 16 1320 ( 15 77.7 ( 0.7 13.6 ( 0.6 8.7 ( 0.2

2 97.6 ( 0.5 668 ( 6

91.5 ( 0.4 8.5 ( 0.1

3 72.8 ( 0.3 585 ( 10

94.8 ( 0.3 5.2 ( 0.1

4 57.3 ( 0.3 461 ( 20

96.4 ( 0.3 3.6 ( 0.2

In the cases analyzed, k was found to be 8 ( 1 ms/nm. Once the discrete relaxation peaks (T21, A22; T22, A22) are converted into the continuous relaxation spectrum according to the methodology exposed in section 2.5 (Materials and Methods), the knowledge of k allows converting the continuous time relaxation spectrum into the distribution of mesh size. Figure 5 shows this distribution in terms of the occurrence probability P(ξ) of the mesh diameter ξ. It can be noticed that both in the cases of 1 and 2% there is a bimodal distribution of mesh diameters and this directly descends from the presence of two principal relaxation times (T21, T22). Specifically, these gels show a smaller mesh of approximately 6-7 nm and a larger one of about 13-14 nm. This can be traced back to local inhomogeneity as to the dimensions of the meshes as already pointed out. Interestingly, a Cp increase from 1 to 2% causes a sensible increase of the importance (abundance) of smaller meshes with respect the bigger ones. As the alginate concentration in the hydrogel is increased to 4%, the fraction of the bigger meshes vanishes and only the smaller size (approximately 8 nm) meshes exist. In this case, the high polymer concentration allows obtaining a monomodal distribution of the junctions over all the area of the hydrogel and the relaxation mode of the water molecules within is averaged out. 3.2. Spherical Alginate Hydrogels (Microbeads). The relaxometry of the calcium saturated microbeads was explored at different alginate concentration (Table 2). In the case of 1% alginate microbeads, three exponentials were necessary to fit the time decay of the signal (I), indicating the presence of three types of water of different mobility. By comparison with the relaxation of water molecules in alginate solution, the longer relaxation time, that is, T23, can be safely assigned to some residual external water which has not been completely dried out in sample preparation. At variance, the alginate microbeads with a higher polysaccharide concentration, namely, from 2 to 4%, showed an experimental magnetization decay which was efficiently fitted by an equation with two exponentials. As a consequence of the analyses performed with the cylindrical alginate hydrogels (i.e., those used also for the rheological characterization), and in light of its low value and high abundance (see table 2), the shorter relaxation time, that is, T21, can be reasonably considered as stemming from water molecules entrapped within the hydrogel network. The same relaxometric analysis revealed the presence of two sets of water molecules within the cylindrical hydrogel at 1 and 2% alginate concentration, while only one relaxation mode is present, regardless the polysaccharide concentration, in the case of the microbeads. This can be likely traced back to sample dimensions that lead, in the case of alginate microbeads, to an averaging out of the contributions of all the internal water molecules. Hence, the two kinds of water giving rise to two 1277

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Figure 6. Dependence of the shorter transverse relaxation time (T21) from the alginate concentration in the microbeads formed in the presence of 50 mM (9) and 200 mM (0) of CaCl2. Lines represent the fitting of the experimental data with the equation y = xb (R2 = 0.97 for 50 mM and R2 = 0.98 for 200 mM). Inset: dependence of the relaxation rate (1/T21) from the alginate concentration in the microbeads. Lines represent the linear fit of the experimental data.

relaxation times recorded for the 1% alginate cylinders, namely 47 and 112 ms (Table 1), are collapsed in one single relaxation mode (107 ms) when alginate microbeads are considered (Table 2). The T21 obtained for the 4% alginate microbeads (57.3 ms) is in very good agreement with the one calculated for the alginate cylinders (58 ms). This underlines the consistency of the two different procedures for the preparation of the hydrogels of different shapes. Focusing on the trend of the spin densities reported in Table 2, the large majority of the water molecules are represented by the short relaxation time T21. This once more supports its assignation to the water molecules which are entrapped within the hydrogel network. The short spin-spin relaxation times increase with decreasing the alginate concentration in the calcium saturated microbeads. In fact, T21 increases from 57.3 to 106.8 ms when the alginate concentration is decreased from 4 to 1%, respectively, with a scaling low of T21 µ Cp-0.52(0.07(Figure 6). The size of the meshes was evaluated dividing the T21 values reported in Table 2 for the average k value (8 ms/nm) calculated for the cylindrical gels according to eq 10. The average mesh size ξ h was found to be 13.5, 12.3, 9.2, and 7.2 nm for the microbeads at 1, 2, 3 and 4%, and microbeads, respectively. The comparison of these results with the data shown in Figure 5, reveals a reasonably good agreement between the mesh size distribution of cylindrical gels and the average mesh size ξ h of microbeads. Indeed, for Cp = 1 and 2%, the microbeads ξh lies in between the peaks given by the bimodal distribution of the cylindrical hydrogels (i.e, those approximately centered in hξ = 6 nm and hξ = 14 nm). When Cp = 4%, the cylindrical gel peak is just a little bigger than the ξh value pertaining to average mesh size of microbeads. As rheology can not provide information on microbeads’ internal structure, an additional insight was obtained by Image analysis investigation based on TEM images collected at 22000 magnification factor (Figure 7a). Mesh size distribution was deduced from the measurement of the diameter of the solvent cavities delimited by polymer chains in the segmented picture (Figure 7b). All the cavities with a diameter equal to one pixel were excluded because considered as background noise

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embedded in the original image. Figure 7c shows the distribution of the mesh size (ξ) in terms of the occurrence probability P(ξ). As it can be seen, the mesh size distribution is not symmetric and shows the highest occurrence probability in correspondence to about 9 nm. This is in good with previous findings55 and with what we found according to the low field NMR analysis. Indeed, assuming that the constant k relating the relaxation time and the mesh diameter is the same we found for cylindrical gels (∼8 ms/nm), it turns out that LF NMR estimates a mesh diameter of about 12 nm. The relaxometric measurements were also performed on alginate microbeads prepared in the presence of 200 mM CaCl2 and the T21 values are reported in Figure 6. For all the alginate concentrations considered, the T21 values decrease with the increasing of the calcium ions concentration. This can be traced back to the denser polysaccharide chain packing that is reached upon increasing the concentration of cross-linking ions in the reservoir for the microbeads formation. A scaling law of T21 µ Cp-0.43(0.05 holds in this case and for both the 50 mM and 200 mM the relaxation rate was found to have a linear dependence from alginate concentration (Figure 6, inset). The interpretation of the intermediate relaxation time, T22, represents a challenge. An important point to be stressed is the low spin population (less than 10%) associated to this relaxation time. Britton and co-workers65 discussed extensively this aspect reaching the conclusion that the intermediate relaxation time can be correlated to water molecules remaining in the pores between the microbeads compacted in the sample tube. The values of T22 detected for the alginate microbeads and alginate cylinders are in the same order of magnitude of the longer relaxation time recorded in the case of the hydrogel kinetics. Although a clear assignation is not possible at this time, it can be concluded that T22 relaxation mode is correlated to water molecules, which are just minimally affected by the physical properties of the network structure, like compactness. The slight decrease in A22 with increasing alginate concentration, compensated obviously by a variation of A21, might arise from a different porosity among the microbeads as a consequence of their variation in compactness, and to some extent, dimension. To gain a deeper insight into the alginate hydrogel structure and additional data on the assignations of water relaxation modes, alginate microbeads were rehydrated with the gelling solution and the effect of the added solvent was monitored by means of relaxometry measurements (Table 3). The presence of calcium chloride in the added solvent prevented the loosening of the microbead structure and no volume variation was observed. Focusing in Table 3, the first comment concerns the fitting of the experimental NMR data which, in all the cases considered, required an equation composed by three exponential terms. Hence, in the resuspended alginate microbeads three kinds of water, with different mobility, are recognized and characterized by different relaxation times, namely, T21 (short), T22 (intermediate), and T23 (long). It was noted that they all scale with the volume of solvent added as T2x µ ΔVβ (Figure 8a). As an example, the scaling laws for the calcium saturated microbeads with a total polymer concentration of 2% were T21 µ ΔV0.06, T22 µ ΔV0.34, and T23 µ ΔV0.22, respectively. The comparison between the microbeads revealed quite similar β factor for the same relaxation mode irrespective of the overall alginate concentration (Figure 8b). In fact, averaging the scaling factors corresponding to the long relaxation time T23 among the microbeads at different alginate content, a value of 0.25 ( 0.06 was found for β. Similarly, the intermediate 1278

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Figure 7. (a) Original TEM image (22000), (b) segmented TEM image (22000), and (c) mesh size distribution of alginate microbeads at a total polymer concentration Cp of 2%.

transverse relaxation time, T22, shows an average value for β of 0.37 ( 0.06. These results seem to indicate that these two relaxation modes describe water molecules, which have a very similar dependence from the added gelling solution. Hence, they are both believed to belong to water molecules external with respect to the alginate chains composing the network. At variance, the shorter relaxation time, T21, shows very little dependence from the added solvent, with a scaling factor β, averaged over the different alginate concentrations, of approximately 0.054 ( 0.008. This shows that the water molecules characterized by this relaxation mode are entrapped within a network structure which is basically independent from the addition of the gelling solution, that is, the inner part of the alginate gel. The presence of two relaxation processes associated with external water molecules should not be regarded as peculiar or ambiguous. Three relaxation times were already reported in the case of alginate gels at fixed concentration.65 Moreover, when glass microbeads of dimension comparable to our microbeads were considered, two relaxation times (namely, 200 ms (88%) and 600 ms (12%)) where noted, stemming necessarily from water molecules on the outer part of the glass structure. It is reasonable to conclude that these relaxation modes stem from water molecules filling up the cavities formed in the packing of the glass microbeads and from some water trapped within their

interstices. The latter is strongly associated with the chemical groups exposed by the glass bead, and hence, it should be characterized by the shorter relaxation time. It is tempting to interpret the data and the considerations above-reported in terms of their correlation with the alginate hydrogel structure. Indeed, in the present work two models have been considered as equally fitting and complying to the experimental observations (Scheme 1). The common concept underlying both of them is that the short relaxation time (T21) refers to the water molecules, which are in close contact with the alginate network (junctions and elastically active chains) within the hydrogel. This overall picture is also sustained by the dependence of T21 from the alginate concentration in the hydrogel: the higher the polymer concentration, the more compact are the network meshes and the faster is the relaxation of the water molecules within the hydrogel. This is in line with the results obtained from the mechanical spectroscopy (cylindrical hydrogels), where a more compact network was obtained upon increasing the polymer concentration. Similarly, the long transverse relaxation times (T23) are associated with water, which is external to the hydrogel and has comparatively high mobility. The two models slightly differ, although not diverge, on the interpretation of the intermediate relaxation times. Nevertheless, both models foresee such intermediate relaxation mode as belonging to water molecules, 1279

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which represent a transition boundary from internal, fast relaxing, and external, slow relaxing water molecules. The first model (Scheme 1a) is indicated as “solid-core” and considers the inner part of the alginate hydrogel as composed by evenly distributed alginate chains and junctions. These form a macromolecular continuum (on length scale much larger than Table 3. Transverse Relaxation Times (T2x) and Spin Density (A2x) for Approximately 1 cm3 of Alginate Microbeads upon Addition of Gelling Solution total volume added

100 μL

300 μL

600 μL

Alginate 1% T21 (ms) A21 (%)

106.8 ( 0.7 76.0 ( 0.6

109.5 ( 0.7 63.5 ( 0.6

103.0 ( 0.8 58.4 ( 0.6

T22 (ms) A22 (%)

521.0 ( 10.0

588.0 ( 8.0

620.0 ( 10.0

11.0 ( 0.2

11.3 ( 0.3

11.3 ( 0.26

T23 (ms)

1734.0 ( 6.0

1895.0 ( 2

1978.0 ( 2.0

A23 (%)

13.0 ( 0.2

25.1 ( 0.2

30.3 ( 0.16

T21 (ms)

Alginate 2% 90.3 ( 0.5 95.6 ( 0.6

100.2 ( 1.1

A21 (%) T22 (ms)

76.7 ( 0.51 453.0 ( 10.0

58.6 ( 0.4 677.7 ( 10.0

43.9 ( 0.5 829.0 ( 14.0 11.6 ( 0.2

A22 (%)

11.0 ( 0.24

13.5 ( 0.2

T23 (ms)

1438.0 ( 7.0

1755.0 ( 3.7

2017 ( 2.3

A23 (%)

12.3 ( 0.25

27.8 ( 0.3

43.9 ( 0.5

T21 (ms)

Alginate 3% 71.2 ( 0.57 76.8 ( 0.72

76.0 ( 0.7

A21 (%)

79.1 ( 0.4

44.4 ( 0.3

T22 (ms)

443.0 ( 12.0

700.0 ( 11.8

808 ( 12.8

A22 (%) T23 (ms)

9.8 ( 0.4 1344.9 ( 9.0

13.2 ( 0.2 1763.0 ( 4.4

11.4 ( 0.24 2040.0 ( 2.1

A23 (%)

11.1 ( 0.2

26.8 ( 0.24

44.2 ( 0.46

T21 (ms)

Alginate 4% 59.0 ( 0.34 62.0 ( 0.4

64.5 ( 0.9

A21 (%)

80.4 ( 0.46

62.4 ( 0.6

47.0 ( 0.61

T22 (ms)

393.0 ( 10.0

663.4 ( 8.0

857.0 ( 12.5

A22 (%)

9.0 ( 0.24

13.0 ( 0.2

13.2 ( 0.17

T23 (ms) A23 (%)

1161.0 ( 11.0 10.6 ( 0.3

1763.0 ( 3.66 24.6 ( 0.24

2040.0 ( 2.5 39.8 ( 0.21

60.0 ( 0.5

the persistence length of the polymer) in which the water molecules are entrapped and relax much faster than bulk water molecules (polymer free solvent). According to the “solid-core” model, both transverse relaxation times T22 and T23 are allocated to water molecules, which are external to the hydrogel structure. As T23 is detected when solvent is added in the NMR tube, this is assigned to water filling the holes between the alginate microbeads which are determined by their packing. It remains to assign the intermediate transverse relaxation time T22.65 Although a more detailed analysis needs to be done (forthcoming work), it seems safe, within the framework of this model, to assign it to external water which is interstitial between the microbeads, thus, in close contact with the polyanion alginate. This water represents an arbitrary layer which marks the physical transition between the two water reservoirs: the “solid-like” one, which is represented by the bound water molecules, and the “liquid-like” one, that is, the bulk “free” water. Based on the same results, a second model can be proposed for the description of the alginate hydrogels. This is reported as “channels” model in Scheme 1. In this case, the assignation of both the short (T21) and long (T23) transverse relaxation times are equivalent to those of the previous model. However, in this case the intermediate transverse relaxation time T22 is considered belonging to external water which fills the channels (internal pores) of the hydrogel structure. Still, this water represents a transient interlayer between the two very different and extreme kinds of water molecules. The discrimination between these two models is, at present, not possible and outside the scope of the present work. However, a more in-depth analysis comparing alginate samples of different Scheme 1. Representation of the Models for Alginate Hydrogel Microbeads: (a) “Solid Core” Model and (b) “Channels” Model

Figure 8. (a) Dependence of the transverse relaxation time T21 (2), T22 (O), and T23 (9) from the total volume of added solvent for the alginate microbeads at polymer concentration of 2%. Lines represent the best fit of the experimental data with the equation y = xb (R2 = 0.97 for T21, R2 = 0.96 for T22, R2 = 0.98 for T23). (b) Exponent β for the relaxation times T21, T22, and T23 averaged over the different concentrations of alginate in the microbeads. 1280

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Biomacromolecules composition (now in progress) might help in shedding some light and discriminating among the two models here proposed.

4. CONCLUSIONS The present work focused on the synergistic combination of two techniques for the characterization of alginate hydrogels. The mechanical spectroscopy of the alginate cylinders was interpreted in terms of the rubber elasticity theory by introducing a front factor which was related to the average length of the G-blocks in the polysaccharide chains. This allowed calculating in a realistic way the average network mesh size of the hydrogel. The cylindrical hydrogels were screened also exploring the water relaxation measurements and a comparison was performed with the mechanical data allowing for an estimation of the mesh size distribution within the network based on T2 data. It is interesting to point out that, although macroscopically homogeneous cylinders were used, local inhomogeinities, reflected by a bimodal pore size distribution, were detected. The relaxometric analysis was performed also on alginate microbeads leading to similar conclusions. The lack of possibility of performing mechanical measurements on this geometry of the hydrogel was overtaken by performing a statistical analysis of their TEM images to calculate the average distribution of the pores. These resulted to be in good agreement with the dimensions calculated for the cylinders, although a monomodal distribution was found. Nevertheless, the latter aspect is in good agreement with the detection of only one relaxation time for the water entrapped within the alginate microbeads. ’ ASSOCIATED CONTENT

bS

Supporting Information. Model for the evaluation of the front factor for the saturated alginate cylinders. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ39 040 558 3682. Fax: þ39 040 558 3692. E-mail: [email protected].

’ ACKNOWLEDGMENT This work has been supported by the Italian Ministry of Education (PRIN2008 (2008HCAJ9T)). ’ REFERENCES (1) Stanford, E. C. C. British Patent 142, 1881. (2) Stanford, E. C. C. Chem. News 1883, 47, 254–257. (3) Fisher, F. G.; D€orfel, H. Z. Physiol. Chem. 1955, 302, 186–203. (4) Haug, A.; Smidsrød, O. Acta Chem. Scand. 1965, 19, 1221–1226. (5) Haug, A.; Larsen, B.; Smidsrød, O. Acta Chem. Scand. 1966, 20, 183–190. (6) Haug, A.; Larsen, B.; Smidsrød, O. Acta Chem. Scand. 1967, 21, 691–704. (7) Grant, G. T.; Morris, E. R.; Rees, D. A.; Smith, P. J. C.; Thom, D. FEBS Lett. 1973, 32 (1), 195–198. (8) Morris, E. R.; Rees, D. A.; Thom, D.; Boyd, J. Carbohydr. Res. 1978, 66 (1), 145–154. (9) Smidsrød, O. Faraday Discuss. 1974, 57, 263–274. (10) Atkins, E. D.; Nieduszynski, I. A.; Mackie, W.; Parker, K. D.; Smolko, E. E. Biopolymers 1973, 12 (8), 1879–1887.

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