HYDROGEL COMPOSITE MIMICS BIOLOGICAL TISSUES

Abstract

A novel composite hydrogel was developed that shows remarkable similarities to load bearing biological tissues. The composite gel consisting of a poly(vinyl alcohol (PVA) matrix filled with poly(acrylic acid) (PAA) microgel particles exhibits osmotic and mechanical properties that are qualitatively different from regular gels. In the PVA/PAA system the swollen PAA particles “inflate” the PVA network. The swelling of the PAA is limited by the tensile stress P_el developing in the PVA matrix. P_el increases with increasing swelling degree, which is opposite to the decrease of the elastic pressure observed in regular gels. The maximum tensile stress P_el^max can be identified as a quantity that defines the load bearing ability of the composite gel. Systematic osmotic swelling pressure measurements have been made on PVA/PAA gels to determine the effects of PVA stiffness, PAA crosslink density, and Ca²⁺ ion concentration on P_el^max. It is found that P_el^max increases with the stiffness of the PVA matrix, and decreases with (i) increasing crosslink density of the PAA and (ii) increasing Ca²⁺ ion concentration. Small angle neutron scattering (SANS) measurements indicate only a weak interaction between the PVA and PAA gels. It is demonstrated that the osmotic swelling pressure of PVA/PAA composite gels reproduces the osmotic behavior of healthy and osteoarthritic cartilage.

Graphical Abstract

INTRODUCTION

Recent studies have shown the potential of hydrogels to mimic the biomechanical properties of the extracellular matrix (ECM).^1-12 The ECM is a complex environment consisting of collagen, proteoglycans (PGs) and other soluble molecules, ions and water. In cartilage the bottlebrush-shaped aggrecan molecules self-assemble into large microgel-like aggregates composed of approximately 100 aggrecan molecules, which are noncovalently linked to a linear hyaluronic acid (HA) chain.^13-20 These large aggrecan-HA assemblies are enmeshed in a network of type II collagen fibers. PG assemblies swell against the confining collagen network producing an osmotically pre-stressed tissue matrix that is capable of resisting mechanical loads. Recent research revealed the role of large microgel-like aggrecan-HA aggregates in improving load bearing, dimensional stability and lubricating ability.^21-26 The remarkable insensitivity of the aggrecan-HA microgels to changes in the ionic environment, particularly to calcium ions is essential for normal cartilage and bone function.

Understanding the physical-chemical properties of microgels is important not only because PGs form microgels in the ECM but also because these materials have a great potential in biomedical and materials science applications. “Microgels” are polymeric gel “particles” composed of a network whose dimensions are often on the order of molecular or micron dimensions typical of colloidal particles, which are capable of swelling in a solvent dependent on the “solvent quality”, and the extent of cross-linking in the network, with a higher crosslink density normally leading to reduced maximum extent of swelling. In many cases the swelling and stiffness of microgel particles can be tuned by external stimuli such as temperature, pH, ionic strength and electric field. Although the chemical composition and the equilibrium thermodynamic properties of microgels are similar to those of the corresponding macrogels, there are significant differences between the two forms of these chemically identical materials. For example macrogels exhibit viscoelastic behavior, while microgels are low viscosity dispersions. Furthermore, the response of macrogels to changes in the environment (e.g., temperature, ionic strength, pH) is relatively slow; in contrast, microgels response rapidly to such changes. This ability enables the use of microgels in different applications, such as chemical and biological sensors, controlled release, drug delivery, etc.^27-33

Engineered ECM is widely used for tissue engineering and regenerative medicine applications. Significant effort is being made to develop biomimetic hydrogels to facilitate cartilage tissue replacement, repair, and regeneration. Owing to their high water content (> 90%) hydrogels are usually viscoelastic materials and resemble the properties of articular cartilage. Various natural and synthetic polymers, such as HA, collagen, poly(vinyl alcohol) (PVA), have been used to replace diseased or damaged cartilage tissue.^34-44 From the materials science perspective, we view cartilage as a natural fiber-reinforced composite hydrogel consisting of mainly PGs (10-15%), type II collagen (10-20%), chondrocytes (cartilage cells, 1-5%) and approximately 65-80% water by weight. PVA exhibits excellent biocompatibility and is a particularly promising biomaterial in tissue engineering applications. PVA hydrogels mimic the water content of cartilage and possess low friction coefficient, which is a basic requirement for joint lubrication. Clinical studies have shown that PVA is a potential synthetic alternative to native cartilage replacement. Highly swollen PVA hydrogels have been successfully used for implants that reconstruct meniscus function and prevent the progression of osteoarthritis (OA) in cartilage.^46-49

Hydrogels designed for orthopedic applications must possess comparable mechanical properties to the native tissue. Although certain properties of PVA gels resemble the behavior of cartilage tissue (e.g., stiffness, high water content), regular PVA gels are too week to resist the high compressive loads imposed on joint surfaces. Several attempts have been made to improve the mechanical strength of PVA hydrogels such as crosslinking of the polymer molecules (e.g., by dialdehydes), introducing filler particles (e.g., glass), inducing partial crystallization (e.g., by freeze thawing).^50-55 In recent years new preparation techniques have been developed (e.g., in situ co-precipitation, sol–gel method, solvent casting technology). The in-situ co-precipitation method has received particular attention because it shows similarity to the in situ mineralization of hydroxyapatite in bone.^56-58

Knowledge of the role of various components and their interactions in defining the mechanical properties of ECM is essential for developing advanced tissue engineering/regenerative medicine strategies. Here we describe a novel composite hydrogel that mimics the biomechanical properties of cartilage ECM. The composite gel consists of a PVA network filled with small (≈10 μm) poly(acrylic) acid (PAA) gel particles. The present composite gel is conceptually different from the traditional filler reinforced systems. Inorganic fillers (e.g., fumed silica) are solid particles that improve the mechanical properties (elastic modulus, etc.) of the gels by making additional contacts between the polymer chains. However, in the PVA/PAA gel the “filler” is a soft gel that inflates the surrounding matrix.

Despite the many obvious material differences between cartilage and PVA/PAA hydrogels, these systems share an important common feature, namely, that their networks are both in tension in the absence of external loading. In cartilage, intracellularly synthesized aggrecan bottlebrushes are secreted into the ECM, where they form supramolecular aggregates with HA stabilized by a link protein.^16-19 The collagen network is inflated by the highly swollen aggrecan/HA complexes enmeshed in the matrix. The osmotic swelling pressure of the charged PG assemblies keeps the collagen in a pre-stressed state. In PVA/PAA gels the PAA particles inflate the PVA matrix. We found that the PVA/PAA hydrogel exhibits qualitatively similar mechanical and osmotic properties to cartilage, which renders this system an appropriate biomimetic model of cartilage.¹⁰⁵ In this model the PVA network corresponds to the collagen matrix while the PAA microgel phase plays the role of the PG.

It has been recognized that pre-stress plays important role in the biomechanics of various biological tissues. However, the consequences of pre-stress and tissue inflation on the load bearing properties have not yet been previously explored. An elegant approach based on the tensegrity model was proposed to elucidate how mechanical stresses are transmitted to individual cells and transduced into a biochemical response.^59,60

We argue that pre-stress is a key determinant of the unique mechanical properties of load bearing biological tissues, particularly those made of soft and “squishy” polymeric materials. Therefore, systematic studies made on inflated model hydrogels is expected to provide invaluable information on the effect of various factors (matrix stiffness, swelling pressure, charge density of the gel particles, etc.) on the macroscopic mechanical/swelling properties, and ultimately the load bearing ability of these systems. Similar information cannot be obtained from measurements made on biological tissues because their composition and physical properties (e,g., stiffness, charge density) cannot currently be independently and systematically varied.

This paper is organized as follows: First, we discuss the osmotic behavior of the two polymeric components (PVA and PAA gels) individually. The effect of gel stiffness on the osmotic swelling pressure and elastic pressure is determined by the osmotic stress technique. Then, we present results obtained for PVA/PAA composite hydrogels. We systematically vary (i) the stiffness of the PVA matrix, (ii) the crosslink density of the PAA gel particles, and (iii) the Ca²⁺ ion concentration of the equilibrium solution. Small angle neutron scattering (SANS) measurements are made to quantify the interactions between the two polymeric components over a broad range of length scales. A comparison is made between the osmotic response of PVA/PAA hydrogels and swelling pressure data reported for healthy and osteoarthritic cartilage in the literature.

THEORETICAL SECTION

Swelling and elastic properties of gels

The Flory-Rehner model^61-63 assumes additivity of the free energy of mixing of the polymer and solvent molecules (ΔF_mix), and the free energy of elastic deformation of the network chains (ΔF_el),

$$\Delta \mathrm{F}=\Delta {\mathrm{F}}_{\text{mix}}+\Delta {\mathrm{F}}_{\text{el}}$$ (1)

The osmotic swelling pressure II_sw is is the sum of two components: the osmotic mixing pressure II_mix that tends to expand the gel and the elastic pressure II_el that counteracts II_mix and limits gel swelling. At equilibrium we have

$${\text{II}}_{\text{sw}}=\text{-}\partial \Delta \mathrm{F}∕\partial \mathrm{V}={\text{II}}_{\text{mix}}+{\text{II}}_{\text{el}}$$ (2)

where V is the volume of the gel.

Non-zero values of Π_sw can be achieved by equilibrating the gel with a solution of an osmotic stressing agent of known osmotic pressure^64,65 or vapor pressure^66-68, or by squeezing water out of the swollen network by applying an external mechanical (hydrostatic) pressure.^69,70

In the semidilute concentration regime II_mix can be satisfactorily described by the Flory-Huggins expression^71-76

$${\text{II}}_{\text{mix}}=\text{-}(\text{RT}∕{\mathrm{V}}_1)[\text{ln}(1-\phi )+\phi +{\chi }_0{\phi }^2+{\chi }_1{\phi }^3]$$ (3)

where V₁ is the partial molar volume of the solvent, φ is the volume fraction of the polymer, χ₀ and χ₁ are interaction parameters related to the second and third virial coefficients, R is the universal gas constant and T is the absolute temperature.

To estimate the elastic free energy of polymer networks several models have been proposed. In the classical models of Wall and Flory, and James and Guth the polymer chains are idealized, volumeless, Gaussian chains.^77-82 More advanced models take into account inter-chain or ‘entanglement’ interactions defined in terms of topological constraints due to chain uncrossability and correlations arising from molecular packing of the network chains. For our purposes, a minimal statistical mechanical model of rubber elasticity must incorporate three main features: (i) connected network of flexible polymer chains, (ii) entanglement constraints, and (iii) finite volume of the network chains. The Localization Model (LM) directly addresses the interchain interactions, which can be large in the condensed state, just as molecules in a liquid state have larger intermolecular interactions than when in a gaseous state.^83-85,99 An examination of the LM in comparison stress-strain data reported in the literature indicated that this elegantly simple and conceptually clear model of rubber elasticity provided a good description of the experimental results both in the swollen and dry states.⁸⁶

In the LM the elastic free energy of the polymer network consisting of flexible chains is given as

$$\Delta {\mathrm{F}}_{\text{LM}}=({\mathrm{G}}_{\mathrm{c}}∕2)[({\lambda }_{\mathrm{x}}^2+{\lambda }_{\mathrm{y}}^2+{\lambda }_{\mathrm{z}}^2\text{-}3)∕3]+{\mathrm{G}}_{\mathrm{e}}[({\lambda }_{\mathrm{x}}+{\lambda }_{\mathrm{y}}+{\lambda }_{\mathrm{z}}-3)∕3$$ (4)

where λ_x, λ_y and λ_z are deformation ratios along the x, y and z directions. The shear modulus G_c is proportional to the number of elastic chains ν in the network

$${\mathrm{G}}_{\mathrm{c}}={\mathrm{C}}_{0}v{k}_B\mathrm{T}$$ (5)

where k_B is the Boltzmann constant. C₀ depends on the details of the network structure (dangling ends, junction functionality, etc.). In the model of Wall and Flory C₀ = 1, while in the model of James and Guth, C₀ = 1/2. The entanglement contribution G_e to the network free energy contains a cross-term proportional to G_c,

$${\mathrm{G}}_{\mathrm{e}}=\gamma {\mathrm{G}}_{\mathrm{c}}+{{\mathrm{G}}^{\ast }}_{\mathrm{N}}$$ (6)

In equation 6, the γ parameter is an empirical parameter describing the cross-correlation of the crosslinking on the inter-chain entanglement interaction. The crosslink independent contribution (G*_N) to G_e is identified with the independently measurable plateau modulus of the polymer melt, G*_N.^83,84 The localization model can be extended to swollen networks by introducing a swelling factor λ_s.⁹⁹ In the case of isotropic swelling λ_s = λ_x = λ_y = λ_z = (V/V_d)^1/3, where V and V_d are the volumes of the swollen and dry networks, respectively.

In many network systems encountered in biological materials, the chains are relatively stiff so that the elasticity model based on a flexible chain model no longer applies. In the limit of small enough deformations, however, where linear elasticity still applies, we may still treat such materials as being Hookean so that the standard rubber elasticity model can be formally derived even from a continuum perspective, but we cannot expect this model to be predictive over a large range of deformations.

Vilgis and Edwards adopted an idealized model of such semi-flexible polymer networks as a collection of rods connected by freely-jointed tethers where it was found that the change of free energy of the network arising from altering the network junction points rather than deforming chains gave to a strongly non-linear change in the network free energy ΔF(Vilgis-Edwards) of the form, ΔF(Vilgis-Edwards) ~ exp [(λ_x² + λ_y² + λ_z²)], at large network deformations.⁸⁷ Lin et al.⁹⁸ introduced a model that interpolated the exact low deformation scaling relation for ΔF for deformation in the linear elasticity regime and at the same recovered the asymptotic scaling form for ΔF for large deformations derived by Vilgis and Edwards for the semi-flexible polymer network. (The rather complex integral equation-based theory of Edwards and Vilgis only allowed for limiting asymptotic behavior of the network.). We emphasize again that the entropic elasticity in this rod network model derives entirely from the deformation of the junction positions rather than from stretching the network polymer chains, so the physics is quite different from the flexible chain network model. The specific expression for the elasticity of semi-flexible polymer networks deduced from the arguments of Lin et al.⁹⁸ provides a simple closed form relation for ΔF(semi-flexible) that can be expected to apply to many networks involving stiff polymers,

$$\Delta \mathrm{F}(\text{semi-flexible})=({\mathrm{G}}_{\mathrm{c}}∕2\mathrm{b})\{\text{exp}[b[({\lambda }_{\mathrm{x}}^2+{\lambda }_{\mathrm{y}}^2+{\lambda }_{\mathrm{z}}^2\text{-}3)]∕3-1]\text{-}1\}$$ (7)

where G_c scales with the number of cross-links as in chain elasticity of flexible polymer networks and b is a parameter that characterizes the amount of deformation required before non-linear effects of deformation of the network junctions makes a prevalent contribution to the network elasticity. Interestingly, it was then realized after deriving eq. (7) that this functional form is of the same general form as the purely phenomenological “Fung hyperelasticity model“ that has been employed in many studies of the elasticity of many biological materials.^88,100-102 This lends some credence to the model in the applications considered in the present paper. Lin et al.⁹⁸ also extended this semi-flexible chain model to address interchain interactions.

Small angle neutron scattering

Small-angle scattering provides information on the structure and interactions within polymer solutions and gels over a broad range of length scales. In a polymer solution of overlapping polymer chains, the scattering intensity arising from thermodynamic concentration-fluctuations is given by the Ornstein-Zernike expression for the structure factor^88.89

$$I_{{}_{SOL}}(q)=a\frac{kT({\rho }_{{}_P}-{\rho }_{{}_S}{)}^2{\phi }^2}{K_{{}_{OS}}}\frac{1}{1+(q\xi {)}^2}$$ (8)

where ρ_p and ρ_s are the scattering length densities of the polymer and solvent, respectively, K_OS [= φ(∂Π_mix/∂φ)] is the osmotic compression modulus of the solution, ξ is the polymer-polymer correlation length, a is a constant and kT is the Boltzmann factor. In equation 8, q is the scattering wave vector, i.e., q = (4π/λ)sin(θ/2), where λ and θ are the wavelength of the incident radiation and the scattering angle, respectively.

Gels generally contain static inhomogeneities frozen in by the crosslinks, which contribute to the scattering response I_ST(q).⁹⁰⁼⁹³

The total scattering intensity from a polymer gel is taken to be the sum of dynamic (solution-like) and static contributions,

$$I_{GEL}(q)=I_{DYN}(q)+I_{ST}(q)$$ (9)

where the functional form of the first term is similar to that of the corresponding polymer solution while the second term depends on the particular network system.

In many neutral gels the scattering form structural inhomogeneities can be described by a Debye-Bueche structure factor and I_GEL(q) is given by

$$I_{{}_{GEL}}(q)=I_{{}_{DYN}}(q)+\frac{I_{{}_{ST}}(0)}{(1+q^2{\Xi }^2{)}^2}$$ (10)

where I_ST(0) is the extrapolated intensity at q = 0 and Ξ is the characteristic size of the inhomogeneities in the network.⁹⁴

In gels comprised of polyelectrolyte chains the static component displays a power law behavior,

$$I_{ST}(q)=A{q}^{\text{-}m}$$ (11)

where m is a constant.^73-76 Such a power-law scattering intensity is indicative of fractal-like structures. For scattering from three-dimensional objects with fractal surface, the power law exponent is negative - (6 – D_s), where D_s is the fractal dimension of the surface (2 < D_s < 3). D_s = 2 represents a smooth surface.

MATERIALS AND METHODS

Gel preparation

Poly(vinyl-alcohol) (PVA) gels were made by crosslinking with glutaraldehyde at pH = 1.0 in aqueous solutions.⁹³ For the experiments a fully hydrolyzed and fractionated PVA sample was used (M_w,PVA = 110 kDa). Crosslinks were introduced at 4% (w/w) polymer concentrations, the molar ratio of monomer units to the molecules of crosslinker was 200. Gels were cast between two glass microscope slides with 2 mm thick spacers. After gelation the samples were equilibrated with 100 mM NaCl solution to remove HCl and uncrosslinked polymer (sol fraction). Then the gels were dried in an oven at 95 °C, reswollen in 100 mM NaCl solution for 24 hours, and exposed to two (PVA1), four (PVA2) six (PVA3) and eight (PVA4) cycles of freezing for 12-14 hours at − 20 °C and thawing the samples for 10 hours at 25 °C.

The preparation of polyacrylic acid (PAA) gels has been described previously.^71,72 Poly(acrylic acid) gels were synthesized by free-radical copolymerization of partially neutralized acrylic acid and N,N′-methylenebis(acrylamide) in aqueous solution. The monomer concentration was 30% (w/w). The concentration of the crosslinker was 0.3 (PAA1), 0.6 (PAA2), 0.9 (PAA3) and 1.2 % (PAA4). In the initial mixture 35% of the monomers were neutralized by sodium hydroxide. After the components were mixed, dissolved oxygen that would inhibit the polymerization reaction was eliminated by bubbling nitrogen through the solution. The polymerization reaction was initiated by ammonium persulfate (0.5 g/L). After gelation the acrylic acid units were first neutralized with NaOH solution and then dried at 90 °C for 48 hours. The dry polymer was ground into a powder having an average particle size less than 10 microns.

PVA/PAA composite gels were prepared by crosslinking PVA in solution containing PAA particles. In the initial solution the concentrations of both polymers were 4%. First the HCl was added to the solution (pH ≈ 1) to suppress the swelling of PAA. Then the crosslinker glutaraldehyde was added to the suspension. The molar ratio of the monomer units to the crosslinker was the same as in the pure PVA gels. The composite gels were treated by the freeze thaw process similarly to the PVA gels. The sample code is defined by the composition and the code of the corresponding PVA and PAA gel. For example, PVA1/PAA1 is a composite gel made by crosslinking a PVA solution containing PAA particles (crosslinker concentration: 0.3 %) and applying 2 freeze-thaw cycles.

Osmotic stress measurements

Gels were equilibrated with poly(vinyl pyrrolidone) (PVP) solutions (molecular weight: 29 kDa) of known osmotic pressure.^64,65,95 A semi-permeable membrane was used to prevent penetration of the PVP into the network. When equilibrium was reached, the polymer concentration in both phases was measured. This procedure yields for each gel the dependence of the osmotic swelling pressure on the polymer concentration.

SANS measurements

SANS measurements were made on the NG3 instrument at NIST, Gaithersburg MD. The incident wavelength was 8 Å. The sample-detector distances were 1.2, 4 and 13.1 m corresponding to a wave vector range 0.005 Å⁻¹ < q < 0.1 Å⁻¹. The ambient temperature during the experiments was 25 ± 0.1 °C. Gel samples were prepared in D₂O solutions in 2 mm thick sample cells. After azimuthal averaging, corrections for incoherent background, detector response and cell window scattering were applied.⁹⁶

RESULTS AND DISCUSSION

Osmotic and elastic properties

PVA and PAA gels

Figure 1a shows the variation of the osmotic swelling pressure Π_sw as a function of the swelling degree 1/φ for four PVA gels. Network stiffness varies according to the series, PVA1 < PVA2 < PVA3 < PVA4. We see that Π_sw decreases with increasing gel stiffness and with increasing swelling degree. At equilibrium with the pure diluent (100 mM NaCl solution) Π_sw = 0. The dashed red curve represents the osmotic mixing pressure for the crosslinked PVA calculated by equation 3 with χ₀ = 0.494 and χ₁ = 0.⁹⁷ The difference between Π_mix and Π_sw is the elastic pressure of the crosslinked polymer Π_el defined by eq. 2. At equilibrium with the pure solvent, Π_el = Π_mix. The inset shows that Π_el strongly increases with decreasing swelling ratio. The observed increase can be attributed to crystallization, and hydrogen bonding between the hydroxyl groups on the PVA chains. It is well documented in the literature that the freeze-thaw procedure promotes the crystallization of PVA.^51-54 Microcrystallites and other molecular associations can act as physical crosslinks.

Figure 1.

Π_sw vs 1/φ plots for PVA (figure a) and PAA (figure b) gels. Continuous curves through the data points are guides to the eyes. The red dashed curves show Π_mix vs 1/φ for the solutions of the corresponding uncrosslinked polymers. Inset: Π_el vs 1/φ plots. Dashed lines: prediction of the phantom network model (eq. 12); continuous curves: fits of eq. 13.

For isotropically swollen networks [λ_x = λ_y = λ_z = (V/V_d)^1/3] the phantom network model and the Flory-Rehner theory indicates,

$${\text{II}}_{\text{el}}=\partial \{(3{\mathrm{G}}_{\mathrm{c}}∕2)[(\mathrm{V}∕{\mathrm{V}}_{\mathrm{d}}{)}^{2∕3}\text{-}1]\}∕\partial \mathrm{V}=\mathrm{K}{\phi }^{1∕3}$$ (12)

where K is a constant (= C₀ ν* RT, and ν* is the concentration of the elastic chains in the dry network).

The dashed curves in the inset show the elastic pressure predicted by the phantom network model (equation 12). This model underestimates the experimental data over the entire concentration range explored in the present experiment.

The continuous lines through the data point are fits to eq. 13 derived from the Localization Model for highly crosslinked gels^98,99

$${\text{II}}_{\text{el}}={\mathrm{K}}_1{\phi }^{1∕3}+{\mathrm{K}}_2{\phi }^{4∕3}$$ (13)

where K₁ and K₂ are constants (listed in Table 1).

Table 1.

Fitting parameters for the II_el vs φ plots

Sample	K1 (kPa)	K2 (kPa)
PVA1	314	1236
PVA2	201	737
PVA3	127	738
PVA4	61	566
PAA1	46	193
PAA2	93	194
PAA3	143	195
PAA4	194	192

In Figure 1b, are shown the Π_sw vs 1/φ plots for PAA gels. These gels exhibit qualitatively similar behavior to the PVA gels. Evidently, Π_sw decreases with increasing crosslink density and for high degrees of swelling Π_sw exceeds the values found for PVA gels. The inset in Figure 1b shows that in PAA gels the increase of the elastic pressure Π_el (= Π_sw - Π_mix) with decreasing swelling degree is less steep than in PVA gels. The fit to equation 12 is reasonable over an extended range of swelling (dashed lines), and the upturn of the II_el vs 1/φ curves occurs at high polymer concentrations. The continuous lines show the fits to eq. 13 derived from the Localization Model. The values of the fitting parameters K₁ and K₂ are listed in Table 1.

In principle, eq. 3 is applicable only for uncharged gels. For polyelectrolytes an ion-dependent term must also be included. However, previous experimental studies, as well as molecular dynamics simulations indicated that the Flory–Huggins formalism is satisfactory for describing polyelectrolyte solution behavior in the presence of added salt having a concentration of physiological relevance and for polymer concentrations high enough for mean field theory to apply.³⁸ Simulations showed that under equilibrium conditions cancellation (i.e., enthalpy-entropy compensation) arises between the electrostatic and the counter-ion excluded volume contributions to the osmotic pressure. It was demonstrated that eq. 3, which accounts for neither electrostatic nor counter-ion excluded-volume effects, still fits both experimental and simulated data for various polyelectrolyte solutions.^73-76 Therefore, we do not include an explicit ionic contribution in the free energy function. This is an adequate approximation for the total free energy of the present gel system; however, ions play an important role in defining the osmotic swelling pressure of the PAA gels.

PVA/PAA composite gels

The situation in the composite gel is illustrated schematically in Figure 2. The PAA particles swell more than the PVA matrix resulting in a pre-stress that is generated in the inflated matrix.

Figure 2.

Schematic drawing illustrating gel inflation. Above the crossover point the enclosed gel particles swell more than the surrounding matrix. The matrix becomes inflated and prevents further swelling.

Figure 3 shows the variation of Π_sw as a function of 1/φ for PVA/PAA composite gels (ratio of PVA to PAA is 1:1). We focus on the effects of matrix stiffness (figure 3a), crosslink density of the PAA component (figure 3b), and Ca²⁺ ion concentration (figure 3c). Figure 3a shows that (i) the curves for the composite gels are always steeper than for the corresponding PVA gels (see Figure 1a) and (ii) displaced to lower swelling degrees. Decrease of the swelling degree is typical for gels containing filler particles. Physical interactions between the filler and the polymer matrix (e.g., adsorption) are expected to play a similar role as chemical crosslinks. Furthermore, the secondary structure of the filler (e.g., interparticle aggregates) may also affect gel stiffness. The dashed curve shows the variation of the swelling pressure of the PAA as a function of 1/φ.

Figure 3.

Π_sw vs 1/φ plots for PVA/PAA composite gels. a. PVA/PAA gels with varying network stiffnesses (continuous curves), PAA gel (dashed curve). Symbols: ▲ PVA1/PAA1, ▼ PVA2/PAA1, ■ PVA3/PAA1 ● PVA4/PAA1. b. PVA4/PAA gels containing PAA particles of varying nominal crosslink densities: ● 0.03, ■ 0.06, ▼ 0.09, ▲ 1.20 %). Dashed curves: Π_sw vs 1/φ plots for PAA gels with varying crosslink densities (red: 0.03%, blue: 0.06%. green: 0.09%, black: 1.2%). c. PVA4/PAA gels containing PAA particles swollen in CaCl₂ solutions of varying concentrations: ● 0 mM, ■ 0.1 mM, ▼ 0.2 mM, ▲ 0.3 mM. Dashed curves: Π_sw vs 1/φ plots for PAA gels in CaCl₂ solutions of varying concentrations (red: 0 mM, blue: 0.1 mM, green: 0.2 mM, black: 0.3 mM). Insets: tensile stress (P_el) vs 1/φ plots for the same gels shown in the main figures.

There is an important conceptual difference between the swelling behavior of the pure PVA gels and the PVA/PAA composite gels. In the latter, the PAA particles are trapped in the PVA matrix. As the swelling degree of the PAA increases the PVA matrix becomes inflated (see Figure 2), however, the PVA matrix limits the swelling of the PAA. So when the composite gel is fully swollen (Π_sw = 0), the PVA matrix is in tension. The tensile stress of the inflated gel is defined as

$${\mathrm{P}}_{\text{el}}={\Pi }_{\text{PAA}}\text{-}{\Pi }_{\text{sw}}$$ (14)

When Π_sw = Π_PAA the PVA and PAA gels are in equilibrium and the tensile stress P_el = 0. The inset in Figure 3a illustrates that the pre-stress P_el increases with increasing network stiffness and reaches a maximum, P_el^max, at the fully swollen state, i.e., at Π_sw = 0. Clearly, matrix stiffness plays multiple roles in controlling the osmotic properties of composite gels: (i) it defines the tensile stress that develops in the inflated system, and (ii) it limits the swelling of the encapsulated gel particles.

We analyzed P_el by fitting an exponential function to the data as predicted by the Fung model. The agreement with the prediction of the semi-flexible chain network model of Lin et al.⁹⁸ (or equivalently the “Fung model”) is surprisingly good since we tend to think of PVA and PAA as being relatively flexible polymers. However, it is well documented in the literature that microcrystalline domains formed in the freeze-thaw process can significantly increase the stiffness of the PVA network. Furthermore, PAA inflates the PVA matrix thus increasing the overall rigidity of the composite system.

Determination of the optimal crosslink density of PAA particles to maximize gel strength is not obvious although considering the two extremes of weak and dense crosslinking suggests that such an optimum exists. Weakly crosslinked PAA exhibits high swelling pressure that eventually destabilizes and destroys the PVA matrix. On the other hand, the limited swelling of densely crosslinked PAA particles may not be sufficient to inflate the PVA gel.

Figure 3b shows the influence of the crosslink density of the PAA particles on the swelling pressure of PVA/PAA composite gels. Increasing crosslink density progressively reduces the swelling of the PAA particles, and shifts the Π_sw vs 1/φ plots toward lower swelling pressures. The inset in Figure 3b illustrates that (i) P_el in the present system gradually decreases with increasing crosslink density of the PAA and (ii) the P_el vs 1/φ plots are nearly parallel. This finding implies that the main effect of the crosslink density of PAA is defining P_el^max.

In Figure 3c are shown the effect of Ca²⁺ ions on the swelling pressure of PVA/PAA composite gels. This experiment aimed to model the influence of fixed charge density on the osmotic properties. The NaCl concentration was kept constant (c_NaCl = 100 mM) and the CaCl₂ concentration was varied in the range 0 < c_CaCl2 ≤ 0.3 mM. [At higher CaCl₂ concentration (c_CaCl2 > 0.8 mM) the PAA gels collapse.] Figure 3c indicates that the ionic environment strongly affects the shape of the PAA curves: both the numerical values of Π_sw as well as the slope of the Π_sw vs 1/φ plots strongly decreases with increasing CaCl₂ concentration. Clearly, Ca²⁺ ions reduce the effective charge on the polymer chains, i.e., the repulsive electrostatic interactions between the polymer molecules. This effect resembles that of increasing crosslink density, however, the underlying molecular mechanism is entirely different. Ca²⁺ ions do not form crosslinks between neighboring PAA chains as demonstrated in the literature.^71,72,76

In summary, in “uninflated” gels the elastic pressure primarily arises from entropic retractive forces, which develop as the network swells and the number of degrees of freedom of the chains is reduced. At equilibrium the decrease of the free energy due to mixing of the polymer and solvent molecules is balanced by the free energy increase due to stretching of the network chains. In this physical situation, the osmotic mixing pressure of the crosslinked polymer is always greater than the swelling pressure of the gel, and the elastic pressure Π_el decreases with increasing swelling degree as shown in Figure 1. By contrast, for gels inflated by swelling particle inclusions, the reduction of the elastic pressure is compensated by the tensile stress developing in the matrix due to swelling of the trapped gel particles. Consequently, P_el gradually increases as the swelling degree increases. The Π_sw vs 1/φ curve of the PVA matrix intercepts that of the PAA gel. At their intersection Π_sw^composite ₌ Π_sw^PAA and P_el = 0. The position of the intersection and the magnitude of P_el depend on (i) the stiffness of the PVA network, (ii) the crosslink density of the PAA particles, and (iii) the Ca²⁺ ion concentration of the equilibrium salt solution. With increasing swelling degree P_el increases and reaches a maximum P_el^max when the gel is fully swollen. P_el^max increases with the stiffness of the PVA matrix, and decreases with increasing crosslink density and decreasing effective charge density of the PAA particles. P_el^max defines the load bearing ability of composite gels.

Small angle neutron scattering

Although osmotic swelling pressure measurements provide invaluable insight into the thermodynamics of composite hydrogels they do not provide information on the organization of the polymer components. SANS allows us to probe the structure of composite gels over a broad range of length scales and quantify the interactions that govern the macroscopic thermodynamic properties.

Figure 4 shows typical SANS profiles of PVA and PAA gels. Data are presented for two PVA gels (PVA1 and PVA3) differing in network stiffness. The scattering curves of these PVA gels exhibit similar qualitative features. In PVA1 two plateaus are clearly distinguishable; one in the intermediate q regime and the other one at low q. In both PVA samples the shoulder at high q corresponds to the Ornstein–Zernike thermal contribution to the scattering signal, while the excess scattering at low q can be attributed to structural inhomogeneities (large polymer clusters, etc.) frozen in by the crosslinks. The scattering profiles show that the intensity arising from inhomogeneities increases with increasing stiffness. In PVA3 the low q plateau is less pronounced indicating that the size of the inhomogeneities varies nearly continuously over the length scale range from 10 Å to approximately 500 Å explored in the SANS experiment. It is known that PVA gels contain microcrystallites, which are also expected to contribute to the scattering intensity, since they modify the local polymer concentration. At high q the PVA1 and PVA3 signals are practically indistinguishable indicating that the local structure of the PVA chains is not influenced by the presence of larger scale objects.

Figure 4.

SANS profiles of PVA and PAA gels. Continuous curves through the data points are least squares fits of eq. 15 (PVA gels) and eq. 16 (PAA gel). The intensity of the PAA curve is divided by 10 for clarity. Inset: Comparison of the SANS response of composite gels with the sum of the SANS curves of the components. The intensity of the PVA1+PAA1 curve is divided by 10 for clarity.

The dashed curves through the PVA data points are least squares fits of

$$I(q)=\frac{A_1}{\left(1+q^2{\xi }^2\right)}+\frac{A_2}{\left(1+q^2{\Xi }^2\right)}$$ (15)

where A₁ and A₂ are constants. The values of A₁, A₂, ξ and Ξ listed in Table 2 show that the intensities as well as the characteristic lengths increase with increasing network stiffness.

Table 2.

Fitting parameters to the SANS profiles of PVA and PAA gels

Sample	A1 (cm−1)	A2 (cm−1)	ξ (Å)	Ξ (Å)	m
PVA1	1.75	12.9	46	308	--
PVA3	3.2	13.6	62	397	--
PAA1	0.3	2x10−7	23	---	−3.2

The scattering response of the PAA gel significantly differs from that of the PVA gels. At low q (< 0.08 Å⁻¹) a power law behavior is observed characteristic of scattering from large clusters. This behavior is typical of polyelectrolyte gels and solutions.^{24,26,76,103-105} Because of the absence of a shoulder in this region, the size of the clusters cannot be estimated from the SANS profile. At low q the slope varies as m ≈ −3.2. Such a power-law behavior indicates that in the low q regime the PAA gel exhibits fractal-like behavior. As discussed earlier for scattering from objects with fractal surface, the power law exponent is related to the fractal dimension. The slope of the log-log plot in Figure 4 yields D_s ≈ 2.8. At intermediate q a plateau region is distinguishable, which is described by the first term of equation 16. The dashed curve is fit to the equation

$$I(q)=\frac{A_1}{\left(1+q^2{\xi }^2\right)}+A_2{q}^{-m}$$ (16)

The fitting parameters are displayed in the last row of Table 2.

To glean additional information about the interaction between the two polymers we also made SANS measurements on composite gels. SANS reveals the length scales over which the components interact and provides information on the nature and the strength of their interaction, and the changes occurring in the underlying molecular and supramolecular structure. In the inset in Figure 4 the SANS response of PVA/PAA composite gels are compared with the sum of the SANS profiles of the components. The shape of the measured and calculated curves is similar, indicating the absence of significant interaction between the two polymer gels. This finding implies that the two crosslinked polymers in the PVA/PAA composite gel can be treated as independent entities.

Biomedical relevance of load bearing composite gels

Swelling pressure of PVA/PAA composite gels and cartilage specimen

In this section we compare the osmotic response of the present composite gels with osmotic swelling pressure data reported for cartilage specimens in the literature.¹⁸ The authors determined the tensile stress of the collagen matrix P_el as a function of hydration for healthy human cartilage samples, and for cartilage from an osteoarthritic (OA) joint (Figure 5a). In healthy cartilage the P_el vs hydration curves exhibited a steep increase with increasing hydration. High PG concentration, high charge density, and high Π_PG reflect the large stiffness of the collagen matrix. During loading of healthy cartilage, changes in tissue swelling are relatively small. By contrast, the P_el vs hydration curve for the OA specimen was significantly less steep and displaced to higher hydrations, indicating that in OA cartilage the collagen network is much weaker (i.e., more flaccid), and the tissue swells more. Because of its high water content the OA cartilage cannot develop high PG concentration and its load bearing capacity is limited (Figure 5a inset).

Figure 5.

Comparison between the swelling behavior of cartilage samples (figure a) and PVA/PAA composite gels (figure b). In figure a the x-axis represents the hydration of the cartilage, V_Total is the total tissue volume and V_Coll is the volume of the collagen Insets: tensile stress vs hydration curves.

Figure 5b illustrates that PVA/PAA composite hydrogels exhibit qualitatively similar osmotic response to cartilage tissue. The PVA4/PAA1 gel mimics the healthy cartilage, while the osmotic behavior of the OA cartilage is close to that of the PVA2/PAA1 gel. In the latter system the stiffness of the PVA gel is about half of the PVA component in the PVA4/PAA1 gel. This reduction in the stiffness of the matrix polymer reproduces the reduced swelling pressure of the OA specimen.^18,106 The biomimetic model describes both the shape of the cartilage curves and the numerical values of the experimental swelling pressure.

Tailoring the osmotic properties of implants

Recent advances in tissue engineering have enabled remarkable progress in controlling the properties of implants. There are numerous structural and functional requirements that the engineered tissue should meet to be clinically applicable as an ECM substitute. One of the biggest challenges is the integration of the engineered construct with native tissues. The biomechanical properties of the implant (e.g., swelling pressure, compressive, tensile, and shear properties) should match as closely as possible the properties of the host tissue in which it is implanted. Matching the osmotic and mechanical properties at the site of implantation and perfect integration of the implant with the surrounding tissue insures that in the course of the healing process tissue regeneration is not compromised by mechanical failure. Therefore, knowing the osmotic properties of the implant is critically important for tailoring its biomechanical/biochemical properties to develop successful regenerative medicine strategies.

Engineering pre-stressed tissue implants

The aim of cartilage tissue engineering is the creation of a replacement tissue to restore normal joint function. Although, engineered cartilage exhibits histological and biochemical characteristics similar to those of the native tissue, the implants fail to possess suitable mechanical properties.^107,108 In previous studies the importance of tissue inflation has been largely overlooked. However, pre-stress governs the load bearing properties and is a critically important factor for designing and engineering cartilage repair implants. The load bearing ability depends not only on the amounts of collagen and PGs but also on their structural organization. The ability of collagen to resist tension ultimately provides the shear stiffness of the tissue. The role of PG assemblies is to inflate the collagen matrix but PGs alone do not improve tissue stiffness. The tensile stress developing in the collagen network ensures that the tissue operates in the inflated state (i.e., at increased matrix stiffness) and exhibits enhanced load bearing properties. High collagen content is a basic requirement for load bearing. There are biochemical methods to control the collagen to aggrecan ratio. For example, catabolic enzymes (e.g., chondroitinase, hyaluronidase) deplete PGs.^109,110 Suppression of GAG synthesis may be beneficial for engineering an inflated matrix, thus improving the mechanical properties of the implant. However, reducing the PG concentration also reduces the pre-stress, and ultimately the stiffness of the tissue. Our biomimetic model makes it possible to systematically investigate the effect of different factors and develop strategies to optimize the load bearing properties of cartilage implants.

Conclusions

Systematic osmotic swelling pressure measurements are reported for a composite gel system which mimics articular cartilage, consisting of a crosslinked PVA hydrogel containing PAA gel particles. The measurements were made in near-physiological salt solutions. The effects of the stiffness of the PVA gel, the crosslink density of the PAA and the Ca²⁺ ion concentration were studied.

In PVA/PAA composite gels the PAA component inflates the PVA matrix and enhances the load bearing ability of the system. The swollen PAA particles generate a tensile stress in the matrix, which increases as the gel adsorbs more liquid. The functional form of P_el can be described by the Fung-model derived for stiff polymers.

SANS measurements made on PVA/PAA composite gels indicate the absence of considerable interaction between the two polymeric components.

The osmotic behavior of gels inflated by swollen inclusions is qualitatively different from that of ordinary (noninflated) gels. In the latter gels the osmotic mixing pressure of the crosslinked polymer always exceeds the swelling pressure of the gel, and the elastic pressure gradually decreases as the network swells. By contrast, in inflated gels the swelling pressure vs. swelling degree curve of the enclosed particles (PAA) intercepts that of the composite gel. At the intersection Π_sw^composite = Π_sw^PAA and P_el = 0. P_el steeply increases with the swelling degree and it reaches a maximum P_el^max when the composite gel is fully swollen (Π_sw = 0). The position of the intersection and P_el^max is defined by (i) the stiffness of the PVA network, (ii) the crosslink density of the PAA particles, and (iii) the Ca²⁺ ion concentration of the equilibrium solution.

A comparison has been made between the osmotic response of PVA/PAA composite gels and healthy and osteoarthritic cartilage specimens. It is found that the composite gels satisfactorily reproduce not only the shape of the cartilage curves but also the numerical values reported for the swelling pressure of cartilage.