Macroscopic and Microscopic Elasticity of Heterogeneous Polymer Gels

Abstract

Polymer-network gels often exhibit local defects and spatial heterogeneity of their cross-linking density, which may differently affect their elasticity on microscopic and macroscopic scales. To appraise this effect, we prepare polymeric gels with defined extents of nanostructural heterogeneity and use atomic force microscopy to probe their local microscopic Young's moduli in comparison to their macroscopic elastic moduli measured by shear rheology. In this comparison, the moduli of the heterogeneous gels are found to be progressively smaller if the length scale of the probed gel region exceeds the size of the purposely imparted polymer-network heterogeneities. This finding can be explained with a conceptual picture of nonaffine deformation of the densely cross-linked polymer network domains in the heterogeneous gels. P olymer gels consist of three-dimensional assemblies of cross-linked polymer chains swollen in a solvent. 1,2 If they are formed by uncontrolled polymerization, these gels exhibit an inhomogeneous spacing of their network cross-linking junctions in the form of densely cross-linked local domains randomly distributed within a loosely cross-linked background. 3−6 As a result, such heterogeneous polymer gels display pronounced concentration fluctuations on length scales of several ten nanometers 7 that have been investigated by light, X-ray, neutron scattering, 8−11 NMR spectroscopy, 12,13 and microscopy techniques. 14,15 It has been shown that the elastic modulus of a gel, as probed by rheology, decreases with increasing degree of inhomogeneity in the gel, as probed by light scattering, 6,16,17 such that the elastic moduli of heterogeneous gels synthesized by free radical copolymerization of mono-and bifunctional monomers 6,16,18 are lower than the moduli of more homogeneous gels prepared by either controlled polymerization or by postpolymerization crosslinking of linear precursor chains. 19−21 Nevertheless, the elastic moduli of both of these types of gels are generally lower than what would be expected from their content of cross-linker on the basis of the statistical theory of rubber elasticity. 22,23 These observations have been explained by two different arguments. One argument is the formation of elastically ineffective network defects such as loops and dangling chains during the gelnetwork polymerization. 24 The other argument is the possible presence of very short network strands with a length close to the persistence length of the polymer, which are too rigid to deform and store elastic energy. In densely cross-linked domains that contain multiple of such short chains, several cross-links therefore just act as one single cross-linking supernode of high functionality but limited ability for elasticenergy storage. 25,26 In an extension of this conceptual picture, it was suggested that heterogeneous gels deform in a nonaffine fashion. 27−29 One hypothesis is that stiff, densely cross-linked gel domains deform less than the surrounding soft, loosely cross-linked background and, therefore, just pa...

Self-assembly of collagen bundles and enhanced piezoelectricity induced by chemical crosslinking

“…18 The heterogeneity of the collagen fibre network may also result in the observed differences in values: in heterogeneously crosslinked pNIPAm hydrogels the average macroscopic Young's modulus was roughly 3 times the measured value by AFM. 35 Furthermore, substrate stiffness has been reported to have a significant effect on the force curves obtained from AFM measurements when the deformation achieved is greater than 10% of the sample thickness. 36 The non-negligible effect of the substrate stiffness may hold not only for an AFM tip, but for cells that effectively act as probes for the surface properties.…”

Mechanically Defined Microgels by Droplet Microfluidics

“…[132][133][134][135] Di Lorenzo et al specifically addressed the effect of probing the mechanical properties of nanoscopic inhomogeneous poly(Nisopropylacrylamide) (PNIPAAm) hydrogel films on different length scales. [42] For their study, hydrogels from linear PNIPAAm precursors with defined amounts of functional crosslinking groups were prepared. To achieve nm-sized heterogeneities in stiffness within the hydrogel network, they mixed chains with only a few crosslinking sites with a small amount of higher functionalized chains.…”

“…Revisiting the concept of gel networks with defined physicochemical properties, we provide insights in the fabrication of microgels with adjustable mechanical properties. In this context, the influence of spatial inhomogeneities in hydrogels crosslinking density, whose occurrence is depending on the synthetic approach, cannot be neglected . Accordingly, it is crucial to discuss mechanical properties on an appropriate length scale.…”

Proton conductivity in crosslinked hydrophilic ionic polymer system: Competitive hydration, crosslink heterogeneity, and ineffective domains

“…In particular, the stacking of crosslinks in these systems gives rise to what is termed as static inhomogeneity or crosslink heterogeneity, which is of length scale 10–100 Å . In recent times, the characterization of this crosslink heterogeneity and its role in determining mechanical properties is being investigated . The recognition of presence of crosslink heterogeneity and its contribution in explaining the observed proton conductivity behavior in crosslinked hydrophilic ionic polymer system is unexplored.…”

“…15 In recent times, the characterization of this crosslink heterogeneity and its role in determining mechanical properties is being investigated. 16 The recognition of presence of crosslink heterogeneity and its contribution in explaining the observed proton conductivity behavior in crosslinked hydrophilic ionic polymer system is unexplored. Despite the promising properties of hydrophilic polymers as PEM, the proton transport is not well understood in them.…”