Counting primary loops in polymer gels

Abstract

Much of our fundamental knowledge related to polymer networks is built on an assumption of ideal end-linked network structure. Real networks invariably possess topological imperfections that negatively affect mechanical properties; modifications of classical network theories have been developed to account for these defects. Despite decades of effort, there are no known experimental protocols for precise quantification of even the simplest topological network imperfections: primary loops. Here we present a simple conceptual framework that enables primary loop quantification in polymeric materials. We apply this framework to measure the fraction of primary loop junctions in trifunctional PEG-based hydrogels. We anticipate that the concepts described here will open new avenues of theoretical and experimental research related to polymer network structure.responsive materials | topology | network disassembly spectrometry | tetrazine T he properties of all known polymer networks, from commodity materials like nylon, rubber, and plastics, to biological tissues such as the extracellular matrix (ECM) and cartilage, are defined by the network's chemical composition and structural topology (1-3). Much of our fundamental knowledge related to polymer materials, e.g., theories of elasticity and gelation, was built more than half a century ago upon an assumption of ideal end-linked network structure (Fig. 1A) (2, 4-7). Real networks invariably possess imperfections such as first-order elastically inactive dangling chains and primary loops (Fig. 1B), and higher-order elastic loop structures and chain entanglements; modifications of classical network theories have been developed to account for these defects (8-11).First-order network imperfections (Fig. 1B) have the most direct negative impact on the mechanical properties of materials. Dangling chains can be minimized if efficient end-linking reactions are used between functional groups present at 1:1 ratio. In contrast, kinetic constraints demand that primary loops exist regardless of functional group conversion (12). Unlike dangling chains, which can be readily quantified via titration or spectroscopy, there are no known methods for quantification of primary loops. Their prevalence is estimated from pregel measurements or variations between the properties of a given material and theoretical model networks (2,4,(7)(8)(9)(12)(13)(14)(15)(16)(17). These molecular-level mechanical imperfections could critically impact modern applications of polymer networks and gels (18-28), especially those built on an end-linked network architecture (29-33).Here we present a simple conceptual framework called network disassembly spectrometry (NDS) that enables facile, simultaneous quantification of the fraction of primary loops and the numbers and structures of dangling chains in end-linked materials via site-selective network disassembly. We apply this framework to degradable PEG hydrogels, which are similar to materials frequently used in tissue engineering applications (29,32).

Universal Cyclic Topology in Polymer Networks

“…Experimental techniques such as rheology/spectroscopy and multiple-quantum NMR can provide semi-quantitative information related to the loop structure [31][32][33]. Recently, Zhou et al reported 'network disassembly spectrometry' (NDS), which is the first experimental method for directly quantifying primary loops [34,35]. Theory that can fully describe the dilution and chain-length effects on primary loop fraction observed in experiments is lacking.…”

Synthesis of bioactive protein hydrogels by genetically encoded SpyTag-SpyCatcher chemistry

“…The experimental storage modulus (∼0.3 kPa) is much lower than the predicted value, suggesting incomplete cross-linking or the formation of elastically ineffective loops. Loop formation would be expected to be enhanced by the fact that the network precursors AAA and BB were mixed at millimolar concentrations; for example, Zhou et al (21) showed that loop fractions approach 80% in networks formed from telechelic polyethylene glycol oligomers at concentrations of ∼5 mM. In addition, the excluded volume of the ELP domain may slow the binding of SpyCatcher to internal SpyTag sites (13), and favor chain extension at the expense of cross-linking.…”

Physics of engineered protein hydrogels

“…196 For PEG segments with a degree of polymerization of $15, 194 each PEG arm contributes a length of approximately 3 nm to the overall polymer chain. 197 Therefore, a change in chain length from $11 to $7.5 nm upon ligand binding is anticipated. This 32% decrease in chain length would result in a 69% reduction in gel volume for isotropic deswelling, consistent with the volume decrease observed for the largest swelling levels.…”