Stochastic model of randomly end-linked polymer network micro-regions

Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue engineering. While considerable research has been devoted to the modeling of polymer networks to determine averaged, mean-field, global properties, there are fewer studies that specifically examine the variance of the composition across "micro-regions" (composed of a large, but finite, number of polymer network strands) within the larger polymer network.Here, we mathematically model the stochastic formation of polymer networks comprised of linear homobifunctional network strands that undergo an end-linking gelation process. We introduce a master equation that describes the evolution of the probabilities of possible network micro-region configurations as a function of time and extent of reaction. We specifically focus on the dynamics of network formation and the statistical variability of the gel micro-regions, particularly at intermediate extents of reaction. We also consider possible annealing effects and study how cooperative binding between the two end-groups on a single network-strand affects network formation. Our results allow for a more detailed and thorough understanding of polymer network dynamics and variability of network properties.Comment: 16 pages, 9 figure

Solution Behavior of Topological Isomers of Poly [11-(4\u27-cyanophenyl-4\u27\u27-phenoxy) undecyl acrylate] s Prepared by Atom Transfer and Conventional Radical Polymerizations

The solution behavior of linear, three-arm star, and comb poly[11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate]s previously synthesized by atom transfer radical polymerization was investigated by gel permeation chromatography (GPCPSt) and light scattering measurements in CH2Cl2, THF, and CHCl3 in order to correlate their size and shape with their molecular architecture and in order to investigate the extent of branching in the corresponding polymer prepared by conventional radical polymerization. The inaccuracy of the GPCPSt molecular weights increases as the polymers become more branched:  linear \u3c three-arm star \u3c comb; the discrepancy between the GPCPSt and absolute molecular weights of polymers fractionated from the conventional radical polymerization is between those of the three-arm star and comb polymers in all three solvents. Light scattering studies demonstrate that CH2Cl2 is the best solvent for all of the polymers, resulting in either no aggregation or an insignificant amount of aggregation, whereas all of the topologies except the comb polymers tend to aggregate in THF and CHCl3; nevertheless, the extent of aggregation is not great enough to be detected by variations in the average GPCLS-determined molecular weights measured in any of these solvents. The tendency to aggregate in all of the solvents and the radius of gyration in CH2Cl2 decrease as the branching increases:  linear \u3e three-arm star \u3e comb, with the polymer prepared by conventional radical polymerization being similar to the branched polymers. The scaling coefficients (Rg = KMν) of all of the polymers are similar in CH2Cl2, with ν = 0.37 for the three-arm star polymers, ν = 0.39 for the comb polymers, and ν = 0.32 for the polymer prepared by conventional radical polymerization. The relative values of the contraction factors, g = Rg2br/Rg2lin, decrease in the order gstar \u3e gcomb \u3e gradical for the three-arm star polymers, the comb polymers, and the polymer prepared by conventional radical polymerization, respectively, in CH2Cl2

Comparison of the Thermotropic and Solution Behavior of Six-Arm Star and Comb Poly [11-(4\u27-cyanophenyl-4\u27\u27-phenoxy) undecyl acrylate] s

“Six-arm star” poly[11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate]s with 13−112 (gel permeation chromatography, GPC, relative to linear polystyrene) or 23−756 (GPC using a light scattering detector) repeat units were synthesized from the hexafunctional initiator, 1,2,3,4,5,6-hexa((4‘-methyl(2‘ ‘-bromopropionate)phenoxymethyl)benzene, by atom transfer radical polymerization of 11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate, followed by fractionation to narrow the polydispersity to 1.06−1.57. The absolute molecular weight, size, and shape of these polymers were characterized by light scattering in CH2Cl2, and their thermotropic behavior was analyzed by differential scanning calorimetry; both types of properties were compared to those of the other architectures, especially the corresponding comb poly[11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate]s with six branches. The solution and thermotropic behavior of the six-arm star and comb polymers are similar

Measurement of Chain Transfer Constants to Polymer Using Oligomers and Model Compounds: Chain Transfer to Poly [11-(4\u27-cyanophenyl-4\u27\u27-phenoxy) undecyl acrylate] in Radical Polymerization

The chain transfer constant to polymer (CP) for poly[11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate] was measured directly by the Mayo method by following the decrease in molecular weight at low monomer conversion by gel permeation chromatography of poly(methyl acrylate) generated in the presence of increasing amounts of 11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl propionate (CP = (6.62 ± 0.476) × 10-3) and 11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl isobutyrate (CP = (4.27 ± 0.858) × 10-3) as model compounds that mimic one repeat unit of the polymer and oligo[11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate] with nine repeat units (CP = (5.54 ± 0.608) × 10-3) synthesized by atom transfer radical polymerization. The mean chain transfer constant, CP = 5.48 × 10-3, was used to calculate the extent of branching (ρ) in poly[11-(4‘-cyanophenyl-4‘ ‘-phenoxy)undecyl acrylate] (DPn = 37) synthesized by conventional radical polymerization:  ρ = 0.0042−0.020 at 72−99% conversion, which corresponds to one branch per 6.4−1.4 chains, respectively, of 37 repeat units

Multivalent 3D Display of Glycopolymer Chains for Enhanced Lectin Interaction

Synthetic glycoprotein conjugates were synthesized through the polymerization of glycomonomers (mannose and/or galactose acrylate) directly from a protein macroinitiator. This design combines the multivalency of polymer structures with 3D display of saccharides randomly arranged around a central protein structure. The conjugates were tested for their interaction with mannose binding lectin (MBL), a key protein of immune complement. Increasing mannose number (controlled through polymer chain length) and density (controlled through comonomer feed ratio of mannose versus galactose) result in greater interaction with MBL. Most significantly, mannose glycopolymers displayed in a multivalent and 3D configuration from the protein exhibit dramatically enhanced interaction with MBL compared to linear glycopolymer chains with similar total valency but lacking 3D display. These findings demonstrate the importance of the 3D presentation of ligand structures for designing biomimetic materials

Effect of Branching Density on Avidity of Hyperbranched Glycomimetics for Mannose Binding Lectin

Hyperbranched glycopolymers containing mannose units in the branch point were synthesized through the copolymerization of a mannose inimer and mannose acrylate via atom transfer radical polymerization (ATRP). Incorporating a saccharide residue at the branch point results in a closer analogue to natural branched polysaccharides. Gel permeation chromatography characterization of the polymers qualitatively indicates branching in samples from polymerizations utilizing the mannose inimer. Deprotection of the acetate protecting groups from the hyperbranched mannose polymers yields water-soluble polymers that interact with mannose binding lectin (MBL), a key protein of the innate immunity complement system. MBL interaction increases with increasing polymer molecular weight and increasing branching density. Notably, incorporating mannose into the branching repeat unit also increases the interaction of the glycopolymers with MBL compared with glycopolymers with the same branching density but with no mannose at the branch point

Biodegradable Aromatic–Aliphatic Poly(ester–amides) from Monolignol-Based Ester Dimers

Biobased polymers with tunable properties have received increased attention in the literature due to a decline in petroleum reserves. Owing to its low cost, abundance, and aromatic structure, lignin has great potential as a feedstock for value-added polymeric products. In this work, we condensed carboxylic acid precursors with monolignols to generate reactive dimers for polymer synthesis. Three different aromatic ester dimers, each corresponding to a different monolignol, were synthesized and characterized. The dicarboxylic acid dimers were converted to the corresponding diacid chloride in situ with thionyl chloride, and a series of poly­(ester–amides) were synthesized via interfacial polymerization of these diacid chlorides with seven different aliphatic or aromatic diamines. The thermal properties (decomposition, glass transition temperature, and melting temperature) and hydrolytic stability in acidic and neutral aqueous conditions of the resulting polymers were studied

Photodegradable Macromers and Hydrogels for Live Cell Encapsulation and Release

Hydrogel scaffolds are commonly used as 3D carriers for cells because their properties can be tailored to match natural extracellular matrix. Hydrogels may be used in tissue engineering and regenerative medicine to deliver therapeutic cells to injured or diseased tissue through controlled degradation. Hydrolysis and enzymolysis are the two most common mechanisms employed for hydrogel degradation, but neither allows sequential or staged release of cells. In contrast, photodegradation allows external real-time spatial and temporal control over hydrogel degradation, and allows for staged and sequential release of cells. We synthesized and characterized a series of macromers incorporating photodegradbale <i>ortho</i>-nitrobenzyl (<i>o</i>-NB) groups in the macromer backbone. We formed hydrogels from these macromers via redox polymerization and quantified the apparent rate constants of degradation (<i>k</i>_app) of each via photorheology at 370 nm, 10 mW/cm². Decreasing the number of aryl ethers on the <i>o</i>-NB group increases <i>k</i>_app, and changing the functionality from primary to seconday at the benzylic site dramatically increases <i>k</i>_app. Human mesenchymal stem cells (hMSCs) survive encapsulation in the hydrogels (90% viability postencapsulation). By exploiting the differences in reactivity of two different <i>o</i>-NB linkers, we quantitatively demonstrate the biased release of one stem cell population (green-fluoroescent protein expressing hMSCs) over another (red-fluorescent protein expressing hMSCs)

Poly(methyl 6‑acryloyl-β‑d‑glucosaminoside) as a Cationic Glycomimetic of Chitosan

Chitosan, a cationic polysaccharide derived from one of the most abundant natural polymers, chitin, has been investigated extensively for its antimicrobial properties. However, it suffers from the inherent drawbacks of natural products such as batch-to-batch variability, limited supply, contamination, and potential adverse reaction. Additionally, its solubility depends on the degree of deacetylation and pH, as it is only soluble under acidic conditions. As an alternative to chitosan, we synthesized the protected cationic glycomimetic monomer methyl <i>N</i>-Fmoc-6-acryloyl-β-d-glucosaminoside from glucosamine. This monomer retains structural features critical to recapitulating the properties of the chitosan repeat unit, namely, the p<i>K</i>_a of the protonated amine. We optimized the free radical polymerization of methyl <i>N</i>-Fmoc-6-acryloyl-β-d-glucosaminoside and fractionated the resultant poly­(methyl <i>N</i>-Fmoc-6-acryloyl-β-d-glucosaminoside) to obtain a range of molecular weights. Following Fmoc deprotection, the cationic glycopolymers retained 95% of their expected amine content by mass and exhibited a p<i>K</i>_a of 6.61. Poly­(methyl 6-acryloyl-β-d-glucosaminoside) mimicked the molecular weight-dependent bacterial inhibitory property of chitosan in acidic solutions. Importantly, poly­(methyl 6-acryloyl-β-d-glucosaminoside) remained soluble at elevated pH (conditions under which chitosan is insoluble) and maintained its antibacterial activity. Mammalian cell viability in the presence of poly­(methyl 6-acryloyl-β-d-glucosaminoside) at acidic pH is good, although somewhat lower than viability in the presence of chitosan. No cytotoxic effect was observed at neutral pH. These results demonstrate that poly­(methyl 6-acryloyl-β-d-glucosaminoside) is not only a suitable biomimetic for chitosan, but that it can be utilized as an antibacterial agent in a broader range of biologically relevant pHs