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The chain walking (CW) polymerization technique has the unique property of a movable catalyst synthesizing its own path by creating branch-on-branch structures. By successive attachment of monomers, the resulting architecture ranges from dendritic to linear growth depending on the walking rate, which is defined by the ratio of walking steps and reaction events of the catalyst. The transition regime is characterized by local dendritic sub-structures (dendritic blobs) and a global linear chain feature forming a dendritic bottle-brush. A scaling model for structures obtained by CW catalysis is presented and validated by computer simulation relating the extensions of CW structures to the catalyst’s walking ability. The limiting case of linear (low walking rate) and dendritic growth (high walking rate) is recovered, and the latter is shown to bear analogies to the Barabási–Albert graph and Bernoulli growth random walk. We could quantify the size of the dendritic blob as a function of the walking rate by using spectral properties of the connectivity matrix of the simulated macromolecules. This allows us to fit the numerical constants in the scaling approach. We predict that independent of the underlying chemical process, all CW polymerization syntheses involving a highly mobile catalyst ultimately result in bottle-brush structures whose properties depend on a unique parameter: the walking rate. more...

We use the bond fluctuation model to study the contraction process of two polymer loops with $N$ segments that are connected each to the bottom and top parts of a Feringa engine. The change in the size of the molecules as well as the folding of the two strands follows approximately scaling predictions that are derived by assuming that the strands are confined inside an effective tube. Conformation data can be overlapped when plotting it as a function of ${W}_{\text{n}}{N}^{\ensuremath{-}1/4}$, where ${W}_{\text{n}}$ is the winding number of the two strands that is proportional to the number of blobs inside the ``knotted'' region of the molecule and $N$ is the degree of polymerization of the strands. Our data support a weak localization of the knots along the contour of flexible cyclic athermal polymers with a localization exponent $t\ensuremath{\approx}0.78$. more...

Thermoresponsive interpenetrating networks (IPNs) were prepared by sequential synthesis of a biohybrid network of star-shaped poly(ethylene glycol) [starPEG] and heparin and a poly(N-isopropylacryl... more...

Recently developed chain walking (CW) catalysis is an elegant approach to produce materials with controllable structure and properties. However, there is still a lack in understanding of how the reaction mechanism influences the macromolecular structures. In this study, a series of dendritic polyethylenes (PE) synthesized by Pd-α-diimine-complex through CW catalysis (CWPE) is investigated by means of theory and experiment. Thereby, the exceptional ability of in situ tailoring polymer structure by varying synthesis parameters was exploited to tune the branching architecture, which allowed us to establish a precise relationship between synthesis, structure, and solution properties. The systematically produced polymers were characterized by state-of-the-art multidetector separation and neutron scattering experiments as well as atomic force microscopy to access molecular properties of CWPE. On a global scale, the CWPE appear in a worm-like conformation independently on the synthesis conditions. However, severe differences in their contraction factors suggested that CWPE differ substantially in topology. These observations were verified by NMR studies that showed that CWPE possess a constant total number of branches but varying branching distribution. Small angle neutron scattering experiments gave access to structural characteristics from global to segmental scale and revealed the unique heterogeneity of CWPE, which is predominantly based on differences in their dendritic side chains. The experimental data were compared to theoretical CW structures modeled with different reaction-to-walking probabilities. Simple theoretical arguments predict a crossover from dendritic to linear topologies yielding a structural range from purely linear to dendritic chain growth. Yet, comparison of theoretical and empirical scattering curves gave the first evidence that a transition state to worm-like topologies is actually experimentally accessible. This crossover regime is characterized by linear global features and dendritic local substructures contrary to randomly hyperbranched systems. Instead, the obtained CWPE systems have characteristics of disordered dendritic bottle brushes and can be adjusted by the walking rate/reaction probability of the catalyst. more...

We study dendrimers embedded in a solution of linear chains with various degrees of polymerization and concentrations. We distinguish the term “crowding”, addressing the impact of the polymer envir... more...

Thermoresponsive interpenetrating networks (IPNs) were prepared by sequential synthesis of a biohybrid network of star-shaped poly(ethylene glycol) [starPEG] and heparin and a poly(

The conformational and thermodynamic properties of single dendritic–linear copolymers are investigated by analytical models and computer simulations. Applying poor solvent conditions on the dendritic part, these molecules are known to form single unimolecular micelle-like structures. A mean-field model applying the Daoud–Cotton approach and a surface tension argument is presented and suggests the splitting of the unimolecular single-core structure into a multicore structure with increasing dendrimers generation and decreasing solvent selectivity. Monte Carlo simulations utilizing the bond fluctuation model with explicit solvent are performed which show the formation of multicore structures for trifunctional codendrimers of different generations and spacer lengths with linear chains attached to the terminal groups. These findings are aimed to understand the physics of spontaneous self-assembly of codendrimers in various well-defined macro-conformations under change of environmental conditions with potentia... more...

Sulfation patterns of glycosaminoglycans (GAG) govern the electrostatic complexation of biomolecules and thus allow for modulating the release profiles of growth factors from GAG-based hydrogels. To explore options related to this, selectively desulfated heparin derivatives were prepared, thoroughly characterized, and covalently converted with star-shaped poly(ethylene glycol) into binary polymer networks. The impact of the GAG sulfation pattern on the network characteristics of the obtained hydrogels was theoretically evaluated by mean field methods and experimentally analyzed by rheometry and swelling measurements. Sulfation-dependent differences of reactivity and miscibility of the heparin derivatives were shown to determine network formation. A theory-based design concept for customizing growth factor affinity and physical characteristics was introduced and validated by quantifying the release of fibroblast growth factor 2 from a set of biohybrid gels. The resulting new class of cell-instructive polymer matrices with tunable GAG sulfation will be instrumental for multiple applications in biotechnology and medicine. more...

Cell-instructive characteristics of extracellular matrices (ECM) resulting from a subtle balance of biomolecular and biophysical signals must be recapitulated in engineered biomaterials to facilitate regenerative therapies. However, no material explored so far allows the independent tuning of the involved molecular and physical cues due to the inherent correlation between biopolymer concentration and material properties. Addressing the resulting challenge, a rational design strategy for ECM-inspired biohybrid hydrogels based on multi-armed poly(ethylene glycol) and heparin, adapting a mean field approach to identify conditions at which the balance of elastic, electrostatic, and excluded volume forces results in constant heparin concentrations within swollen polymer networks with gradually varied physical properties is introduced. Applying heparin-based biofunctionalization schemes, multiple distinct combinations of matrix parameters could be identified to effectively stimulate the pro-angiogenic state of human endothelial cells and the differentiation of human mesenchymal stem cells. The study demonstrates the power of joint theoretical and experimental efforts in creating bioactive materials with specifically and independently controllable characteristics. more...

The swelling properties of a new class of biohybrid gels made of heparin and 4-arm star-poly(ethylene glycol) (PEG) were studied using mean-field concepts. Heparin acts as a multifunctional cross-linker and is highly charged in aqueous environments allowing for the functionalization of the gels with a plethora of biologically active molecules. The elasticity of the gels is provided by the flexible arms of the PEG. Varying the mole fraction of the heparin at preparation changes both the elasticity and the charge of the gel. We combine the classical Flory−Rehner model with a free energy contribution due to trapped counterions and derive a general equation for the equilibrium swelling of the gel as a function of the heparin-content at preparation, size of PEG molecules and salt concentration of the solvent. Varying the heparin content in the state of preparation results in opposite tendencies of the swelling behavior in the limit of low and high salt concentrations. At intermediate salt concentrations we fin... more...

We study the segregation of two long chains from parallel but randomly twisted start conformations under good solvent conditions using Monte Carlo simulations to mimic chromatin segregation after replication in eukaryotic cells in the end of prophase. To measure the segregation process, we consider the center-of-mass separation between the two chains and the average square distance between the monomers which were connected before segregation starts. We argue that segregation is dominated by free diffusion of the chains, assuming that untwisting can be achieved by Rouse-like fluctuations on the length scale of a twisted loop. Using scaling analysis, we find that chain dynamics is in very good agreement with the free diffusion hypothesis, and segregation dynamics follows this scaling nearly. Long chains, however, show retardation effects that can be described by a new (to us) dynamical exponent, which is slightly larger than the dynamical exponent for Rouse-like diffusion. Our results indicate that nearly free diffusion of chains during a timescale of a few Rouse-times can lead to segregation of chains. A main obstacle during segregation by free diffusion is random twists between daughter strands. We have calculated the number of twists formed by the daughter strands in the start conformations, which turns out to be rather low and increases only with the square-root of the chain length. more...

We study the changes in the conformations of brushes upon the addition of crosslinks between the chains using the bond fluctuation model. The Flory-Rehner model applied to uni-axially swollen networks predicts a collapse for large degrees of crosslinking $q$ proportional to $q^{-1/3}$ in disagreement with our simulation data. We show that the height reduction of the brushes is driven by monomer fluctuations in direction perpendicular to the grafting plane and not due to network elasticity. We observe that the impact of crosslinking is different for reactions between monomers of the same or on different chains. If the length reduction of the effective chain length due to both types of reactions is accounted for in a function $\beta(q)$, the height of the brush can be derived from a Flory approach for the equilibrium brush height leading to $H(q)\approx H_{b}\beta(q)^{1/3}$, whereby $H_{b}$ denotes the height of the non-crosslinked brush. more...