By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these polymers form soft nano-objects (so-called single-chain nanoparticles, SCNPs), resulting from the purely intramolecular cross-linking of the reactive functional groups. Here we show that the competition between intra- and intermolecular bonds at finite concentration is governed by a delicate balance of various entropic contributions and leads to a density dependent effective valence. System-spanning networks are formed at relatively low monomer densities and their stability is mediated by just a small number of intermolecular connections per chain. The formation of intermolecular bonds furthermore can induce a non-monotonic dependence of the polymer size on the density for long bond lifetimes. Concomitantly, the polymers in the percolating cluster adopt an intramolecular structure characteristic for self-avoiding chains, which constitutes a strong contrast to the fractal globular behavior of irreversible SCNPs in crowded solutions with purely topological interactions (no intermolecular bonds). Finally, we study the dynamics of the system, which displays signatures expected for reversible gel-forming systems. An interesting behavior emerges in the reorganization dynamics of the percolating cluster. The relaxation is mostly mediated by the diffusion over long distances, through breaking and formation of bonds, of chains that do not leave the percolating cluster. Regarding the few chains that are transiently free, the time they spend until they reattach to the cluster is solely governed by the bond strength.
Reversible diffusion limited cluster aggregation of hard spheres with rigid bonds was simulated and the self diffusion coefficient was determined for equilibrated systems. The effect of increasing attraction strength was determined for systems at different volume fractions and different interaction ranges. It was found that the slowing down of the diffusion coefficient due to crowding is decoupled from that due to cluster formation. The diffusion coefficient could be calculated from the cluster size distribution and became zero only at infinite attraction strength when permanent gels are forme…
Colloidal gels are a prototypical example of a heterogeneous network solid whose complex properties are governed by thermally-activated dynamics. In this Letter we experimentally establish the connection between the intermittent dynamics of individual particles and their local connectivity. We interpret our experiments with a model that describes single-particle dynamics based on highly cooperative thermal debonding. The model, in quantitative agreement with experiments, provides a microscopic picture for the structural origin of dynamical heterogeneity in colloidal gels and sheds new light on…
We investigate the dynamics of alginate gels, an important class of biopolymer-based viscoelastic materials, by combining mechanical tests and non-conventional, time-resolved light scattering methods. Two relaxation modes are observed upon applying a compressive or shear stress. Dynamic light scattering and diffusive wave spectroscopy measurements reveal that these modes are associated with discontinuous rearrangement events that restructure the gel network via anomalous, non-diffusive microscopic dynamics. We show that these dynamics are due to both thermal activation and internal stress stor…
We introduced silica nanoparticles into poly ($N$,$N$-dimethylacrylamide) gel, (PDAM-NC gel), and poly (acrylamide) gel (PAM-NC gel), and carried out SAXS measurements under uniaxial elongation. It is well known that PDAM chains are strongly adsorbed onto silica nanoparticles while PAM chains are not. Interestingly, we found from SAXS measurements that scattering profiles depend on the polymer-nanoparticle interaction. A four-spot pattern was observed in the 2D structure factors of PDAM-NC gel, which was assigned to a movement of the nanoparticles affinely under elongation. However, unexpected…
Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image (both types of deformation yield affinely stretched images in $θ$ solvents). We show that in ordinary solids with spatially inhomogeneous profile of the shear modulus, isotropic stretching leads to distorted density …
Reversible crosslinking is a design paradigm for polymeric materials, wherein they are microscopically reinforced with chemical species that form transient crosslinks between the polymer chains. Besides the potential for self-healing, recent experimental work suggests that freely diffusing reversible crosslinks in polymer networks, such as gels, can enhance the toughness of the material without substantial change in elasticity. This presents the opportunity for making highly elastic materials that can be strained to a large extent before rupturing. Here, we employ Gaussian chain theory, molecu…
The resistance to fracture of reversible biopolymer hydrogels is an important control factor of the cutting/slicing and eating characteristics of food gels. It is also critical for their utilization in tissue engineering, for which mechanical protection of encapsulated components is needed. Its dependence on loading rate and, recently, on the density and strength of cross-links has been investigated. But no attention was paid so far to solvent nor to environment effects. Here we report a systematic study of crack dynamics in gels of gelatin in water/glycerol mixtures. We show on this model sys…
We study the phase diagram of a binary mixture of patchy particles which has been designed to form a reversible gel. For this we perform Monte Carlo and molecular dynamics simulations to investigate the thermodynamics of such a system and compare our numerical results with predictions based on the analytical parameter-free Wertheim theory. We explore a wide range of the temperature-density-composition space that defines the three-dimensional phase diagram of the system. As a result, we delimit the region of thermodynamic stability of the fluid. We find that for a large region of the phase diag…
We model the behaviour of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local micro-cavity, containing the particle and any free volume created by its motion. This cavity exists only as long as the particle is actuated and, when present, reduces the local density of the material, leading to swelling. We show that the model exhibits rich resonance features, but is overall characterised by clear scaling laws at low and high driving frequ…
Restricting the number of attractive physical "bonds" that can form between particles in a fluid suppresses the usual demixing phase transition to very low particle concentrations, allowing for the formation of open, percolated, and homogeneous states, aptly called equilibrium or "empty" gels. Most demonstrations of this concept have directly limited the microscopic particle valence via anisotropic (patchy) attractions; however, an alternative macroscopic valence limitation would be desirable for greater experimental tunability and responsiveness. One possibility, explored in this paper, is to…
Using computer simulations, we study the dynamic arrest in a schematic model of colloid-polymer mixtures combining short-ranged attractions with long-ranged repulsions. The arrested gel is a dilute rigid network of colloidal particles bonded due to the strong attractions. Without repulsions, the gel forms at the spinodal through arrested phase separation. In the ergodic suspension at sufficiently high densities, colloidal clusters form temporary networks that percolate space. Recently [Nat. Commun. 7, 11817 (2016)], it has been proposed that the transition of these networks to directed percola…
We study analytically the intricate phase behavior of cross-linked $AB$ diblock copolymer melts, which can undergo two main phase transitions due to quenched random constraints: Gelation, i.e., spatially random localization of polymers forming a system-spanning cluster, is driven by increasing the number parameter $μ$ of irreversible, type-selective cross-links between random pairs of $A$ blocks. Self-assembly into a periodic pattern of $A$/$B$-rich microdomains (microphase separation) is controlled by the $AB$ incompatibility $χ$ inversely proportional to temperature. Our model aims to captur…
Recently developed linker-mediated vitrimers based on metathesis of dioxaborolanes with various commercially available polymers have shown both good processability and outstanding performance, such as mechanical, thermal, and chemical resistance, suggesting new ways of processing cross-linked polymers in industry, of which the design principle remains unknown [M. Rottger, et al., Science 356, 62 (2017)]. Here we formulate a theoretical framework to elucidate the phase behaviour of the linker-mediated vitrimers, in which entropy plays a governing role. We find that with increasing the linker co…
Hydrogels have had a profound impact in the fields of tissue engineering, drug delivery, and materials science as a whole. Due to the network architecture of these materials, imbibement with water often results in uniform swelling and isotropic expansion which scales with the degree of cross-linking. However, the development of internal stresses during swelling can have dramatic consequences, leading to surface instabilities as well as rupture or bursting events. To better understand hydrogel behavior, macroscopic mechanical characterization techniques (e.g.\ tensile testing, rheometry) are of…
We investigated the surface structure of hydrogels of poly(N,N-dimethylacrylamide) (PDMA) hydrogels synthesized and cross-linked simultaneously by redox free radical polymerization. We demonstrate the existence of a less cross-linked layer at the surface of the gel at least at two different length scales characterized by shear rheology and by neutron reflectivity, suggesting the existence of a gradient in cross-linking. The composition of the layer is shown to depend on the degree of hydrophobicity of the mold surface and is weaker for more hydrophobic molds. While the macroscopic tests proved…
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 ma…
The interaction of amphiphilic polymers with small colloids, capable to reversibly stick onto the chains, is studied. Adhesive small colloids in solution are able to dynamically bind two polymer segments. This association leads to topological changes in the polymer network configurations, such as looping and cross-linking, although the reversible adhesion permits the colloid to slide along the chain backbone. Previous analyses only consider static topologies in the chain network. We show that the sliding degree of freedom ensures the dominance of small loops, over other structures, giving rise…
Graphene-based nanostructured systems and van-der-Waals heterostructures comprise a material class of growing technological and scientific importance. Joining materials with vastly different properties, polymer-graphene heterosystems promise diverse applications in surface- and nanotechnology, including photovoltaics or nanotribology. Fundamentally, molecular adsorbates are prototypical systems to study confinement-induced phase transitions exhibiting intricate dynamics, which require a comprehensive understanding of the dynamical and static properties on molecular time and length scales. Here…
Vegetable oil based hybrid films were developed thanks to a novel solvent- and heating- free method at the air-water interface using silylated castor oil cross-linked via a sol-gel reaction. To understand the mechanism of the hybrid film formation, the reaction kinetics was studied in detail by using complementary techniques: rheology, thermogravimetric analysis, and infrared spectroscopy. The mechanical properties of the final films were investigated by nano-indentation, whereas their structure was studied using a combination of wide-angle X-ray scattering, electron diffraction, and atomic fo…
