Acrylate Network Formation by Free-Radical Polymerization Modeled Using Random Graphs

Dose-response of Fricke- and PAGAT-dosimetry gels in kilovoltage and megavoltage photon beams: Impact of LET on sensitivity

PURPOSE

Dosimetry of ionizing radiation quantifies the energy deposited by an incident beam to the medium. This study presents the relative response of two types of gel dosimeters describing their differences by estimating radiation chemical yields produced in water radiolysis.

METHODS

Two types of gel dosimeter were used, namely an acid ferrous ion solution infused with xylenol orange known as Fricke gel and a polymer gel based on acrylamide and N,N'-methylenebis(acrylamide) known as PAGAT. Samples were irradiated using two photon beam energies, one from a conventional X-ray tube operated at 44 kV and the other one from a LINAC operated at 6 MV. The dosimeters were analyzed by optical absorbance and magnetic resonance imaging. Additionally, the linear energy transfer of each beam was calculated using Monte Carlo simulations for further estimation of the radiation chemical yields produced during water radiolysis.

RESULTS

Obtained results for both gel dosimeters indicate that their response at 44 kV and 6 MV are different, regardless of the read-out technique. On average, the sensitivity at 44 kV was found to be 65 % of the response at 6 MV. The calculated radiation chemical yields are in agreement with the observed experimental results.

CONCLUSIONS

The main reason for the difference in the response of the dosimeters may be related to the linear energy transfer of each photon beam, which varies the production of primary chemical species during water radiolysis.

Coloured random graphs explain the structure and dynamics of cross-linked polymer networks

Step-growth and chain-growth are two major families of chemical reactions that result in polymer networks with drastically different physical properties, often referred to as hyper-branched and cross-linked networks. In contrast to step-growth polymerisation, chain-growth forms networks that are history-dependent. Such networks are defined not just by the degree distribution, but also by their entire formation history, which entails a modelling and conceptual challenges. We show that the structure of chain-growth polymer networks corresponds to an edge-coloured random graph with a defined multivariate degree distribution, where the colour labels represent the formation times of chemical bonds. The theory quantifies and explains the gelation in free-radical polymerisation of cross-linked polymers and predicts conditions when history dependance has the most significant effect on the global properties of a polymer network. As such, the edge colouring is identified as the key driver behind the difference in the physical properties of step-growth and chain-growth networks. We expect that this findings will stimulate usage of network science tools for discovery and design of cross-linked polymers.

Spatiotemporally Controlled Photoresponsive Hydrogels: Design and Predictive Modeling from Processing through Application

Photoresponsive hydrogels (PRHs) are soft materials whose mechanical and chemical properties can be tuned spatially and temporally with relative ease. Both photo-crosslinkable and photodegradable hydrogels find utility in a range of biomedical applications that require tissue-like properties or programmable responses. Progress in engineering with PRHs is facilitated by the development of theoretical tools that enable optimization of their photochemistry, polymer matrices, nanofillers, and architecture. This review brings together models and design principles that enable key applications of PRHs in tissue engineering, drug delivery, and soft robotics, and highlights ongoing challenges in both modeling and application.

Effect of volume growth on the percolation threshold in random directed acyclic graphs with a given degree distribution

In every network, a distance between a pair of nodes can be defined as the length of the shortest path connecting these nodes, and therefore one may speak of a ball, its volume, and how it grows as a function of the radius. Spatial networks tend to feature peculiar volume scaling functions, as well as other topological features, including clustering, degree-degree correlation, clique complexes, and heterogeneity. Here we investigate a nongeometric random graph with a given degree distribution and an additional constraint on the volume scaling function. We show that such structures fall into the category of m-colored random graphs and study the percolation transition by using this theory. We prove that for a given degree distribution the percolation threshold for weakly connected components is not affected by the volume growth function. Additionally, we show that the size of the giant component and the cyclomatic number are not affected by volume scaling. These findings may explain the surprisingly good performance of network models that neglect volume scaling. Even though this paper focuses on the implications of the volume growth, the model is generic and might lead to insights in the field of random directed acyclic graphs and their applications.

Connecting polymer synthesis and chemical recycling on a chain-by-chain basis: a unified matrix-based kinetic Monte Carlo strategy

Polymer synthesis and subsequent depolymerisation/degradation are linked at the molecular level.

Dynamic Networks that Drive the Process of Irreversible Step-Growth Polymerization

Many research fields, reaching from social networks and epidemiology to biology and physics, have experienced great advance from recent developments in random graphs and network theory. In this paper we propose a generic model of step-growth polymerisation as a promising application of the percolation on a directed random graph. This polymerisation process is used to manufacture a broad range of polymeric materials, including: polyesters, polyurethanes, polyamides, and many others. We link features of step-growth polymerisation to the properties of the directed configuration model. In this way, we obtain new analytical expressions describing the polymeric microstructure and compare them to data from experiments and computer simulations. The molecular weight distribution is related to the sizes of connected components, gelation to the emergence of the giant component, and the molecular gyration radii to the Wiener index of these components. A model on this level of generality is instrumental in accelerating the design of new materials and optimizing their properties, as well as it provides a vital link between network science and experimentally observable physics of polymers.

Modeling the free-radical polymerization of hexanediol diacrylate (HDDA): a molecular dynamics and graph theory approach

In the printing, coating and ink industries, photocurable systems are becoming increasingly popular and multi-functional acrylates are one of the most commonly used monomers due to their high reactivity (fast curing). In this paper, we use molecular dynamics and graph theory tools to investigate the thermo-mechanical properties and topology of hexanediol diacrylate (HDDA) polymer networks. The gel point was determined as the point where a giant component was formed. For the conditions of our simulations, we found the gel point to be around 0.18 bond conversion. A detailed analysis of the network topology showed, unexpectedly, that the flexibility of the HDDA molecules plays an important role in increasing the conversion of double bonds, while delaying the gel point. This is due to a back-biting type of reaction mechanism that promotes the formation of small cycles. The glass transition temperature for several degrees of curing was obtained from the change in the thermal expansion coefficient. For a bond conversion close to experimental values we obtained a glass transition temperature around 400 K. For the same bond conversion we estimate a Young's modulus of 3 GPa. Both of these values are in good agreement with experiments.