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.
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.
A novel technique is developed to predict the evolving topology of a diacrylate polymer network under photocuring conditions, covering the low‐viscous initial state to full transition into polymer gel. The model is based on a new graph theoretical concept being introduced in the framework of population balance equations (PBEs) for monomer states (mPBEs). A trivariate degree distribution that describes the topology of the network locally is obtained from the mPBE, which serves as an input for a directional random graph model. Thus, access is granted to global properties of the acrylate network which include molecular size distribution, distributions of molecules with a specific number of crosslinks/radicals, gelation time/conversion, and gel/sol weight fraction. Furthermore, an analytic criterion for gelation is derived. This criterion connects weight fractions of converted monomers and the transition into the gel regime. Valid results in both sol and gel regimes are obtained by the new model, which is confirmed by a comparison with a “classical” macromolecular PBE model. The model predicts full transition of polymer into gel at very low vinyl conversion (<2%). Typically, this low‐conversion network is very sparse, as becomes apparent from the predicted crosslink distribution.
Front Cover: The image depicts samples of cross‐linked molecules as obtained from the random graph model for diacrylate polymer networks shortly after the onset of the topological phase transition. The vast variability in molecular sizes, topologies, and shapes that can be seen in the image is completely defined by a relatively small amount of information – the degree distribution of the underlying random graph. More information can be found in article number https://doi.org/10.1002/mats.201700047 by Verena Schamboeck,* Ivan Kryven, and Pieter D. Iedema.
The association between thermo-mechanical properties in polymers and functionality of monomer precursors is frequently exploited in the materials science. However, it is not known if there are more variables beyond monomer functionality that have a similar link. Here, by using simulations to generate spatial networks from chemically different monomers with identical functionality we show that such networks have universal graph-theoretical properties as well as a near-universal elastic modulus. The vitrification temperature was found to be universal only up to a certain network density, as measured by the bond conversion. The latter observation is explained by the fact that monomer’s tendency to coil enhances formation of topological holes, which, when accumulated, amount to a percolating cell complex restricting network’s mobility. This higher-order percolation occurs late after gelation and is shown to coincide with the onset of brittleness, as indicated by a sudden increase in the glass transition temperature.
This paper presents a novel prognostic method to estimate the remaining useful life (RUL) of generators using the SCADA (Supervisory Control And Data Acquisition) systems installed in wind turbines. A data-driven wind turbine anomaly classification method is developed. The anomalies are quantified into a health indicator to measure the component degradation over time. An Autoregressive Integrated Moving Average (ARIMA) time series forecasting technique is then applied to predict the RUL of the wind turbine generator. The proposed method has been validated using industry field data showing accurate predictions of RUL with a 21 day lead time for maintenance of the turbine.
Thermo-mechanical properties of polymer networks are known to depend on the functionality of monomer precursors -an association that is frequently exploited in materials science. We use molecular simulations to generate physical networks from chemically different monomers with identical functionality and show that such networks have several universal graphtheoretical properties as well as near universal Young's modulus, whereas the vitrification temperature is universal only up to a certain density of the network, as measured by the bond conversion. The latter observation is explained by noticing that monomer's tendency to coil is shown to enhance formation of topological holes, which, when accumulated in the network, result in a phase transition marked by the emergence of a percolating cell complex restricting network's mobility. This higher-order percolation occurs late after gelation and is shown to coincide with the onset of brittleness indicated by a sudden increase in the glass transition temperature.
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 crosslinked 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. Already in the early days of network science it has been realised that in dynamic networks the entire time trajectory of network formation may reflect on the topological features of the structure that is formed at the end. In other words, that the structure of a dynamic network may have memory of its past. Some examples of evolving network models include Price's (1965) preferential attachment model 1 , the vertex copying model 2 , network optimisation models 3 , and branching simlicial complexes 4,5. Preferential attachment, vertex copying models, and branching simplicial complexes all result in heavy-tailed degree distributions. In this work, we introduce an evolving network model with an arbitrary degree distribution to show that the different effects induced by the two most common polymerisation processes on the resulting materials are provoked by the presence or absence of memory in the underlaying network structures. Step-growth and chain-growth polymerisation are two major families of chemical reactions that result in polymer networks. For step-growth, such polymers include polyethylene (PE), polyvinyl chloride (PVC), polypropylene (PP) and polyacrylates 6 , which have a variety of applications: including paints and adhesives 7,8 , food packaging 9 , biomaterials and medical devices 10,11. Well-known examples of chain-growth polymers are gels that find applications as absorbents for medical, chemical and agricultural purposes 12 , and coatings made by photopolymerisation 13,14. The reason for the difference in the physical and mechanical properties of the step-and chain-growth derived polymers lies in the distinct network structures. Moreover, the structure of chain-growth networks can be manipulated by adjusting polymerisation conditions and species concentrators in order to optimise physical and mechanical properties. ...
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