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

Abstract

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.

Photochemical Study of a Three‐Component Photocyclic Initiating System for Free Radical Photopolymerization: Implementing a Model for Digital Light Processing 3D Printing

“…It can seem rather low for a diacrylate monomer, but this result is close to recent findings where a gel point at 12±1 % conversion was found for a photocured mixture of 50 wt% monoacrylate and 50 wt% diacrylate . Similarly, a recent model predicts the gelation at a conversion as low as 2 % for a photopolymerizable diacrylate monomer . Furthermore, multifunctional acrylates are prone to Trommsdorff effect which can occur after gelification around 5–10 % …”

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

“…Using the random graph method 42,43 (RG), in which the system properties are determined from the mean behaviour of all possible topologies that can be recovered from a given degree distribution, we also obtained the evolution of the largest component size [42][43][44] . The agreement with the directly monitored largest component from MD is excellent at high conversion but again the gel point is slightly underestimated ( Figure 6).…”

Coloured random graphs explain the structure and dynamics of cross-linked 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.…”

“…One striking feature of history-dependent processes is that the moment in time when an extensive cluster emerges, that is the gel point 13 , differs from the percolation threshold found when randomly removing bonds in the final network. This provides a strong contrast to network formation by step-growth polymerisation, where the polymerisation process is equivalent to random percolation on the final network topology 21,23,24 .…”

“…This provides a strong contrast to network formation by step-growth polymerisation, where the polymerisation process is equivalent to random percolation on the final network topology 21,23,24 . In some cases, however, the uncoloured random graph gives a surprisingly good estimate of the phase transition and the gel fraction 13 , which suggests that under certain conditions chain growth polymerisation may not induce a significant history dependency. Beyond polymers, strong history dependence is characteristic to processes on networks that can be reformulated as an annealed dynamics 33 .…”