Calculation of gel points taking account of cyclization reactions

On the Network Topology of Cross-Linked Acrylate Photopolymers: A Molecular Dynamics Case Study

“…The gel point is of particular interest to both conventional and additive manufacturing since this value loosely defines the theoretical lower limit at which the “part” exists: the conversion at which the propagating polymer spans the volume of the system. , In atomistic or particle-based simulations two methods have been used to extract the gel point, both based on the sizes of the propagating or percolating polymer networks. ,, A simulated polymerization, as in the present work, that begins with N radical sites rapidly forms N small oligomers. These oligomers continue to react and eventually coalesce into larger units, and the size of the largest growing polymer network may be obtained at each simulation time step, noting that the size of this largest polymer undergoes a step change when two propagating networks merge.…”

Analysis of the Gel Point of Polymer Model Networks by Computer Simulations

“…provides the total number of intra-molecular reactions in the reaction bath 61 . It has been argued by several authors 6,11,[15][16][17][18][19][20][21][22] that the formation of finite loops (intra-molecular reactions) controls the displacement of the gel point with respect to p c,id , since each intra-molecular reaction diminishes the number of branching reactions by one. Thus, we estimate the shift of the gel point due to intra-molecular reactions, ∆p, with respect to the total number of possible reactions, 2M, through…”

“…Then, the cycle rank (total number of independent circuits in the graph) provides the total number of intramolecular reactions in the reaction bath . It has been argued by several authors ,,− that the formation of finite loops (intramolecular reactions) controls the displacement of the gel point with respect to p c,id , as each intramolecular reaction diminishes the number of branching reactions by one. Thus, we estimate the shift of the gel point due to intramolecular reactions, Δ p , with respect to the total number of possible reactions, 2 M , through then provides a self-consistent mean field estimate for the gel point, p c , that is corrected by intramolecular reactions.…”

“…Polymer networks and gels are materials that have reached a wide range of applications ranging from car tires to drug delivery, removal of pollutants, artificial muscles, or stretchable electronics. − One point of major interest for theory, processing, and application is the exact location of the gel point , because there, the reacting liquid turns into a solid. The properties next to the gel point are well understood for critical percolation and mean field models as a function of the distance to the gel point.…”

“…The prediction of the percolation threshold or the gel point itself remains a challenging problem for theorists. − Typically, the classical Flory–Stockmayer (FS) theory , or an equivalent mean field model , is taken for a first estimate based upon an ideal system whereby both intramolecular reactions prior to gelation and the positions of the reacting molecules in space are neglected. Previous generalizations of the FS theory ,− focus essentially on corrections due to intramolecular reactions (“loops”) because the self-contacts of random walks or branched polymers in semi-dilute solutions are well understood. The impact of the spatial arrangement of the reacting molecules on the position of the gel point was essentially ignored in the literature due to the lack of an analytical approach that allows for a quantitative treatment of this point.…”