Critical exponents for off-lattice gelation of polymer chains

Abstract

The random polycondensation of telechelic linear chains cured with triand tetrafunctional cross-linkers has been simulated. Calculations are done for both bulk and solution reactions; critical points are located by different methods, with results in good agreement with experiment. Critical exponents ß and 7 vary from system to system, with average values ß = 0.300 ± 0.024 and 7 = 1.77 ± 0.16. The average value C_/C+ = 13.58 ± 3.50 is slightly larger than that from standard percolation.

Microstructure–property–quality‐correlated paint design: An LMC‐based approach

“…The gel point formation in the system can be revealed through plotting the relationship between the conversion and the reduced weight average molecular weight of the system (i.e., the weight average molecular weight of the system excluding the largest molecule) 31. In this study, the gel point appears when the conversion reaches 30% (see Figure 8a).…”

Computer simulations of radiation-cured networks

“…In these early studies, the polymers used were copolymers of acrylic acid containing minor quantities (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) mol % ) of naphthylmethyl methacrylate (NMMA) which were end-trapped with anthracene to demonstrate the efficiency of energy transfer. In these early studies, the polymers used were copolymers of acrylic acid containing minor quantities (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) mol % ) of naphthylmethyl methacrylate (NMMA) which were end-trapped with anthracene to demonstrate the efficiency of energy transfer.…”

Molecular Dynamics Simulation of the Formation of Polymer Networks

“…Similar results have also been reported in Shy's work. [12] Meanwhile, Figure 3a and b also indicates that the precursor chain length and initial system number density have no influence on the reaction extent dependence of intramolecular reaction fraction after the network formed. In order to study the kinetics of the end-linking process, we plotted Figure 4 to show the fraction of unreacted chain ends n calculated by n ¼ [ [34][35][36][37] to investigate the time evolution of the irreversible diffusive recombination process in which two kinds of free particle combine and annihilate or form an inert species.…”

“…Since simulations can exert better control over the crosslinking process than experiments, we can easily quantify the effects of various macroscopic parameters, such as the strand length, extent of reaction and crosslinking density on the microscopic structure, and obtain information about the dynamics by choosing proper molecular models. Early contributions to the work on the simulation of network formation was made by Eichinger et al [10][11][12][13] They employed a static crosslinking method to obtain the structural properties of trifunctional and tetrafunctional end-linked networks and evaluated the defects of the networks. However, the crosslinking reactions were not been conducted by a molecular dynamics simulation method, but instead by resorting to changing a capture radius for static molecules to crosslink.…”

“…To estimate the gel point via the computer simulations, general methods have been investigated by Shy et al [12] who made use of the weight-average degree of polymerization (DP w ) and the maximum reduced average cluster size (RDP w ) [31] to locate the upper and lower bound of the gel point. Whenever there are two or more large particles formed in the system, RDP w reaches a maximum value during the cross-linking process, which gives a lower bound to the true gel point.…”