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PDF Particulate Morphology: Mathematics Applied to Particle Assemblies (Elsevier Insights)
At the same time, there are many complex effects in microgels that are respectively more sensitive to the precise inner structure of the network. That said, new frontiers in microgels exploration require the knowledge of detailed and realistic structures of the microgel networks.
For example, the study of microphase separation inside microgels or of the self-organized core-shell structures in swollen microgels is impossible without the consideration of spatial correlations of subchains length distribution, entanglements and dandling ends. Also, the in silico synthesis of more sophisticated structures, such as compolymer and block-copolymer microgels, interpenetrating network microgels is required for more reliable results.
In answer to that demand, in this paper we formulated the method of coarse-grained simulations of the realistic precipitation polymerization formation of PNIPA-like microgel particles. We prepared the realistic structures of PNIPA-like microgels by simulating the free-radical precipitation polymerization process. For this purpose, we prepared the solution of initial components: monomer M , cross-linker L and initiator I.
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The mass ratio of components M:L:I was Simulation box was randomly filled with particles up to total mass density equal to 2. The implicit solvent model in NVT ensemble was used i.
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Then each CG particle was assigned with valence, defining the maximum number of bonds it can form: two for monomer particles M, four for cross-linker particles L, and one for initiator particles I. Additionally, active center marks were assigned to initiator particles. The active center mark is passed from the initiator to the monomer particle.
The active center mark is passed to the second monomer particle.
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The active center mark is passed from the monomer to the cross-linker particle. The active center mark is passed from the cross-linker to the monomer particle. According to work 32 the cross-linker—cross-linker reaction rate BIS—BIS is lower by two orders of magnitude than the normal propagation steps, both monomer—monomer and monomer—cross-linker, thus this reaction was neglected in our model.
These reactions were implemented probabilistically. A new bond was formed with the probability p react. We started from value of p react small enough to keep quasi-equilibrium conditions in a vicinity of reaction centers, and increased it as the concentration of free monomers decreased. The following protocol was used:. Modified LAMMPS module, run script sample and resulting synthesized particle microgel structure with sol fraction cut out are available for download We studied in detail the kinetics of microgel formation using the model described above.
During the polymerization process, we observed the changes of the following parameters. Conversion c was calculated as a ratio between the number of created bonds and maximum possible number of bonds in the system. The mass of the largest macromolecule, the number and total mass of other macromolecules were calculated by topological analysis.
The data were averaged by 10 independent runs, error bars show the standard deviation.
The largest macromolecule mass fraction, sol mass fraction and total number of macromolecules depending on the conversion. Inserts show snapshots of a system at various stages of polymerization. Monomer and cross-linker particles are shown in cyan single particles and red in polymer chains ; initiator particles are shown in blue. At the initial setup, the components monomer, initiator, cross-linker are completely soluble at any concentrations, but growing chains collapse at some degree of polymerization, which is the main feature of precipitation polymerization.
Phase i lasts up to conversion of 0. In this phase, chains are too short to collapse, thus they grow independently, which is confirmed by almost constant number of polymer chains in the system. Then, eventually, some of these molecules cross-link with other ones and start the collapse process. The number of macromolecules begins to decay from this moment, as seen on Fig. Phase i takes approximately 2. Phases ii and iii are characterized by gradual growth of all macromolecules and simultaneous slow merging of individual chains.
The primary difference between these phases is shown on inset snapshots of Fig.
Towards the realistic computer model of precipitation polymerization microgels | Scientific Reports
During phase iv , the largest macromolecule rapidly grows by adsorbing and cross-linking with other long chains: the largest macromolecule size black curve on Fig. We found several important features of the polymerization process which are almost impossible to capture experimentally due to very fast passing of the first three phases.
First, the collapse of the chain on the nucleus during phases i and ii does not lead to its immediate merging with the nucleus by cross-linking. Second, there is no significant increase of either reagents concentration or reaction speed after the nucleus formation. Microgel particle grows gradually during the diffusion of the initial components from the solution.
Templated Formation of Luminescent Virus-like Particles by Tailor-Made Pt(II) Amphiphiles
The reasons are purely entropic: it is too unfavorable for the single particles to be absorbed, even in the solvent of poor quality. These results directly demonstrate that the microgels particle synthesis should not be considered finished when the solution turns opaque — that indicates the formation of nuclei on phase ii. Thus the synthesis should be continued for several more hours to obtain stable microgel particles.
To verify a computer model, one needs to compare the obtained in silico microgels with experimental systems. One of the most impressive features of polymer chains is their ability to change the conformational state from coil to globule depending on the solvent quality, which brings the variety of stimuli-responsive applications. Both collapse curves show the similar dependence of microgel size on solvent quality with the sharp transition from swollen to shrunken state. The swelling ratios are of the same magnitude for both systems 2.
- Towards the realistic computer model of precipitation polymerization microgels.
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Also typical snapshots are presented. The results are shown in Fig. With some limitations, the Flory-Rehner theory allows us to directly correlate simulation and experimental parameters.
In future, this can help to choose the simulation parameters more accurately. More details should be said about the effective density of cross-links, which also could be estimated with the use of Flory-Rehner model. The theoretical curve, corresponding to that value, is shown on Fig. One could see that this curve is too sharp and the resulting swelling ratio is too high for a realistic system, and does not fit neither experimental data nor computer simulations results. To obtain better fitting we had to use a model with higher cross-link density values f.