Marginally compact hyperbranched polymer trees

Magnetic Hyperbranched Molecular Materials for Treatment of Oily Sewage Containing Polymer in Oilfield Compound Flooding

With the continuous improvement in oilfield development and the application of tertiary oil recovery technology, the water content of oilfield-produced fluids has gradually increased, and a large number of oilfield sewage with complex components has also been produced after oil–water separation, and effective treatment is urgently needed. ASP flooding sewage contains alkali, various surfactants, polymers, microemulsion oil droplets, and solid impurities, which are difficult to be effectively treated by traditional water treatment agents and methods. In this study, aminopropyl triethoxysilane (APTES) was used to modify the nano-Fe3O4 coated with tetraethyl silicate (TEOS). The product was used as the ferromagnetic nano-core for the iterative reaction of Michael addition and ester amidation to synthesize a magnetic hyperbranched polyamide amine, and its performance in the treatment of ASP flooding wastewater was evaluated experimentally. For the preparation of APTES-modified Fe3O4@SiO2 (FOSN) product, TEOS was coated over Fe3O4 in an ethanol aqueous solution environment and then APTES was added dropwise. The first-generation branched product (1-FSMN) was obtained by the reaction of FOSN and methyl acrylate graft product (FOSN-M) with ethylenediamine, and the highest yield was 93.7%. The highest yield of the second-generation branched product (2-FSMN) was 91.6%. In this study, a composite flooding wastewater sample from a block in the Bohai oilfield was taken. The suspended solids content was 143 mg/L, the oil content was 921.09 mg/L, the turbidity was 135 NTU, and the zeta potential was −47 mV. The third-generation hyperbranched polymer (3-FSMN) and its quaternary ammonium salt (3-FSMN-Q) performed best in the appropriate dosage range, with the highest oil removal rate of 97%, suspended solid removal rate of 90.3%, turbidity reduction rate of 86.6% and zeta potential reduction rate of 88%. For 3-FSMN and its quaternary ammonium salt, the gravity/magnetic PAC compound treatment experiment was carried out. In the settlement time of only 5 min, 3-FSMN/PAC and 3-FSMN-Q/PAC can achieve the maximum oil removal rate of 87.1% and suspended solids removal rate of 87.3% for polymer containing wastewater from ASP flooding, and 86.3 and 86.0% for 120 mg/L. Its treatment capacity was much better than that of common treatment agent combination (CPAM/PAC).

Many-body contacts in fractal polymer chains and fractional Brownian trajectories

We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension d_{f} visits the same spot n≥3 times, at given moments t_{1},...,t_{n}, and obtain a determinant expression for these probabilities in terms of a displacement-displacement covariance matrix. Except for the standard Brownian trajectories with d_{f}=2, the resulting many-body contact probabilities cannot be factorized into a product of single-loop contributions. Within a Gaussian network model of a self-interacting polymer chain, which we suggested recently [K. Polovnikov et al., Soft Matter 14, 6561 (2018)1744-683X10.1039/C8SM00785C], the probabilities we calculate here can be interpreted as probabilities of multibody contacts in a fractal polymer conformation with the same fractal dimension d_{f}. This Gaussian approach, which implies a mapping from fractional Brownian motion trajectories to polymer conformations, can be used as a semiquantitative model of polymer chains in topologically stabilized conformations, e.g., in melts of unconcatenated rings or in the chromatin fiber, which is the material medium containing genetic information. The model presented here can be used, therefore, as a benchmark for interpretation of the data of many-body contacts in genomes, which we expect to be available soon in, e.g., Hi-C experiments.

Effective Hamiltonian of topologically stabilized polymer states

Topologically stabilized polymer conformations in melts of nonconcatenated polymer rings and crumpled globules are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems still remains unknown. We describe a polymer conformation by a Gaussian network - a system with a Hamiltonian quadratic in all coordinates - and show that by tuning interaction constants, one can obtain equilibrium conformations with any fractal dimension between 2 (an ideal polymer chain) and 3 (a crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the polymer conformations are mapped onto the trajectories of a subdiffusive fractal Brownian particle. Moreover, we explicitly show that the quadratic Hamiltonian with a hierarchical set of coupling constants provides the microscopic background for the description of the path integral of the fractional Brownian motion with an algebraically decaying kernel.

Marginally compact fractal trees with semiflexibility

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.