We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.

Polybetaines have received widespread attention due to their smart response properties and structures which resemble biological polymers like peptides and DNA. However, few studies have focused on the controlled synthesis and self-assembly of hydrophobically modified polybetaines due to the difficulty of synthesizing these materials. We report the first molecular weight-controlled synthesis of hydrophobically modified polycarboxybetaines (HMPCB). Poly­(dodecyl grafted aminocrotonate -methacrylic acid) (P­(DACRO-MAA)) was synthesized via the reversible addition–fragmentation chain-transfer (RAFT) polymerization approach. The two different tautomers of the monomer were also successfully identified and separated via thin layer chromatography (TLC) and column chromatography, making it possible to obtain pure polycarboxybetaine via RAFT synthesis. Both the successfully separated enamine form of the monomer and the resulting polycarboxybetaine were confirmed via FTIR and NMR. The polycarboxybetaine was found to have a low polydispersity (PDI) of 1.214, and its molecular weight was determined as 70590 g/mol via gel permeation chromatography (GPC) measurements. Spherical, rodlike, and fractal assembled structures for the P­(DACRO-MAA) were observed with pH change using TEM, zeta sizer, and dynamic light scattering (DLS). The unique self-assembled structures of HMPCB synthesized via RAFT provide an opportunity to understand fundamental polymer science and can be engineered for broad applications.

In this work, we report the first molecular weight-controlled amphiphilic polybetaine synthesis using various hydrocarbons via reversible addition−fragmentation chain-transfer (RAFT) polymerization. The experimental separation of the alkyl aminocrotonate tautomers, which has been the subject of debate, was completed for the first time. The enamine form of these tautomers was further used as a monomer for the RAFT polymerization of amphiphilic polycarboxybetaines. Self-assembly of the amphiphilic polycarboxybetaines showed micelle structures from spherical, rod-like to fractal in the aqueous media due to the competition between both electrostatic and hydrophobic forces. Hydrophobically dominant interactions among amphiphilic polycarboxybetaines and long-chain hydrocarbon alkane molecules were investigated to understand long-chain hydrocarbon alkane crystallization using alkane crystal deposition and viscosity experiments. Strong hydrophobic forces between poly(hexadecyl-grafted aminocrotonate−methacrylic acid) and long-chain hydrocarbon alkane molecules changed the surface properties of the long-chain hydrocarbon alkane nucleus and inhibited the growth of paraffin crystals.