Stability of stars

We may annotate here that the adiabatic expansion in the gravity field plays a certain role for the stability of stars. The Schwarzschild criterion for stability is based on the adiabatic expansion of a gas in the interior of a star under the influence of gravity. 

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Abstract After some historical remarks we discuss different criteria of dynamical stability of stars and the properties of the critical states where the loss of dynamical stability leads to a collapse with formation of a neutron star or a black hole. At the end some observational and theoretical problems related to quark stars are discussed. 

The core-first method, which uses an active multifimctional core to initiate growth of polymer chains, was apphcable to make hybrid POSS-core star-shaped polyoxazohnes that showed an increase in Tg, compared to that of polyoxazohne initiated by methyl p-toluenesulfonate (MeOTs) with poly(2-methyl-2-oxazohne) (POZO) [76]. Other hybrid star-shaped polyoxazohnes initiated by cube-OTs or cube-benzyl revealed the same phenomenon. This was attributed to the reduction of segmental mobifity of POZO in starshaped polyoxazolines, which was caused by the incorporation of hard, compact POSS moiety to the core of star polymer with the core-first technique. The conclusions were drawn that the thermal stabilities of star-shaped polymers increased as the POSS wt % was increased, and this was used as a measure of the effect of the inorganic POSS unit on polymer thermal properties. 

Mechanical Stability of Star-Shaped Polymers Bead-Rod Model. 172... 

Agarwal and co-workers adopted Odell and Keller s bead-rod model to predict the shear stability of star-shaped polymers [228]. As illustrated in Fig. 27, they adopted a key assumption that all arms are fully stretched before any scission event. For a linear polymer, the tensile force built at the midpoint is tr id (Eq. 13). For a six-arm star molecule bearing the same N, the force at the base of each arm ffaim is... 

Compared with (14), ep of star-shaped polymers follows the same 2 dependence on M but its value is higher than in linear polymers according to (31). The structure of the core in the number of parallel Unks (n) and the number of arms (/ann) both improve the shear stability of star-shaped polymers. 

Unlike previous researchers, Xue and Agarwal were more interested in the effect of core structure on the shear stability of star-shaped polymers. They synthesized six-arm star poly(methyl methacrylate) (PMMA) bearing either a linear core (A, M = 2,350 kDa) or a fused core (B, M = 2,100 kDa) (Fig. 31) [228,... 

Recently, we have also prepared nanosized polymersomes through self-assembly of star-shaped PEG-b-PLLA block copolymers (eight-arm PEG-b-PLLA) using a film hydration technique [233]. The polymersomes can encapsulate FITC-labeled Dex, as model of a water-soluble macromolecular (bug, into the hydrophilic interior space. The eight-arm PEG-b-PLLA polymersomes showed relatively high stability compared to that of polymersomes of linear PEG-b-PLLA copolymers with the equal volume fraction. Furthermore, we have developed a novel type of polymersome of amphiphilic polyrotaxane (PRX) composed of PLLA-b-PEG-b-PLLA triblock copolymer and a-cyclodextrin (a-CD) [234]. These polymersomes possess unique structures the surface is covered by PRX structures with multiple a-CDs threaded onto the PEG chain. Since the a-CDs are not covalently bound to the PEG chain, they can slide and rotate along the PEG chain, which forms the outer shell of the polymersomes [235,236]. Thus, the polymersomes could be a novel functional biomedical nanomaterial having a dynamic surface. 

Bisnovatyi-Kogan,G.S., Blinnikov,S.I. (1974). Static criteria for stability of arbitrary rotating stars. Astron. Ap., 31 391 -04. 

Bisnovatyi-Kogan,G.S., Ruzmaikin,A.A. (1973). The stability of rotating supermassive stars. Astron.Ap., 27 209-221. 

Misner, C. W. Zapolsky, H. S. (1964). High-Density Behavior and Dynamical Stability of Neutron Star Models. Phys. Rev. Let., 12 635-637. 

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