Entanglements, identifying

The tube is a construct which we might continue to sketch around an emerging chain as it diffuses out of the original sleeve. Instead, it is convenient to start with the tube initially in place and consider how long it takes for the molecule to escape. The initial entanglements which determine the contours of the tube comprise a set of constraints from which the molecule is relaxing, even if only to diffuse into another similar set. Accordingly, we identify this reptation time as a relaxation time r for the molecule. 

The molecular entities of VOCCs have been well characterized. Ten distinct genes have so far been cloned, six of which have been identified in smooth muscle (Hofmann et al 1999, Ertel et al 2000). In contrast, the molecular counterparts of ROCCs and CCE have long been elusive, due probably to the lack of specific ligands/blockers and the presence of complex entangled regulatory mechanisms. The transient receptor potential (TRP) protein gene... 

For bioadhesive applications, anionic polymers appear to provide the most effective balance between adhesiveness and toxicity, with carboxylic materials preferred over sulfonic polymers [400]. Polyfacrylic acid) microparticles have been identified as particularly effective bioadhesive materials [402]. Studies with poly(acrylic acid) microparticles have indicated that, while water-swollen particles exhibit good bioadhesion, dry polymer particles give no adhesion at all. In addition, adhesive strength increases as the degree of ionization of the polymer is increased [402]. Thus the expanded nature of the polymer network is important to mucoadhesion, probably via polymer interdiffusion and entanglement with mucin [403],... 

The Rouse and Zimm models provide little direct help in dealing with t](y) since each predicts a viscosity which is independent of shear rate. The principal interest here is in concentrated systems where entanglement effects are prominent. Nevertheless, shear rate can influence the viscosity of polymer systems at all levels of concentration, including infinite dilution (307) and melts with M < Mc (308, 315). It is therefore essential to identify the causes of shear rate dependence in systems of isolated or weakly interactions molecules in order to separate intramole-... 

Dynamics of a single macromolecule in an entangled system is defined by the system of non-linear equations (3.52)-(3.54), containing some phenomenological parameters, which will be identified later. 

The critical value of molecular weight can be identified with the transition point between weakly and strongly entangled systems, the position of which was estimated in Sections 4.2.3 and 5.1.2 as... 

With this trick, one can now handle processes where entanglement can be varied at will. The issue is the representation of quantum states of systems having the same material content although a large number of autonomous subsystems are identifiable at a Fence. This is physics and chemistry unified by quantum physics. 

The idea of a chemical bond between two atoms in a molecule is akin to the classical model of a diatomic molecule, and its formation can be discussed along the same lines. The first assumption is that a pair of neighbouring atoms can be identified and isolated for study, well knowing that this action sacrifices all knowledge pertaining to overall intramolecular entanglement. 

The quantum potential can now be identified as a surface effect that exists close to any interface, in this case the vacuum interface. The non-local effects associated with the quantum potential also acquire a physical basis in the form of the vacuum interface, now recognized as the agent responsible for mediating the holistic entanglement of the universe. The causal interpretation of Bohmian mechanics finds immediate support in the postulate of a vacuum interface. There is no difference between classical and quantum entities, apart from size. Logically therefore, the quantum limit depends on... 

The extent of the structural transition must depend on the amount of shear exerted on the system versus the deformability of the droplet and continuous lamellar phase. Furthermore, as mentioned above, the rheological (i.e., functional) properties of a system in the a-gel state depend on parameters such as the number of droplets, their size, and how many times bilayers have folded themselves around several droplets, thus forming entanglements. Among these parameters one can identify one key... 

The parameter a has been identified as the radius of the tube, and its value is close to the root means square of the end-to-end distance of the chain with molecular weight Mg, that is, the molecular weight between entanglements. 

---