Linear polymer chain

Mate and Novotny [42] studied the conformation of 0.5-13 nm thick Z-15 on a clean Si (100) surface by means of AFM and XPS. They found that the height for PFPE molecules to extend above a solid surface was no more than 1.5-2.5 nm, which was considerably less than the diameter of gyration of the lubricant molecules ranging between 3.2-7.3 nm. The measured height corresponds to a few molecular diameters of linear polymer chains whose cross-sectional diameter is estimated as 0.6-0.7 nm. The experimental results imply that molecules on a solid surface have an extended, flat conformation. Furthermore, they brought forward a model, as shown in Fig. 28, which illustrates two... 

For complete rigor the distribution previously presented (Eqs. 1, 2, and 3 and Figs. 51 and 52) for linear polymer chains should be modified through substitution of p for the over-all extent of reaction p. Thus, for example, Eq. (3) for the weight fraction should be replaced with... 

Hydroxyl containing polymers may be cross-linked with diisocyanates. Fordyce and Ferry cross-linked styrene-maleic anhydride copolymers through the action of glycols. The copolymerization of divinyl with vinyl monomers may be looked upon as a method of cross-linking chain polymers. The cross-linkages are introduced simultaneously with the growth of the linear polymer chains, rather than afterwards, but this difference is secondary. 

The most investigated examples are to be formd in the precipitation of polyelectrolytes by metal ions. Here, networks are formed by the random crosslinking of linear polymer chains, and the theory requires some modification. The condition for the formation of an infinite network is that, on average, there must be more than two crosslinks per chain. Thus, the greater the length of a polymer chain the fewer crossUnks in the system as a whole are required. 

The theory of gelation (Flory, 1953,1974) has been summarized in Section 2.2.3. This theory regards gelation as the consequence of the random crosslinking of linear polymer chains to form an infinite three-dimensional network. The phenomenon is, of course, well illustrated by examples drawn from the gelation of polycarboxylic acids by metal ions. 

A novel approach [98], proposed for generating starting configurations of amorphous dense polymeric systems, departs from a continuous vector field and its stream lines. The stream lines of continuous vector fields never intersect. If the backbones of linear polymer chains can be associated with such stream lines, the property of the stream lines partly alleviates the problem of excluded volume, which - due to high density and connectivity - constitutes the major barrier to an efficient packing method of dense polymeric systems. This intrinsic repulsive contact can be compared to an athermal hard-core potential. Considering stream lines immensely simplifies the problem. 

Casassa, E. R and Tagami, Y. An equilibrium theory for exclusion chromatography of branched and linear polymer chains, Macromolecules, 2, 14, 1969. 

There are two end groups on a linear polymer chain. Thus, their molar fraction is... 

A graft copolymer consists of a linear Polymer chain of one type to which has been grafted side-chains of a different type of polymer. The formation of a graft copolymer can be brought about by either of two general methods ... 

Figure 6.5 Illustrations of nanoscale spherical assemblies resulting from block copolymer phase separation in solution are shown, along with the chemical compositions that have been employed to generate each of the nanostructures (a) core crosslinked polymer micelles (b) shell crosslinked polymer micelles (SCKs) with glassy cores (c) SCKs with fluid cores (d) SCKs with crystalline cores (e) nanocages, produced from removal of the core of SCKs (f) SCKs with the crosslinked shell shielded from solution by an additional layer of surface-attached linear polymer chains (g) crosslinked vesicles (h) shaved hollow nanospheres produced from cleavage of the internally and externally attached linear polymer chains from the structure of (g)...

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

The above expressions provide a universal description of the dynamics of a Gaussian chain and are valid for real linear polymer chains on intermediate length scales. The specific (chemical) properties of a polymer enter only in terms of two parameters N =Rl and The friction parameter is gov-... 

Recalling the demands on the polymer architecture of a polymer brush and the projected properties in terms of swelling, wetting and friction, as described in the theoretical work, the brush has to consist of linear polymer chains of the same length at high grafting densities. The closest approximation to this can be obtained by the living anionic SIP (LASIP). The experimental difficulties outlined mean that only relatively few examples of LASIP are documented in the literature. 

These are usually formed from bl-functlonal and trl-functional monomers and contain strong covalent bonds between various linear polymer chains, e.g. bakellte, melamine, etc. These polymers are depicted as follows ... 

The synthesis and proposed cure mechanisms of this resin are described in reference 2. While the cure mechanism of the BCB terminated resin is not yet known, it is speculated that it reacts via one of two different routes. Initially the strained four member ring of the benzocyclobutene undergoes a thermally Induced ring opening. The opened rings then react with one another by a linear type addition to form a network type of structure or by cycloaddition to form linear polymer chains. An Illustration of the proposed polymerization mechanism of benzocyclobutene (BCB) terminated resins is shown below. 

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