Chain randomization

Because shorter chains randomize more upon melting, they have a larger AS than longer chains. Therefore, decreases as the molecular weight is reduced, though this effect becomes important only at relatively low molecular weights. 

Schematic of polymer chains randomly placed in space, with crosslinks also placed randomly, but frequently averaging every 5,000-10,000 g/mol along the chains.

From the optical absorption of two different hexaphenyl films, one with its chains predominantly standing upright on the substrate, the other with the chains randomly distributed in all orientations, similar structure property relations can be concluded [139]. By comparing the calculated absorption coefficient [139J perpendicular to the chains with the observed optical absorption spectra of both films we see that the optical absorption, plotted in Figure 9-9, in the visible and... 

Key words intertwining chains, SARW statistics, conformation, polymer chain, random walks, lattice, thermodynamics, modules of elasticity, forces, work.. 

We appropriate the random chain and notify as nt the numbers of steps of the end of chain random walk along /-directions of d-dimensional lattice. At this,... 

The architecture dependence is also demonstrated in Fig. 33 by the factors of several star macromolecules, flexible cychc chains. Randomly and hyper-branched materials show a more complex behavior because of the large width in the molar mass distribution. Table 5 gives the actual values. The plot of Fig. 33 shows nicely how for a large number of arms the factor for hard spheres is approached. 

Homopolymers of polybutadiene can consist of three basic isomeric forms (czs-1,4, trans-1,4, and 1,2 vinyl), and these can be present in different sequential order. Copolymers may obtain a variety of co-monomers, such as styrene, acrylonitrile, etc. Depending on their distribution in the chain, random copolymers or block copolymers of different types and perfection can be produced. There are many synthetic elastomers based on butadiene available commercially. 

Type I restriction enzymes, such as those encoded in the chromosome of E. coli, are large 300- to 400-kDa proteins composed of at least three kinds of polypeptide chain. They bind at specific sites of a foreign DNA and apparently cleave the chain randomly nearby. They require ATP, Mg2+, and S-adenosylmethion-ine and have the unusual property of promoting the hydrolysis of large amounts of ATP.81 82 The significance of these properties is still unknown. 

Comb, monodisperse back-bone and monodis- = perse side chains, random coupling of the side chains along the backbone... 

There are some important differences between anionic and free-radical addition. First, unlike free-radical initiators, which decompose and start chains randomly throughout the course of the reaction, anionic initiators ionize readily in fairly polar organic solvents or at low concentrations in hydrocarbons, and chains are started immediately, one for each molecule of initiator. Second, in the absence of impurities, there is no termination,... 

P(n) gives the probability that a chain, randomly chosen from our solution, has length ra. We will often use a reduced5 distribution p(y) defined as... 

Since these enzymes cut the cellulose chain randomly, the average chain length is lowered, decreasing the viscosity after a very short time, although the reducing power is only increased by a relatively minor amount. 

Un cas particuli rement interessant de ces modifications de la composition est constitue par la classe des copolym res, lorsque la succession des deux monomferes est distribute au hasard le long de la chaine (random copolymerization). Dans ce cas, T varie d une manitre continue (mais non necessairement monotone) avec la composition (Gordon et Taylor, 1952 Mandelkern et al. 1957 Illers, 1963). 

Theta conditions are of great theoretical interest because the diameter of the polymer chain random coil in solution is thenequal to the diameter it would have in the amorphous bulk polymer at the same temperature. The solvent neither expands nor contracts the macromolecule, which is said to be in its unperturbed state. The theta solution allows the experimenter to obtain polymer molecules which are unperturbed by solvent but separated from each other far enough not to be entangled. Theta solutions are not normally used for molecular weight measurements, because they are on the verge of precipitation. The excluded volume vanishes under theta conditions, along with the second virial coelTicient. 

D > ] the factor from randomization of direction. If the chains all parallel in the crystal are still straight in the amorphous region, but have an isotropic distribution of directions, then D 2, a result first obtained in the polymer context by Flory, I believe. Note in passing that if the emerging chains randomized their directions over the hemisphere we should have D — , but the distribution would not be isotropic to produce isotropy the probability of changing direction by 0 from the normal must be weighted by a factor cos 6 that s how the sun comes to look about equally bright across the whole disc. 

Gels that form from grouts normally used for field work contain 8% to 12% solids. These solids, in the gel, are in the form of long molecular chains, randomly cross-linked to each other. The rest of the grout, 88% to 92% by... 

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