Number of repeat units

In polymer solutions and blends, it becomes of interest to understand how the surface tension depends on the molecular weight (or number of repeat units, IV) of the macromolecule and on the polymer-solvent interactions through the interaction parameter, x- In terms of a Hory lattice model, x is given by the polymer and solvent interactions through... 

The degree of polymerization of a polymer is simply the number of repeat units in a molecule. The degree of polymerization n is given by the ratio of the molecular weight of the polymer to the molecular weight of the repeat unit ... 

Use the unit cell dimensions cited above to determine the crystal density of polyethylene. Examine Fig. 4.10 to decide the number of repeat units per unit cell. 

Unit cell dimensions (A) Number of repeat units per cell Density (g cm 3)... 

The total number of repeat units distributed among these chains is the number of monomer molecules present initially ... 

The number average degree of polymerization is given by dividing the number of repeat units by the number of chains, or... 

When we discussed random walk statistics in Chap. 1, we used n to represent the number of steps in the process and then identified this quantity as the number of repeat units in the polymer chain. We continue to reserve n as the symbol for the degree of polymerization, so the number of diffusion steps is represented by V in this section. 

Due to difficulties and uncertainties in the experimental separation of the porous media [93], and the inevitability of approximations in the analytical treatment [87,89], the nature of the chain movement in a random environment is still far from being well understood, and theoretical predictions are controversial [87,89]. Thus, on the ground of replica calculations within a variational approach, one predicts three regimes [87] in which the chain gyration radius Rg scales with the number of repeatable units N as rI (X for low, R x N for medium, and R x for high... 

One after the other, examine the structures of a number of common polymers. For each, draw the repeating unit, and indicate the chain length (number of repeating units in the strand). Note Each end of a polymer strand has been capped by adding extra atoms. Do not count these atoms as repeating units. Also, use the smallest possible repeating unit. 

Poly acetals are highly crystalline polymers. The number of repeating units ranges from 500 to 3,000. They are characterized by high impact resistance, strength, and a low friction coefficient. 

Unless odierwise specified, all monomers, reactants, and solvents were reagent grade 99+% (from Aldrich or Fluka) and used without further purification. In polymer formulas, n, x, y, and z represent number-average numbers of repeating units. 

The size of a polymer molecule may be defined either by its mass (see Chapter 6) or by the number of repeat units in the molecule. This latter indicator of size is called the degree of polymerisation, DP. The relative molar mass of the polymer is thus the product of the relative molar mass of the repeat unit and the DP. 

Figure 2 Equilibrium swelling degree of gels as predicted by Eq. (9). Z is the average number of repeat units between cross-links (Z lpxVm)-...

Although it is generally true that, as a polymer s chain length increases, its melt viscosity also increases, there are some nuances to this observation. By increasing the chain length, the number of repeat units increases. This creates more entanglements and raises the viscosity. One... 

Here, x is the number of repeat units in one network chain, /-q the number of solvent molecules, n2 the total number of network chains in the system, i the number of ionic groups on the chains, v the number of chains, and v20 the volume fraction of chains during the formation of the network. 

It should be noted that l, m and n are counted by the number of repeating units (CH2) and not by the real length. Rg of a nucleus is given by... 

It should be noted that the critical nucleation process does not depend on M. This can be explained by our model of surface diffusion (Fig. 27). In the model a nucleus will be formed from the absorbed chains. We can estimate the number of repeating units within a critical nucleus (N ) using parameters a, ae, and Ah given in [14]. N is the order of 102-103 for the range of AT in our experiment, which is much smaller than the number of repeating units within a molecule (103-104). This indicates that a critical nucleus should be formed by a part of a molecular chain. Therefore, the nucleation process of the critical nucleus will not depend on M. Thus, it is a natural result that B does not depend on M in this study. This is consistent with the discussion by Hoffman et al. [28] on FCC. They showed that the nucleation process of an FCC does not depend on Mn in the case of Mn > 104. On the contrary they showed that it depends on Mn for Mn < 104, because ae depends on Mn due to the effect of chain ends on the end surface of the critical nucleus. 

Our approach to polymer chain growth modeling is based on population balances for the various polymer species participating in and resulting from chain growth and transfer [34], The kinetics scheme is written below in mathematical fashion and is a precursor to the derivation of population balances. Monomer units are represented as M, and growing polymer chains are represented by the symbol Pn, where n is the number of repeat units attached to the active catalyst. Dormant polymer is represented by An where n is the number of repeat units attached to the CTA. Dead polymer chains, which arise from chain termination events such as hydrogenolysis... 

Figure 9.19 Chemical structure of poly 3-[2-((S)-2-methylbutoxy)ethyl]thiophene. Number of repeating units is 50.

Figures also display an index m (see, for example, l(n) in Figure 6) and this serves to indicate the number of repeating units of the bridge. For l(n), n = 2m + 2...

A high polymer may be defined as one in which the number of repeating units is more than 100 or so. This number is known as the degree of polymerisation (DP). 

The length of the Polymer chain is specified by the number of repeating units in two chain. This is... 

Fig. 20. Plot of the exponent ras a function of the chain lengths between two branching points. Open symbols results by Colby et al. [118,119] for branched polyesters. The variation of this length was achieved by co-condensation of trifunctional monomers with increasing fraction of bifunctional units. Filled symbols refer to polydicyanurates (N Nj ), anhydride cured phenyl monoglycidyl ether with a small fraction of bisphenol A diglyci-dylether as crosslinker (N=8Nj ) and end-functionalized 3-arm polystyrene stars crosslinked by diisocyanate (N 40 N ). N denotes the number of repeating units between two branching points...

The symbol n in Fig. 5.4 refers to the number of repeat units which are joined together in the polymer. This is termed the degree of polymerisation (X ), and could easily be a number as high as 10000. Thus for a repeat unit of mass 28 (ethene), this would give a polymer molar mass (R.M.M., Mj ) of 280000. 

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