Degree of polymerization and polydispersion

In a polymer sample, the degree N of polymerization varies from one polymer to another. We shall denote by PN, the probability that a polymer taken at random in the sample be made of N monomer links. In other words, if the sample is put in solution and if Cis the total number of polymers per unit volume, the number CN of polymers with N links is given by 

In particular, if the polymers are linear the probabilities PN define the polydispersion of the sample. 

In what follows, it will also be convenient to use the symbols 0a (number average), PW (weight average), z (Z average) which are defined by the equalities 

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Cationic polymers are not well-defined molecules in size and homogeneity due to their large degree of polymerization and polydispersity. In addition they can be cytotoxic and can induce complement activation. In an effort to circumvent these problems, low molecular weight synthetic peptides should be preferred because they offer the advantage of controlled synthesis and defined purity. 

B. Calculate the weight average degree of polymerization and polydispersity of this sample. 

Figure 15 displays the average degrees of polymerization and polydispersities expected without and with the decay of the persistent radical and for the parameters given above. The control remains satisfactory, even for the large decay constant ky. On the other hand, the time for 90% conversion is reduced by a factor of about 6. The fraction of unreactive products increases by a factor of 5 but remains small (4%). This confirms the strategy to shorten conver-... 

Figure 3. Degree of polymerization ( ) and polydispersity (O) resulting from anionic polymerizations of 6-[4 -(4"-methoxyphenyl)phenoxy]-hexyl methacrylate initiated by 1, l-diphenyl-3-methylpentyl lithium/ 3 LiCl in THF at -40°C [44].

Figure 5. Degree of polymerization ( ) and polydispersity (O) resulting from ring-opening metathesis polymerizations of (a) 5- [6 -[4"-(4" -methoxyphenyl)phenoxy]hexyl]carbonyl)bicyclo(2.2.1]hept-2-ene [22] and (b) 5-[[[2, 5 -bis[(4"-methoxybenzoyl)oxy]benzyl]oxy]carbonyl]bicyclo[2.2.1]hept-2-ene [182] initiated by Mo(CH- -Bu)(N-2,6-C6H3-i-Pr2)(0-f-Bu)2 or Mo(CHCMe2Ph)(N-2,6-C6H3-i-Pr2)(0-/-Bu)2, respectively, in THF at 25 °C.

The key finding is that the thermodynamics and kinetics of polymerization provides information relative to degrees of polymerization and polydispersity index. Most of the expressions above are cast in terms of DP or kinetic chain length. The actual molecular weight can be easily obtained by multiplying by the mer molecular weight. 

By adding a non-dissolution solvent such as water, ethanol or acetone, cellulose miscible in ILs can be precipitated from solution and then separated from the mixture of IL and nondissolution solvent either by filtration or centrifugation. Due to non-volatile nature of IL, it can be recovered by distillation of the mixture, thus eliminating the non-dissolution solvent. The precipitated cellulose can appear in different forms such as monoliths, fibers and films and can have the same degree of polymerization and polydispersity as native cellulose but it... 

Figures 4 and 5 show that the degree of polymerization and the intrinsic viscosity increase with increasing the comonomer concentration. Thus, the increase in the comonomer concentration would increase DP and, consequently [rj] Eq. (2). However, the exponent of the monomer concentration for the degree of polymerization decreases at a high comonomer concentration. The abrupt change in the exponent at comonomer concentration >2.1 M/L (Eq. 9) may be ascribed to polydispersity. This was found by others [34] to be at 2.1 and 2.2 M/L, although it starts theoretically at 2.0 M/L.

The polydispersity decreases with increasing degree of polymerization and depends only on (N)n ... 

The breadth of the molecular weight distribution is described by the ratio of the weight and number average molecular weights or degrees of polymerization, and is referred to as the polydispersity index (PDI) or molecular weight distribution (MWD) [Eq. (8)]. 

Areas of application of reaction calorimetry include determination of calorimetric data for reactions and process design, for the kinetic characterization of chemical reactions and of physical changes, for on-line monitoring of heat release and other analytical parameters needed in subsequent process development as well as for the development and optimization of chemical processes with the objective, for instance, to increase yield or profitability, control the morphology or degree of polymerization and/or index of polydispersity, etc. 

The expressions for the evolution of the degree of polymerization and the polydispersity index for polymerizations in the stationary state of constant radical concentrations are50... 

Calculate the number-average degree of polymerization and weight-average degree of polymerization for one-dimensional percolation with extent of reaction p = 0.99. What is the polydispersity index of the molecules at this extent of reaction ... 

Living polymerization techniques allow one to prepare block copolymers with exactly predetermined degrees of polymerization and low polydispersities. The degree of polymerization N of the polymer blocks depends on the molar ratio of initiator [I] to monomer [A], [B] concentration, N =[A]/[f] and N =[B]/[7]. The polydispersities are mostly in the range 1.1, which corresponds to a... 

In polydisperse primary chains, therefore, the critical concentration of cross-link-carrying monomer units depends on the mass average degree of polymerization, and not on the number average degree. 

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