Number of polymer molecules

Begin by recognizing that a molecule containing x of the head-to-head links will be cleaved into x + 1 molecules upon reaction. Hence if N is the number of polymer molecules in a sample of mass w, the following relations apply before and after cleavage = (x l)Nj, or w/M = (x + l)(w/Mj,). Solving for x and... 

Over the range in which the rate of polymerization is proportional to the square root of the initiator concentration, Rj, may be replaced in Eq. (36) with the coefficients of the terms being appropriately altered. The contributions of the various sources of chain ends in the polymerization of styrene with benzoyl peroxide at 60°C are shown in Fig. 15 as functions of the initiator concentration.The uppermost curve represents the total number of polymer molecules per unit, and the differences between successive curves represent the contributions of the separate processes indicated. 

Other cyclic compounds such as the N-carboxyanhydrides of a-amino acids,and lactams may be polymerized similarly with regeneration of an amino group at each step. According to the mechanism postulated, the number of polymer molecules formed should equal the number of initiator molecules (e.g., ROH) introduced, and the average number of monomers per polymer molecule should equal the ratio of monomer consumed to initiator. 

Number of particles (Chaps. V and VII). Total number of polymer molecules of all sizes (Chaps. VIII and IX). Number (or number of moles) of primary molecules (Chap. XI). 

The summations extend from n = 2 to n. = oo.) Keii [Kinetics of Ziegler-Natta Polymerization, Kodansha, Tokyo, 1972] has noted that under steady-state reaction conditions, the number of polymer molecules with degree of polymerization n desorbing per unit catalyst surface area in unit time may be written as... 

These initiators may be used in the presence of protic sources such as MeOH.780 The rapid and reversible exchange of propagating alkoxides with alcohol leads to a narrow molecular weight distribution (for example, Mw/Mn<1.15 for oligomeric PCL), with the number of polymer molecules closely approaching the sum of the number of molecules of initiator and alcohol. In the absence of alcohol, the polymerization of CL is less well behaved with Mw/Mn= 1.5, presumably a consequence of unfavorable initiation and propagation rates. 

Direct quantitative determination of the number of initiator fragments combined with the polymer is feasible only under very exceptional circumstances. Another useful method depends on the determination of the Molecular weight by a suitable method. The number of polymer molecules may then be calculated, and assuming termination by coupling, the number of combined, primary radicals may be considered to be twice the number of molecules, still another method for determining the efficiency depends on the reaction of the chain radicals stoichiometrically with certain inhibitors. 

Here Nn gives the number fraction of n-mer in the total number of polymer molecules present, N. The weight fraction Wn, similarly, is given by... 

Under most conditions the number of polymer molecules is vastly greater than the number of catalyst molecules, at least with HC104 and Et30+ salts as catalysts. 

The present author holds the view that since the number of end-groups is always much smaller than the number of polymer molecules, a ring-expansion mechanism, analogous to reaction (4), is the most plausible. This matter will be discussed in Section 5. 

A and B groups. Since each polymer chain has two chain ends, the total number of polymer molecules is one half the total number of chain ends or /Va( I p) I/Vr(I — rp) /2. 

The number-average degree of polymerization Xn is the total number of A—A and B—B molecules initially present divided by the total number of polymer molecules... 

Using the methods described, the values of Cm and Ci in the benzoyl peroxide polymerization of styrene have been found to be 0.00006 and 0.055 respectively [Mayo et al., 1951]. The amount of chain transfer to monomer that occurs is negligible in this polymerization. The chain-transfer constant for benzoyl peroxide is appreciable, and chain transfer with initiator becomes increasingly important as the initiator concentration increases. These effects are shown in Fig. 3-7, where the contributions of the various sources of chain ends are indicated. The topmost plot shows the total number of polymer molecules per 105 styrene monomer units. The difference between successive plots gives the number of polymer molecules terminated by normal coupling termination, transfer to benzoyl peroxide, and transfer to styrene. 

The number of polymer molecules adsorbed per unit area was calculated from adsorption isotherm data and the surface area per unit mass of the sample. 

In the polymerization of MMA initiated with 1 (X=Me), the degree of acceleration became more pronounced as the amount of 3b was increased (Table 2). If the added 3b initiates the polymerization, the number of polymer molecules produced should increase proportionally to the amount of 3b, and, consequently, the Mn value should decrease. However, irrespective of the ratio of 3b to 2, all the polymers formed were of narrow MWD, and the observed Mn values were always close to those expected from the mole ratios of the monomer reacted to 2, indicating that the added 3 does not initiate but only accelerates the polymerization. In this regard, all the produced polymers in Table 2 were silent in GPC when monitored at 263 nm (2,4-di-ferf-butylphenol 263 nm, anisole ... 

Fig. 5. Polymerization of tcrt-butyl methacrylate ( BMA) initiated with (TPP)AlMe (1, X= Me) via an enolatealuminum porphyrin (2, R= Bu) in the presence of trimethylaluminum (Me3Al) [ BMA]o/[l (X=Me)]o=100, [l]o=17.8mM, CH2CI2 as solvent, rt. Correlations of the number-average molecular weight (Mn) and the ratio of the numbers of polymer molecules to 2 (Np/ATxpp) with the initial mole ratio of Me3Al to 2...

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