Chain length average

For any value of p, n is greater for larger values of r stoichiometric imbalance lowers the average chain length of the preparation. 

Hydrogen sulfide reacts with molten sulfur and depresses the viscosity of the latter, particularly at 130—180°C iafrared spectral studies show that polysulfanes, H2S, form. The average chain length of these polysulfanes is shorter than the equiUbrium chain length of molten sulfur alone at the same temperature consequendy, the viscosity of the molten sulfur is markedly reduced (99,100). 

The viscosity of a mixture of fatty acids depends on the average chain length n and can be calculated from the equations (4) ... 

The cyclic trimer (trioxane) and tetramer are obtained by a trace of sulphuric acid acting on hot formaldehyde vapour (i) Figure 19.1). Linear polymers with degrees of polymerisation of about 50 and a terminal hydroxyl group are obtained by evaporation of aqueous solutions of formaldehyde (ii). In the presence of strong acid the average chain length may be doubled. Evaporation of methanol solution leads to products of type (iii). 

In order to get a better notion of the scaling relationship between gyration radius and average chain length for different density regimes, it is convenient... 

The changes in the average chain length of a solution of semi-flexible selfassembling chains confined between two hard repulsive walls as the width of the sht T> is varied, have been studied [61] using two different Monte Carlo models for fast equihbration of the system, that of a shthering snake and of the independent monomer states. A polydisperse system of chain molecules in conditions of equilibrium polymerization, confined in a gap which is either closed (with fixed total density) or open and in contact with an external reservoir, has been considered. 

The average chain length at time t after the system is moved out of equilibrium is given by L t) = [Pg.540]

It turns out that a rather simple description of this nonlinear relaxation in terms of a single relaxation time,, depending on the final average chain length Loo, is suggested by a scaling plot of L t) for different L o, as shown in Fig. 18 for an initial exponential MWD. It is evident from Fig. 18 that the response curves, L o — L t), for different L o may be collapsed onto a single master curve, 1 - L t)lLoo = /(V Loo) measured in units of a... 

Radicals typically are generated in the aqueous phase and it is now generally believed that formation of an oligomer of average chain length z (z-mer P/) occurs in the aqueous phase prior to particle entry.44 The steps involved in forming a radical in the particle phase from an aqueous phase initiator are summarized in Scheme 3.17. The length of the z-mcr depends on the particular monomer and is shorter for more hydrophobic monomers. 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

If the reaction goes to completion, the polymer molecules will have the form B B, and the final concentration of B endgroups will be [B]o-[A]q. The number average chain length is... 

TABLE 13 1 Number Average Chain Lengths for Binary Polycondensations Going to Completion... 

The ratio of weight-to-number average chain lengths is the polydispersity,... 

Example 13.3 The conversion of a self-condensing reaction can be limited to give polymers with finite lengths. How does the polydispersity of these polymers compare with those in Example 13.2 where the reaction went to completion with imperfect stoichiometry Make the comparison at the same average chain length. 

Solution The number and weight average chain lengths for a self-condensing polymerization are obtained from Equation (13.18) and (13.19) by setting Sab= E ... 

Table 13.4 tabulates results at the same value of as in Table 13.3. The polydispersities are lower than when the same average chain length is prepared by a binary polycondensation going to completion. The stoichiometry-limited binary polycondensations have a higher polydispersity because the monomer in stoichiometric excess (the B monomer) is included in the calculations. This broadens the molecular weight distribution.

FIGURE 13.5 Representative profiles of viscosity versus conversion for free-radical and condensation polymerizations. The endpoint is 99.9% conversion with a number average chain length of 1000. 

A binary polycondensation of AMA and BNB is to be performed in a batch reactor. A number average chain length of at least 100 is required. What minimum accuracy is required for weighing the two components ... 

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