Molar monomer concentration

Kambe et al. [63] studied quite recently equilibria in chloral polymerization unfortunately with only one initiator, sodium naphthalene. Unlike the chloral polymerization without solvent where the polymerization temperature is 58°C [62], in the case of one molar monomer concentration it was 12°C [63], the ceiling temperature of chloral polymerization. In Kambe s work the initiator was always added below the polymerization... 

DN gels are synthesized via a two-step network formation the first step is to form a rigid gel that is highly cross-linked, and the second is to form a loosely cross-linked network in tire flrst gel [23]. Hereafter, the DN gels are referred to as Pl -Xl -yi/P2 -X2 -y2, where P,, x, andy, (t = 1,2 for the flrst and second network, respectively) are Are abbreviated polymer name, molar monomer concentration, and the percentage cross-linker concentration (in mol%) with respect to the monomer for the /-th network, respectively. 

I/l(0) in Water Containing Poly(vinylpyrrolidone) at a Molar Monomer Concentration of 0.009... 

Two good approximations can be made to obtain a good analytical solution. First, [Am] in the feed reservoir can be high enough that a low flow rate and relatively little increase of occurs during the reaction. Then, V(t) VJ,. Furthermore, if the half-Ufe of the initiator (e.g., KPS at 60°C) is long compared to the reaction, the approximation can be used that [/](0 UXo- With these approximations, the molar monomer concentration is calculated to be ... 

There was no correlation between tacticity and cis content, but all-cw polymers were mainly highly syndio-tactic and all-trans polymers slightly isotactic when prepared from 3 molar monomer concentration at 20°C. 

Moment Analysis. The zeroth moment is the molar concentration of polymer and is expressed by Equation 5. The first moment is proportioned to the mass of polymer formed and is related to monomer concentration Equation 3, The second moment WA(t) is expressed by... 

Monomer concentration dynamics are presented in Figure 5. Additional observations for Run 5 are accurately correlated during the reactor startup and at final steady state. The observation at one residence time, Run 4, may be in error. The total cummu-lative, molar concentrations of macromolecules as a function of time are presented in Figure 6. The errors associated with this dependent variable are also evident during the steady state analysis of initiation... 

Chain polymerisation Monomer concentration decreases steadily with time. High molar mass polymer is formed at once and the molar mass of such early molecules hardly changes at all as reaction proceeds. Long reaction times give higher yields but do not affect molar mass. The reaction mixture contains only monomer, high molar mass polymer, and a low concentration of growing chains. 

Step polymerisation Monomer concentration drops rapidly to zero early in the reaction. Polymer molar mass rises steadily during reaction. Long reaction times increase molar mass and are essential to obtain very high molar masses. At all stages of the reaction every possible molecular species from dimers to polymers of large degrees of polymerisation are present in a calculable distribution. 

The inhibition method has found wide usage as a means for determining the rate at which chain radicals are introduced into the system either by an initiator or by illumination. It is, however, open to criticism on the ground that some of the inhibitor may be consumed by primary radicals and, hence, that actual chain radicals will not be differentiated from primary radicals some of which would not initiate chains in the absence of the inhibitor. This possibility is rendered unlikely by the very low concentration of inhibitor (10 to 10 molar). The concentration of monomer is at least 10 times that of the inhibitor, yet the reaction rate constant for addition of the primary radical to monomer may be less than that for combination with inhibitor by only a factor of 10 to 10 Hence most of the primary radicals may be expected to react with monomer even in the presence of inhibitor, the action of the latter being confined principally to the termination of chain radicals of very short length. ... 

Let the monomer concentration [M] be 5 molar both in the bulk phase and in the emulsion particles. The comparison is set forth below ... 

The current research shows that the model describing this step-growth polymerization is valid at relatively low conversions. Experimental monomer concentrations and the moments of the distribution are adequately fit, yielding estimates of the model parameters. The simulation demonstrates that fitting molar concentrations of polymeric species is substantially more demanding. 

Figure 3. Effect of EtsA l i-BusA l molar ratio on microstructure. Polymerization conditions monomer concentration, 11 wt % in hexane catalyst concentration, 7.5 X 10 5 mol/L molar ratio Nd(vers), Et3Al2Cls AIRS, 1 1 30 polymerization time, 2 h and 60°C.

Table VII. Effect of organoaluminum compounds on catalyst activity. Polymerization conditions molar ratio butadiene, propylene is 1.1 monomer concentration, 20 wt % in toluene catalyst, 0.8 mmol VO[OCH2C(CH3)3]2Cl phm, 5 mmol Al compound phm reaction time, 4 h and —45°C. Data from Ref. 19.

The effect of monomer concentration on the dependence of the DP on temperature. Further studies [12,52, 62] of the temperature dependence of the DP showed that the Arrhenius plot was approximately linear over the temperature range -5° to -78° for all concentrations of isobutene from about half-molar to undiluted monomer, and that the slope of the line increased with decreasing concentration in such a way that all the lines crossed at approximately the same temperature, -50°. This means that at -50°, the inversion temperature , the DP is independent of monomer concentration at lower temperatures it decreases, at higher temperatures it increases with increasing monomer concentration. This behaviour was found for polymerisation in methyl, ethyl and vinyl chloride as solvents. 

Figure 3.2 compares the level of cyclics on a molar, wt%, or yield basis as a function of reaction concentration. Note that as the reaction concentration dropped, the yield increased to near 100 %, as predicted from theory. However, the amount of cyclic PBT on a molar or wt% in solution basis remained constant at the critical monomer concentration, which is about 0.050 M, regardless of the concentration of polymer in solution. In fact, if one calculates the amount of cyclic present in an equilibrated melt (1-2 %), it is also about 0.05 M cyclic. The same amount of cyclic was generated via the ring-chain equilibration process, regardless of the reaction concentration only the amount of polymer which remains as a by-product... 

In order to deduce the dependence of the polymerisation (propagation) rate and/or molar mass (M ) upon the initiator and/or monomer concentrations, it is necessary to invoke a hypothesis called the Steady State . Employing the Steady State allows one to set the rate of production of the radicals (i. e. Iq [I]) equal to the rate of loss of radicals (i. e. lq[R ] ), which enables one to write Eq. 5.4. 

We noted in Section 5.1, that for conventional polymersiation the propagation rate and molar mass (M ) were dependent on the initiator and monomer concentrations according to equations... 

As a consequence of the free radical polymerization kinetics, the termination rates are extremely fast in comparison to the slow initiation rates. This results in the formation of high molar mass chains at the initial stage of the polymerization and decreasing molar masses in the latter stages due to the decrease in the monomer concentration. Under these circumstances, broad molar mass distributions are inevitable. 

Polymerizations were performed at monomer concentrations from 3.94 to 0.25 molar. The high monomer concentration of 3.94 M requited the use of 50 Vol.-% hydrocarbon, as compared with the 25 Vol.-% hydrocarbon used in the... 

In the large scale Nd-BR production monomer concentrations range between 10-23 wt. %. In order to keep solution viscosities at a manageable level, in the first approximation a very simple approach is applicable The higher the aimed molar mass the lower one has to set the monomer concentration, and vice versa. Apart from molar mass, MMD, branching and monomer conver-... 

The theoretical treatment for the self-assembly of a molecular entity into rings or cages occurring under thermodynamic control is based on two fundamental physicochemical quantities the effective molarity (EM) of the intramolecular interaction of the cyclic n-mer and the value of the stability constant of the intermolecular interaction (fCinter) [5]. The following formula has been derived by Ercolani and allows calculation of the minimum value of the product fCinterEM to obtain a virtually complete self-assembled macrocycle at certain monomer concentration ... 

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