Monomer instantaneous

Moles of monomer remaining Mole fraction of styrene in the monomer Instantaneous mole fraction of styrene in the polymer Cumulative mole fraction of styrene in the polymer... 

Moles of Monomer Remaining Mole Fraction of Styrene in Monomer Instantaneous Mole Fraction of Styrene in Polymer Cumulative Mole Fraction of Styrene in Polymer... 

This equation relates the composition of the copolymer formed to the instantaneous composition of the feedstock and to the parameters rj and r2 which characterize the specific system. Figure 7.1 shows a plot of Fj versus fj-the mole fractions of component 1 in the copolymer and monomer mixture, respec-tively-for several arbitrary values of the parameters rj and r2. Inspection of Fig. 7.1 brings out the following points ... 

The instantaneous monomer concentration must be used. Except at the azeotrope, this changes as the conversion of monomers to polymer progresses. As in Sec. 7.2, we assume that either the initial conditions apply (little change has taken place) or that monomers are continuously being added (replacement of reacted monomer). 

This equation relates the (instantaneous) copolymer composition with the monomer feed of M and M2. Values for and are usually determined by graphical methods (9,10). Today, with the prevalence of powerful desktop computers, numerical minimisa tion methods are often used (11—14). 

Most values of / have been measured at zero or low conversions. During polymerization the viscosity of the medium increases and the concentration of monomer decreases dramatically as conversion increases (i.e. as the volume fraction of polymer increases). The value of / is anticipated to drop accordingly. 32, u 9j % For example, with S polymerization in 50% (v/v) toluene at 70 °C initialed by 0.1 M AIBN the instantaneous" / w as determined to vary from 76% at low conversion to <20% at 90-95% conversion (Figure 3.3).32 The assumption that the rate of initiation (kAf) is invariant with conversion (common to most pre 1990s and many recent kinetic studies of radical polymerization) cannot be supported. 

Figure 3.3 Cumulative ( ) and instantaneous ( ) initiator efficiency (/) of AIBN as initiator in S polymerization (50% v/v toluene, 70 °C) as a function of monomer conversion (lines are a polynomial fit to the datapoints).1,32...

Many emulsion polymerizations can be described by so-called zero-one kinetics. These systems are characterized by particle sizes that are sufficiently small dial entry of a radical into a particle already containing a propagating radical always causes instantaneous termination. Thus, a particle may contain either zero or one propagating radical. The value of n will usually be less than 0.4. In these systems, radical-radical termination is by definition not rate determining. Rates of polymerization are determined by the rates or particle entry and exit rather than by rates of initiation and termination. The main mechanism for exit is thought to be chain transfer to monomer. It follows that radical-radical termination, when it occurs in the particle phase, will usually be between a short species (one that lias just entered) and a long species. 

Figure 7.1 Plot of the instantaneous copolymer composition (FA) v.s monomer feed...

The instantaneous rate of monomer consumption in binary copolymerization is then given by eq. 62 ... 

High Monomer Conversion Usually instantaneous Mp tends to fall with conversion increasing Dp. Dp s in the range 2-5 are common but can be much larger. 

Instantaneous monomer feed flow-rate. Instantaneous initiator feed flow-rate. Time-averaged monomer solution flow-rate in oscillatory steady-state. 

Figures 1-4 show that when polymerizations were carried out at low concentrations of initiator and/or at low temperatures, the agreement between the model predictions and the experimental data is not so good. This is due to the fact that under those reaction conditions where R is low a large kinetic chain length is expected. When this is so, chain transfer to monomer becomes a reaction to be taken into account, since it markedly influences the chain length of the polymer being formed. A decrease in the instantaneous degree of polymerization, due to chain transfer to monomer, will reduce the concentration of the entangled radicals and, consequently, a decrease in the rate of polymerization is expected.

Mol% styrene in the monomer mixture xly Xp/yp Mol% styrene in the instantaneous polymer... 

In the case of vinyl/divinyl copolymerization, the subscript 1 is used to designate mono-vinyl monomer, 2 is used for divinyl monomer. f Q indicates the initial mole fraction of divinyl monomer in the monomer mixture, instantaneous mole fraction of monomer i bound in the polymer chain. 

Equation (7) is a rigorous expression relating the instantaneous vapor and liquid compositions with respect to monomer 1. However, the liquid composition (X ) needs to be related to the polymerization conversion in order to complete the model. 

A way to narrow the MWD and to approach the structure of dendrimers is the addition of a small fraction of a/-functional initiator, to inimers [40,71]. In this process the obtainable degree of polymerization is limited by the ratio of inimer to initiator. It can be conducted in two ways (i) inimer molecules can be added so slowly to the initiator solution that they can only react with the initiator molecules or with the already formed macromolecules, but not with each other (semi-batch process). Thus, each macromolecule generated in such a process will contain one initiator core but no vinyl group. Then, the polydispersity index is quite low and decreases with / M /Mn l-i-l//. (ii) Alternatively, initiator and monomer molecules can be mixed instantaneously (batch process). Here, the normal SCVP process and the process shown above compete and both kinds of macromolecules will be formed. For this process the polydispersity index also decreases with/,but is higher than for the semi-batch process, M /Mn=Pn//. ... 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

The instantaneous composition of a copolymer X formed at a monomer mixture composition x coincides, provided the ideal model is applicable, with stationary vector ji of matrix Q with the elements (8). The mathematical apparatus of the theory of Markov chains permits immediately one to wright out of the expression for the probability of any sequence P Uk in macromolecules formed at given x. This provides an exhaustive solution to the problem of sequence distribution for copolymers synthesized at initial conversions p l when the monomer mixture composition x has had no time to deviate noticeably from its initial value x°. As for the high-conversion copolymerization products they evidently represent a mixture of Markovian copolymers prepared at different times, i.e. under different concentrations of monomers in the reaction system. Consequently, in order to calculate the probability of a certain sequence Uk, it is necessary to average its instantaneous value P Uk over all conversions p preceding the conversion p up to which the synthesis was conducted. 

A user-friendly computer program has been developed (A.S.Yakovlev, S.LKuch-anov Copolymerization for Windows ) which makes it possible at any values of conversion to calculate for m=2-6 along with the composition of monomer mixture x, such statistical characteristics as instantaneous X and average (x j copolymer composition as well as the fractions (P Uk of sequences Uk with k=2-4 and... 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

Upon expressing from the equilibrium condition the complex concentration M12 through the concentrations of monomers, and substituting the expression found into relationship (21) we obtain, invoking the formalism of the Markov chains, final formulas enabling us to calculate instantaneous statistical characteristics of the ensemble of macromolecules with colored units. A subsequent color erasing procedure is carried out in the manner described above. For example, when calculating instantaneous copolymer composition, this procedure corresponds to the summation of the appropriate components of the stationary vector jt of the extended Markov chain ... 

Desilylation model studies were carried out on both the silylated monomer and polymer to develop suitable reaction conditions. The desilylation of the TMSEMA was instantaneous as indicated with GC by the increase in the retention time of the monomer. The desilylation the PTMSEMA was equally facile as determined by NMR spectroscopy Figure 1 shows the disappearance of the -Si(CH3)3 resonance at 0.1 ppm and the appearance of the -OH resonance at 3.3 ppm without detectible ester hydrolysis even after four days. 

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