Methods of initiation

It may be noted that Eq. (6.23) for the rate of polymerization Rp contains a general term R( representing the rate of initiation. The expression for Ri will vary depending on the method used for the generation of primary radicals. For uni-molecular thermal decomposition of initiator compounds [Eq. (6.3)], i is given by Eq. (6.11). Inserting it in Eq. (6.23) yielded the corresponding expression, Eq. (6.24), for the rate of polymerization. 

A variety of other means, besides thermal decomposition of initiator, can be used to produce radicals for chain initiation, such as redox reactions, ultraviolet irradiation, high-energy irradiation, and thermal activation of monomers. The expression for Ri wUl be different in each case and inserting it into the same equation (6.23) will yield the corresponding expression for the rate of polymerization. 

Normally, thermal initiation is used and the critical energy is acquired by collisions. In photochemical initiation the critical energy is accumulated by absorption of radiation. This can only be used if the reactant molecule has a sufficiently strong absorption in an experimentally accessible region, though modem laser techniques for photochemical initiation increase the scope considerably. 

Absorption of radiation excites the reactant to excited states, from which the molecule can be dismpted into various radical fragments. Conventional sources produce steady state concentrations. Flash and laser sources produce much higher concentrations, enabling more accurate concentration determination, and allowing monitoring of production and removal by reaction of these radicals this is something which is not possible with either thermal initiation or conventional photochemical initiation. 

Lasers have such a high intensity that they can give significant absorption of radiation, even though e for the absorbing species and its concentration are both very low. With conventional sources, absorption will be very low, if only one or other of e and the concentration is low. The crucial point is that the absorbance also depends on the intensity of the exciting source, and so with lasers this can outweigh a low concentration and/or a low e. 

Other useful features of photochemical methods include the following. They 

Radiochemical and electric discharge initiation are also used, though these are much less common. These are much higher energy sources, and they have a much more disruptive effect on the reactant molecules, producing electrons, atoms, ions and highly excited molecular and radical species. 

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Pseudo-Order Reactions and the Method of Initial Rates Unfortunately, most reactions of importance in analytical chemistry do not follow these simple first-order and second-order rate laws. We are more likely to encounter the second-order rate law given in equation A5.11 than that in equation A5.10. 

The hydrogen abstraction from —SH groups is faster than from —OH groups. Hebeish et al. [9] and Misra et al. [10,11] reported the chain-transfer method of initiation of graft copolymerization onto cellulosic substrates with azobisisobutyronitrile (AIBN) and benzoyl peroxide (BPO) as initiators. 

All known methods of initiation are used for inducing three-dimensional polymerization of AAm, AAc, and their copolymerization [37, 38]. Some special initiating systems have been also elaborated [39]. There is a wide choice of crosslinking agents various A,A -bis-acrylamides (methylene, ethylene, isopro-pylidene) as well as dimethacrylates of oligoethylene glycols and some others. 

The initiator or iniferter determines the number of growing chains. Several methods of initiation are used. Only three will be considered here. The first involves direct use of a species 1-X (e.g. a dilhiocarbamale ester - Section 9.3.2 or an alkoxyamine - Section 9.3.6) as shown in Scheme 9.4. Ideally, the degree of polymerization is given by eq. I and the molecular weight by eq. 2. 

Once v, is determined under one set of conditions, the procedure is then repeated, varying the concentrations of reactant, catalyst, buffer, etc. The resulting family of v, values can be used to formulate the rate law. This desirable method is probably deserving of wider use in general chemical reactions, just as it is used in biochemical reactions. The method of initial rates is, however, not without its problems. For one thing, the accurate determination of product in the presence of so much substrate is not always feasible. For another, this approach may conceal important effects that come into play only later in the course of the reaction. If the method of initial rates is used, separate experiments must be performed to check these points. 

Since X + In X is a transcendental function, Eq. (2-67) cannot be solved for [A], Two methods are usually used. The method of initial rates is the more common one, since it converts the differential equation into an algebraic one. Values of v(, determined as a function of [A]o, are fit to the equation given for v. This application to enzyme-catalyzed reactions will be taken up in Chapter 4. The other method regularly used relies on numerical integration these techniques are given in Chapter 5. 

This peculiar form applies when a dimeric molecule dissociates to a reactive monomer that then undergoes a first-order or pseudo-first-order reaction. This scheme is considered in Section 4.3. Unless one can work at either of the limits, the form is such that a numerical solution or the method of initial rates will be needed, since the integrated equation has no solution for [A]r. 

Initial rate method. Consider a first-order reaction studied by the method of initial rates. If AY/At represents the slope of the initial linear portion of the recording of Y against time, show that the rate constant is given by... 

The study of reactions with rates that He outside the time frame of ordinary laboratory operations requires specialized instrumentation and techniques. This chapter presents the wide range of methods currently in use for very fast reactions. Extraordinarily slow reactions, on the other hand, have received very little attention. For them, one may resort to measuring a tiny concentration of product over normal times, as in the method of initial rates. 

Method of initial rates (see Initial rates, method of)... 

The monomer 19 can also be polymerized using analogous methods of initiation to those employed in organic polymer science. Radical initiators afford regioirregular polymers, whereas anionic initiators add selectively to the phosphorus atom of the P=C bond and thus yield a regioregular polymer [85]. The product of the initial addition of MeLi across the P=C bond, Mes(Me)P-CPh2Li, was identified spectroscopically. The polymers obtained from anionic initiation are spectroscopically identical to those obtained from the thermolysis. Reasonable molecular weights (ca. 5000-10,000 g mol 0 are obtained when methyllithium is used as an initiator. 

Equations and describe how concentration changes with time when only a single reactant is involved. However, most reactions involve concentration changes for more than one species. Although it is possible to develop equations relating concentration and time for such reactions, such equations are more complicated and more difficult to interpret than the equations that involve just one reactant. Fortunately, it is often possible to simplify the experimental behavior of a reaction. We describe two experimental methods that accomplish this, the isolation method and the method of initial rates. 

A second way to simplify the behavior of a reaction is the method of initial rates. In this method, we measure the rate at the very beginning of the reaction for different concentrations. A set of experiments is done, changing only one initial concentration each time. Instead of measuring the concentration at many different times during the reaction, we make just one measurement for each set of concentrations. The reaction orders can be evaluated from the relationships between the changes in concentration and the changes in initial rates. We illustrate how this works using a gas-phase reaction of H2 with NO 2H2(g) -b 2NO(g) N2(g) + 2H2 0(g)... 

Example provides practice in applying the method of initial rates. 

This technique provides a method of initiating primacord—-and thus any explosive charge—if a regular blasting cap is not available. The device may be rigged as a booby trap with trip wire or it can be fired remotely by the operator. Since the technique does require the destruction of a usable rifle it likely would be used only when there is no other alternative. In addition, care should be taken in all phases of the preparation, because when the weapon is fired it will break into many fragments which would severely injure anyone holding the weapon or close to it. 

The kinetics results of the batch reactor runs lead to the following qualitative observations At low CO pressures (less than about 1 atm) the catalysis appears to be first order in ruthenium over the range 0.018 M to 0.072 M and also in Pco as illustrated by the log Pco vs time plots of Fig. 2 and also shown by the method of initial rates. Changes in the sulfuric acid and water concentrations over the respective ranges 0.25 M to 2.0 M and 4 M to 12 M have relatively small effects on the catalysis rates, although the functionalities are complicated and show concave rate vs concentration curves with maximum rates... 

Reaction rate constants, 21 340 pressure variation and, 13 406 407 of solvents, 10 107 Reaction rates, relative, 10 425 Reactions. See also Chemical reactions Inorganic chemistry reactions Organic chemistry reactions hydrogen peroxide, 14 38—39 methods of initiating, 13 422 microfluidic control of, 26 967—968 Reaction schemes/mechanisms, in kinetic studies, 14 623-625 Reaction solvents, in large-scale... 

The anionic mechanism is similar to that postulated to explain the thermal polymerisation. The apparent general similarity of the polymers produced by the two methods of initiation justifies this. Cross-linking involves additions to the free CN groups, and regular networks with two or more interconnected polymer chains are possible. Thus the structure of the azulmine is highly complex. Termination must occur by reactions of the growing anions with H2CN+ ions formed in the reaction... 

In dispersion polymerization, the monomer and initiator are dissolved in the continuous phase, which acts as a nonsolvent for the developing polymer. The continuous phase can be organic, aqueous, or a mixture of miscible phases. Two methods of initiation have been employed, including gamma radiation [75] and chemical initiation by potassium perox-odisulphate [76]. As the polymer is formed, it precipitates as nanoparticles. These particles are not polymeric precipitates as in precipitation polymerization. Rather, they are swollen by a mixture of the monomer and the continuous phase [39],... 

Given the unreliability of the stab-initiated tests, a second round of testing was performed using a hot nichrome wire to initiate the detonators in place of the NOL-130 stab mix and firing pin. This test was successful and all nine detonators functioned, showing that DBX-1 is more susceptible to this method of initiation. Figure 8 shows the electrical ignition setup. 

Rasmussen and co-workers. Chapter 10, have shown that many free-radical polymerizations can be conducted in two-phase systems using potassium persulfate and either crown ethers or quaternary ammonium salts as initiators. When transferred to the organic phase persulfate performs far more efficiently as an initiator than conventional materials such as azobisisobutyronitrile or benzoyl peroxide. In vinyl polymerizations using PTC-persulfate initiation one can exercise precise control over reaction rates, even at low temperatures. Mechanistic aspects of these complicated systems have been worked out for this highly useful and economical method of initiation of free-radical polymerizations. 

The Methods of Initiating Reaction and their Time Ranges... 

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