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Copolymerizations between pairs of cyclic esters, acetals, sul des, siloxanes, alkenes, lactams, lactones, N-carboxy-a-amino acid anhydrides, imines, and other cyclic monomers

Type a name for the form. Click OK. Access lists the form among the database objects in the Navigation pane.

A (x(t), t) ,



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have been studied [Frisch and Reegan, 1969; Ivin, 1987; Ivin and Saegusa, 1984; Kendrick et al., 1989; Sebenda, 1989; Tomalia and Killat, 1985]. Copolymerizations have also been achieved between closely re lated types of monomers such as cyclic ethers with cyclic acetals or lactones with lactides and cyclic carbonates [Basko et al., 2000; Keul et al., 1988; Kricheldorf et al., 1985]. The interpretation of experimental monomer reactivity ratios is subject to the cautions described above. When copolymerization proceeds with minimal complications, the r values can often be analyzed by considering the effects of ring size on the general tendency toward ring opening (see considerations in Sec. 2-5b) and the reactivity toward attack by the particular propagating species. For those polymerizations involving a cyclic propagating center (e.g., oxonium ions in cyclic ether polymerization), there is also the need to consider the effect of ring size on formation of the propagating center. Some monomers with no tendency toward homopolymerization are found to have some (not high) activity in copolymerization. This behavior is found in cationic copolymerizations of tetrahydropyran, 1,3-dioxane, and 1,4-dioxane with 3,3-bis(chloromethyl)oxetane [Dreyfuss and Dreyfuss, 1969]. These monomers are formally similar in their unusual copolymerization behavior to the radical copolymerization behavior of sterically hindered monomers such as maleic anhydride, stilbene, and diethyl fumarate (Sec. 6-3b-3), but not for the same reason. The copolymerizability of these otherwise unreactive monomers is probably a consequence of the unstable nature of their propagating centers. Consider the copolymerization in which M2 is the cyclic monomer with no tendency to homopolymerize. In homopolymerization, the propagation depropagation equilibrium for M2 is completely toward





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(8.42)

7-120

What (8.42) is supposed to tell us is how x evolves in time. The form (8.42) is really shorthand for the update formula,

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Oct 31, 2018 · Steps to convert excel document to PDF programmatically: Create a new C# console application project. Install the Syncfusion.ExcelToPdfConverter.WinForms NuGet packages as reference to your .NET Framework application from NuGet.org. Include the following namespaces in the Program.cs file.

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monomer. However, with the second monomer M1 present, the species LXXXVIII adds M1 before depropagation can occur and copolymerization of M1 and M2 results. Similar behavior has been observed for the comonomer pairs b-propiolactone g-butyrolactone and cyclopentene cyclohexene [Ivin et al., 1979; Tada et al., 1964]. The second monomer in each pair does not homopolymerize, but copolymerization occurs. The anionic copolymerization (using an acetylated initiator) of E-caprolactam (M1 ) and a-pyrrolidinone (M2 ) illustrates the problem of interpreting r1 and r2 values obtained by employing the standard copolymerization equation (Eq. 6-12). The monomer reactivity ratios have been calculated as r1 0:75 and r2 5:0 with the conclusion that a-caprolactam is about 8 times more reactive than E-pyrrolidinone [Kobayashi and Matsuya, 1963]. However, a detailed study of the system indicates that the copolymer composition is not determined by the rate constants k11 , k12 , k22 , and k21 for the various homo- and cross-propagation reactions [Bar-Zakay et al., 1967]. Transacylation involving an exchange of the monomer segments in the initiating and propagating imides, occurs at a much faster rate than any of the various

x(x + dt) = x(t)

7-121

+ A (x(t), t) dt,

propagation reactions. The copolymer composition is thus dependent on the transacylation equilibrium according to

(8.43)

d M1 Kt M 1 d M2 M 2 7-122

where [M ] and [M ] represent the concentrations of the lactam anions. The ratio [M ]/ 1 2 1 [M ] is determined by the relative acidities of the two monomers by the equilibrium 2

which describes the information content of (8.42) explicitly. In the language of statistics, a variable that evolves in time, such as, x, is called a process. This sort of update formula describes a "memoryless" process in the sense that only the present value of x is required to calculate its update rather than requiring its past values. This process is also deterministic and continuous. 9 Then the natural stochastic generalization of a first-order differential equation is a continuous memoryless stochastic process, usually referred to as a continuous Markov process. Let us look for the most general form the increment of a continuous Markov process X(t) can take.1O As the process X(t) is "memoryless," this increment can only depend on the time step dt, the present time t, and X (t) the present value of our process. So we can write it as a function of dt, t, and X(t): say,

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