Reactivity ratio determination

It is also possible to process copolymer composition data to obtain reactivity ratios for higher order models (e.g. penultimate model or complex participation, etc.). However, composition data have low power in model discrimination (Sections 7.3.1.2 and 7.3.1.3). There has been much published on the subject of the design of experiments for reactivity ratio determination and model discrimination.49 "8 136 137 Attention must be paid to the information that is required the optimal design for obtaining terminal model reactivity ratios may not be ideal for model discrimination.49... 

One final point should be made. The observation of significant solvent effects on kp in homopolymerization and on reactivity ratios in copolymerization (Section 8.3.1) calls into question the methods for reactivity ratio measurement which rely on evaluation of the polymer composition for various monomer feed ratios (Section 7.3.2). If solvent effects arc significant, it would seem to follow that reactivity ratios in bulk copolymerization should be a function of the feed composition.138 Moreover, since the reaction medium alters with conversion, the reactivity ratios may also vary with conversion. Thus the two most common sources of data used in reactivity ratio determination (i.e. low conversion composition measurements and composition conversion measurements) are potentially flawed. A corollary of this statement also provides one explanation for any failure of reactivity ratios to predict copolymer composition at high conversion. The effect of solvents on radical copolymerization remains an area in need of further research. 

The solvent in a bulk copolymerization comprises the monomers. The nature of the solvent will necessarily change with conversion from monomers to a mixture of monomers and polymers, and, in most cases, the ratio of monomers in the feed will also vary with conversion. For S-AN copolymerization, since the reactivity ratios are different in toluene and in acetonitrile, we should anticipate that the reactivity ratios are different in bulk copolymerizations when the monomer mix is either mostly AN or mostly S. This calls into question the usual method of measuring reactivity ratios by examining the copolymer composition for various monomer feed compositions at very low monomer conversion. We can note that reactivity ratios can be estimated for a single monomer feed composition by analyzing the monomer sequence distribution. Analysis of the dependence of reactivity ratios determined in this manner of monomer feed ratio should therefore provide evidence for solvent effects. These considerations should not be ignored in solution polymerization either. 

In addition, the molar mass (which is proportional to the intrinsic viscosity, [t]]. Tab. 6.17) of the copolymer decreases with increasing potential in the silent system, whereas in the sonicated case it is effectively constant. Overall ultrasound also appears to produce a more uniform reaction system in that in the silent system the reactivity ratio (determined by infra red spectroscopy) increases with electrode potential, whilst under sonication it remains fairly constant. 

Table 9 Reactivity ratios determined for 2-oxazoline copolymerizations utilizing both the Mayo-Lewis terminal model (MLTD) and the extended Kelen-Tiidds (KT) method. Initial defines - 20% conversion and final defines >50% conversion...

A method for calculating apparent reactivity ratios based on run number theory has been applied to "starved-feed" styrene/ ethyl acrylate systems. The reactivity ratios found are in agreement with those determined from solution polymerization data. The further confirmation of the observed agreement between reactivity ratios determined at low conversions and those determined by run number theory in "starved-feed" high conversion copolymerization requires the analysis of other comonomer pairs. 

Table 6.3 Summary of reactivity ratios determined by various methods for the bulk copolymerization of styrene with methyl a-hydroxymethyl acrylate at T = 80 °C [226]...

Here [Pf ] is the concentration of growing centres ending in monomer x and kx y is the absolute rate coefficient of reaction of P with monomer y. Two difficulties arise in anionic polymerization. In hydrocarbon solvents with lithium and sodium based initiators, [Pf ] is not the total concentration of polymer units ending in unit x but, due to self-association phenomena, only that part in an active form. The reactivity ratios determined are, however, unaffected by the association phenomena. As each ratio refers to a common active centre, the effective concentration of active species is reduced equally to both monomers. In polar solvents such as tetrahydrofuran, this difficulty does not arise, but there will be two types of each reactive centre Pf, one an anion and the other an ion-pair. Application of eqn. (22) will give apparent rate coefficients as discussed in Section 4 if total concentrations of Pf are used. Reactivities can change with concentration if defined on this basis. 

In copolymerizations of cyclic ethers, too, basicity of the monomers seems to correlate well with the reactivity ratios determined from copolymer composition. Recently, Saegusa et al. [54] have pointed out that the apparent values of the monomer reactivity ratios in cyclic ether copolymerizations may be more influenced by the exchange... 

Recently, the Research Group on NMR, SPSJ, assessed reliability of copolymer analysis by NMR using three samples of radically prepared copolymers of MMA and acrylonitrile with different compositions. 1H and 13C NMR spectra of the copolymers were collected from 46 NMR spectrometers (90 500 MHz) and the composition and sequence distribution were determined.232 Table 14 summarizes the monomer reactivity ratios determined by 13C NMR analysis. The large difference between rxx and r2X indicates the presence of a penultimate effect in this radical copolymerization, as previously reported.233 The values of riy, especially rxx, depended on the comonomer feed ratio, suggesting higher order of neighbouring unit effect on the reactivity of chain-end radicals. 

These equations are based on the assumption that the methoxy proton resonance associated with MMM triads occurs entirely in the A-area. The slopes and intercepts of HR plots indicate the distribution of (MMS+SMM)- and (SMS)- methoxy proton resonances among the A, B and C areas. The reactivity ratios determined in this work are based on the assumption that X = X = 0.5, X" 0.,... 

These equations are similar to those assumed for the reactivity ratio determination. In contrast to what has been observed for conventional styrene-MMA copolymers, however, these equations indicate that a substantial proportion of the (SMM+MMS)-type resonance appears to occur in the C-area. The proportion of methoxy resonance observed in the C-area, in fact, exceeds P(SMS) by a substantial amount for many of the copolymers. This can be due to the assumption of an inadequate model for the copolymerization reaction, to the use of incorrect reactivity ratios and cyclization constants for the calculations or to an inadequate understanding of the methoxy proton resonance patterns of S/MMA copolymers. It is possible that intramolecular reactions between propagating radicals and uncyclized methacrylic anhydride units present on propagating chains result in the formation of macrocycles. Failure to account for the formation of macrocycles would result in overestimation of rc and rc and in underestimation of the proportions of MMA units in SMS triads in the derived S./MMA copolymers. This might account for the results obtained. An alternate possibility is that a high proportion (>50%) of the M-M placements in the copolymers studied in this work can be expected to have meso placements (], J2), whereas only a small proportion of such placements ( 20%) are meso in conventional S/MMA copolymers. Studies with molecular models (20) have indicated that the methoxy protons on MMA units centered in structures such as the following can experience appreciable shielding by next nearest styrene units. 

All IR investigations of sequence distribution so far published rely on the terminal copolymerization model, which assumes that the kinetics of copolymerization are governed only by the probability that monomer units from the feed will be added to the last unit of the growing chain, and that there is only one active site present in the catalyst system, whether homogeneous or heterogeneous. As will be shown later (Section 3.4), this is only an approximation multiple active species are formed by many soluble Ziegler-Natta catalysts, so that the product of reactivity ratios determined from the normal copolymerization equation does not always exactly predict the actual sequence distribution in the copolymer. 

The basicity of esters is similar to that of related ethers, therefore, in copolymerization random structures could be expected. THF (pKb = 5.0) and BCMO (pKb = 5.65) were copolymerized with e-caprolactone (eCL pKb = 5.31) and P-propiolactone (PPL, pKb = 10.06), eCL and cyclic ethers enter the copolymer with nearly the same rates. The reactivity ratios determined by the Mayo-Lewis method are rt(BCMO) = 0.24, r2(eCL) = 0.44 and rt(THF) = 0.7, r2(eCL) = 0.3 4C). r, should be higher for THF(Mj) because the reversibility of THF polymerization has not been taken into account (cf. Sect. 15.1.3.1). rt and r2 values suggest the formation of nearly random copolymers. The microstructure of BCMO-eCL copolymers was studied by NMR spectroscopy, and the new signals B and A due to heterodyad appeared [cf. Eq. (15-41)]. Simultaneously the ratio of signals C/D decreased from 2 to a lower value ... 

Table HI. Comparison of the Reactivity Ratios Determined by Different Authors...

Tbma = 0.77, which agrees well with literature values and with the reactivity ratios determined by NMR (rMMA = 0-75, Tbma = 0.98). 

Table 9 Results of ethene reactivity ratio determinations with soluble catalysts. ...

Sulfobetaine cydopolymers. The first sulfobetaine cyclopolymer series OGQ) consists of the copolymers of 6 with 8 (Scheme 6) (42,43). Compositional analysis of this series of cyclopolymers is listed in Table 3. Reactivity ratios, determined via nonlinear least squares analysis " of chemical compositions determined from gated-decoupled C NMR, indicate random incorporation of the comonomers (ri=1.14 r2=0.97). The five-membered ring structure common to polymerized diallyl ammonium salts was retained in the sulfobetaine mer unit. Weight average molecular weights for this series range from 3.04 x 10" to 6.03 x 10 g mol. Second virial coefficients decrease from 8.78 x 10"" to 2.50 x lO"" ml mol g as the amount of 8 incorporated into the copolymer increases. 

Larraz E, Elvira C, GaUardo A, San Roman J. Radical copolymerization studies of an amphiphilic macromonomer derived from Triton X-100. Reactivity ratios determination hy in situ quantitative H NMR monitoring. Polymer 2005 46 2040-2046. 

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