Reactivity ratios region

The conversion of aromatic monomers relative to C-5—C-6 linear diolefins and olefins in cationic polymerizations may not be proportional to the feedblend composition, resulting in higher resin aromaticity as determined by nmr and ir measurements (43). This can be attributed to the differing reactivity ratios of aromatic and aHphatic monomers under specific Lewis acid catalysis. Intentional blocking of hydrocarbon resins into aromatic and aHphatic regions may be accomplished by sequential cationic polymerization employing multiple reactors and standard polymerization conditions (45). 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Applications of the method to the estimation of reactivity ratios from diad sequence data obtained by NMR indicates that sequence distribution is more informative than composition data. The analysis of the data reported by Yamashita et al. shows that the joint 95% probability region is dependent upon the error structure. Hence this information should be reported and integrated into the analysis of the data. Furthermore reporting only point estimates is generally insufficient and joint probability regions are required. 

Detailed kinetic studies comparing the chemical reactivity ofK-region vs. non-K-region arene oxides have yielded important information. In aqueous solution, the non-K-region epoxides of phenanthrene (the 1,2-oxide and 3,4-oxides) yielded exclusively phenols (the 1-phenol and 4-phenol, respectively, as major products) in an acid-catalyzed reaction, as do epoxides of lower arenes (Fig. 10.1). In contrast, the K-region epoxide (i.e., phenanthrene 9,10-oxide 10.29) gave at pH < 7 the 9-phenol and the 9,10-dihydro-9,10-diol (predominantly trans) in a ratio of ca. 3 1. Under these conditions, the formation of this dihydrodiol was found to result from trapping of the carbonium ion by H20 (Fig. 10.11, Pathway a). At pH > 9, the product formed was nearly ex-... 

The HBA/HNA system provides a more suitable system for study, since it is prepared by melt polymerization of the two monomers and is far more stable at elevated temperatures compared to the PHBA/PET. The HBA/HNA copolymers are soluble in pentafluorophenol permitting use of NMR techniques to characterize diad sequences. In Fig. 13b,c the 13CNMR spectrum of the carboxyl carbon region of the HBA/HNA copolyesters of the 73/27 and 48/52 systems is shown [34]. Also shown in Fig. 13a,d are the spectra of 13C enriched HBA and HNA containing copolymers permitting unique identification of the diad sequences. As a result of this technique it was possible to determine the reactivity ratios of the two monomers by analyzing the 50/50 copolymer after polymerization to a molar mass value of 2000 [35]. Examination of the copolymer by 13C NMR showed the same ratio of monomers as in the starting... 

The calculations of the statistical characteristics of such polymers within the framework of the kinetic models different from the terminal one do not present any difficulties at all. So in the case of the penultimate model, Harwood [193-194] worked out a special computer program for calculating the dependencies of the sequences probabilities on conversion. Within the framework of this model, Eq. (5.2) can be integrated in terms of the elementary functions as it was done earlier [177] in order to calculate copolymer composition distribution in the case of the simplified (r 2 = Fj) penultimate model. In the framework of the latter the possibility of the existence of systems with two azeotropes was proved for the first time and the regions of the reactivity ratios of such systems [6] were determined. In a general version of the penultimate model (2.3-24) the azeotropic compositions x = 1/(1 + 0 ) are determined [6] by the positive roots 0 =0 of the following... 

In order to elucidate the effect of temperature, the authors of Refs. [310,210] determined experimentally the boundary points x x = 0.08 and XgX = 0.65 of the transparency region for the (ST + HA) system at complete conversion, p = 1, when in the course of synthesis the temperature was increased in a given way from 28 °C to 78 °C. Despite a noticeable difference between such a regime and the isothermal one (see Fig. 24), it was found that the regions, in which at p = 1 turbid copolymers were formed, practically coincide. The same could be said about the calculated values of dispersion cr2(l) at the boundary points of the mentioned regions. This might be associated with a rather weak dependence of the reactivity ratios on temperature. A similar practical independence of the turbidity region... 

As shown above, the miniemulsion is a very efficient system for production of copolymer particles from hydrophobic and hydrophilic monomers. In the case of direct (oil-in water) miniemulsion, if the hydrophilic monomer is used in smaller quantities, there is a possibility to form an amphiphilic copolymers close to the interface of the nanoparticles. This shell region of the polymeric particle can be considered as a hydrogel shell. The structure of the hydrogel shell mainly depends on the monomer(s) concentration, reactivity ratios of the monomers, their solubility in water, and the type of surfactant used. 

The first to attempt this were Tosi, Valvassori and Ciampelli [284] who observed a relationship between infrared methyl group absorptions in the region 900—1000 cm and the reactivity ratio product rjTj. These infrared bands were shown to contain characteristic propene absorptions for isolated units at 935 cm and for sequences at 973 cm , and a distribution index containing the rates of these absorptions was found to correlate well with the fractions of E—P(fi2) and E—E(fj i) bonds given by [285]... 

In a subsequent paper (5S), Tarasov and coll, have shown that it is more appropriate to talk about an azeotropic region rather than an azeotropic point and have discussed some cases in which the reactivity ratios are lower or hi er than imity. 

The above conclusion on the role of reactivity ratios on microstructure assumes the absence of rapid transesterification reactions between chains. Since such processes might also tend to randomize the microstructure, it seemed important to isolate the role of interchain transesterification. A unique experiment was designed in which a 13c labeled carbonyl in acetoxy benzoic acid monomer (B ) was reacted with the dimer of HBA-HNA. At 99% enrichment, the only resonances in the carbonyl region of the spectrum will arise from the enriched benzoic acid carbonyl. In the absence of any interchain transesterification the microstructure of the polymer would consist only of B -B dyads (see scheme 1). 

As regards the methyl rocking region, Drushel et at. showed that at certain composition levels (ca. 22 wt %C3) maximum absorption occurs near 10.4 p and they assume that it could be produced by two contiguous C3 units with C2 units on each side. Such an attribution is quite reasonable not only could it offer an alternative interpretation of this complex band, but it could also extend the relationship between IR absorption and sequence distribution beyond the values of the copolymer composition covered by Eq. (2). Unfortunately the uncertainty regarding the absorptivities makes it impossible to reconcile the fractions of C3 units present in sequences of one, two, three or more members, as deduced from the bands at 10.67, 10.4 and 10.3 p and reported in Table 5 of Ref. (25), with those predicted for any value of the product of reactivity ratios. 

A new type of copolymer resist named ESCAP (environmentally stable chemical amplification photoresist) has recently been reported from IBM [163], which is based on a random copolymer of 4-hydroxystyrene with tert-butyl acrylate (TBA) (Fig. 37), which is converted to a copolymer of the hydroxystyrene with acrylic acid through photochemically-induced acid-catalyzed deprotection. The copolymer can be readily synthesized by direct radical copolymerization of 4-hydroxystyrene with tert-butyl acrylate or alternatively by radical copolymerization of 4-acetoxystyrene with the acrylate followed by selective hydrolysis of the acetate group with ammonium hydroxide. The copolymerization behavior as a function of conversion has been simulated for the both systems based on experimentally determined monomer reactivity ratios (Table 1) [164]. In comparison with the above-mentioned partially protected PHOST systems, this copolymer does not undergo thermal deprotection up to 180 °C. Furthermore, as mentioned earlier, the conversion of the terf-butyl ester to carboxylic acid provides an extremely fast dissolution rate in the exposed regions and a large... 

The error-in-variables method was used to estimate the reactivity ratios. This method was developed by Reilly et al. (57, 58), and it was first applied for the determination of reactivity ratios by O Driscoll, Reilly, and co-workers (59, 60). In this work, a modified version by MacGregor and Sutton (61) adapted by Gloor (62) for a continuous stirred tank reactor was used. The error-in-variables method shows two important advantages compared to the other common methods for the determination of copolymer reactivity ratios, which are statistically incorrect, as for example, Fineman-Ross (63) or Kelen-Tiidos (64). First, it accounts for the errors in both dependent and independent variables the other estimation methods assume the measured values of monomer concentration and copolymer composition have no variance. Second, it computes the joint confidence region for the reactivity ratios, the area of which is proportional to the total estimation error. 

Figure 3. Joint confidence regions for the reactivity ratios in AAM-DMAEM at 60 °C. Key —, KPS initiator ---------------, ACV initiator.

Figure 4. Joint confidence region for the reactivity ratios in AAM-DMAEA at 60 °C with ACV as the initiator.

Einally, we are concerned with the precision of the reactivity ratios or, in other words, the joint confidence regions of the parameter estimates. We have stated at the beginning of this section that our objective is to estimate reactivity ratios of maximum precision. This is equivalent to minimizing the joint confidence region of the parameters. The joint confidence regions can be generated using methods such as shown by Polic et al. [117]. 

Two distinct regions can be easily identified in Figure 2.3 a sharp high-crystallinity peak (low a-olefin fraction) and a broad low-crystallinity peak (high a-olefin fraction). These two regions are associated with at least two types of active sites, one with a much lower reactivity ratio toward incorporation of a-olefin than the other. As the relative fractions of polymer under these two modes is varied, we go from HDPE - with a unimodal, high-crystallinity peak and sometimes a small, lower crystalHnity tail - to LLDPE, VLDPE and ULDPE resins, having a very pronounced lower crystallinity peak, which may, sometimes, show additional peaks. 

Random Styrene-Diene Copolymers. Random copolymers of butadiene (SBR) or isoprene (SIR) with styrene can be prepared by addition of small amounts of ethers, amines, or alkali metal alkoxides with alkylhthium initiators. Random copolymers are characterized as having only small amounts of block styrene content. The amoimt of block styrene can be determined by ozonoly-sis or, more simply, by integration of the nmr region corresponding to block polystyrene segments (S = 6.5-6.94 ppm) (180). Monomers reactivity ratios of tb = 0.86 and rs = 0.91 have been reported for copolymerization of butadiene and styrene in the presence of 1 equiv of TMEDA ([TMEDAMRLi] = 1) (181). However, the random SBR produced in the presence of TMEDA will incorporate the butadiene predominantly as 1,2 imits. At 66°C, 50% 1,2-butadiene microstructure will be obtained for copolymerization in the presence of lequiv of TMEDA (134). In the presence of Lewis bases, the amounts of 1,2-polybutadiene enchainment decreases with increasing temperature. 

In this method, nonreactive compounds are employed as the high-refractive-index component [11]. For example, MM A and bromobenzene (BB), which have higher refractive indices than PMMA, can be utilized as the monomer and the nonreactive compound, respectively. The fabrication procedure is the same as in the photo-copolymerization and interfacial-gel polymerization methods. However, the principle of formation the GI profile is different. In contrast to the previous methods that use the difference in the monomer reactivity ratios, in this method the difference in the molecular size is important. Because the molecular size of MM A is smaller than that of BB, MM A more easily diffuses into the gel phase. Thus, BB molecules are concentrated into the middle region to form the GI profile as the polymerization progresses. The mechanism is schematically described in Figure 5.11. 

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