Non-uniqueness in determination of terminal and penultimate model reactivity ratios in the styrene-methyl methacrylate free-radical copolymerization system

The terminal and penultimate model reactivity ratios in the free-radical copolymerization of styrene and methyl methacrylate in bulk at 40°C were calculated by means of the simplex and scanning methods. Calculations showed that for the terminal model r₁ and r₂ vary in comparatively narrow ranges of 0.548–0.552 and 0.480–0.483, respectively. For the penultimate model, the most accurate reactivity ratios calculated by the simplex method, which were r₁₁ = 0.727, r₂₂ = 0.490, r₂₁ = 2.890, r₁₂ = 4.583, are surrounded with sets of reactivity ratio values of equal accuracy. The ranges of variation were found to be 0.711–0.746, 0.487–0.492, 2.810–2.970 and 4.213–5.049, respectively. Numerical values of the penultimate r-parameters calculated with the simplex method depend, due to the structure of the multidimensional space (r₁₁, r₂₂, r₂₁, r₁₂, σ), on the initial guess for the r-parameters. Use of the covariance matrix for the estimation of the indetermination ranges is discussed.     

Comparative recalculation of the monomer reactivity ratios in copolymerization for styrene and methyl methacrylate

The monomer reactivity ratios (MMRs) in radical copolymerization for styrene and methyl methacrylate were recalculated by five different methods using literature copolymerization data. The use of approximate 95% confidence limits and their visual inspection helps to separate possibly biased copolymer composition data. The recalculated mean MRR values were r₁ (styrene) = 0.501 ± 0.031 and r₂ = 0.472 ± 0.031. The results of the linear least-squares calculation procedures seldom approach the quality of the nonlinear least-squares analysis according to the method of Tidwell and Mortimer.     

Monomer reactivity ratios in graft copolymerization

This paper discusses monomer reactivity ratios in various radiation- and redox-initiated graft copolymerizations. The polymers studied were polyethylene, cellulose acetate, poly(vinyl chloride), polytetrafluoroethylene, poly(vinyl alcohol), and poly(methyl methacrylate); the comonomer mixtures were styrene–acrylonitrile, methyl acrylate–styrene, acrylonitrile–methyl acrylate, and vinyl acetate–acrylonitrile. The polymer–comonomer mixture systems were so chosen as to permit study of both homogeneous and heterogeneous systems. The homogeneous systems included systems of low and high viscosity. The heterogeneous systems included both polymers swollen by the comonomer mixture and polymers not swollen by the comonomer mixture. None of the homogeneous grafting systems studied showed deviations from the normal copolymerization behavior under a variety of experimental conditions. Monomer reactivity ratios in graft copolymerization were the same as the values in nongraft copolymerization. The heterogeneous systems in which the polymer was swollen by the comonomer mixture yielded grafted copolymer compositions which were the same as those in nongraft copolymerization. The heterogeneous grafting system polytetrafluoroethylene/styrene–acrylonitrile showed deviations from normal copolymerization behavior at low degrees of grafting when the reaction was only on the polymer surface. The behavior became normal at higher degrees of grafting when the system approaches that in which the polymer is swollen by the comonomers. In all reaction systems, it was found that the use of radiation to initiate the reaction does not in any way affect the copolymerization behavior of the two monomers in a comonomer pair.     

A microcomputer program for estimation of copolymerization reactivity ratios

A user-friendly program has been developed to estimate copolymerization reactivity ratios based on a nonlinear minimization algorithm. The use of an optimal experimental design for copolymerization when the Mayo–Lewis model applies is presented. The applicability of the program is demonstrated using actual and simulated experimental data.     

Fractionation of styrene-methyl methacrylate copolymer

Styrene-methyl methacrylate copolymer was fractionated by the column elution and coacervate extraction techniques. Different solvent-nonsolvent combinations were used; both batchwise and continuous column elution fractionations were carried out. Successful resolution of fractions according to molecular weight was achieved. The effect of the solvent-precipitant pair on the fractionation efficiency, as tested by gel permeation chromatography, is discussed. The results of continuous column elution depend significantly on the elution rate.     

Estimation of reactivity ratios using emulsion copolymerization data

An approach for the estimation of reactivity ratios using cumulative copolymer composition–overall conversion data obtained in batch emulsion copolymerization is presented. The approach is based on an algorithm for parameter estimation in ordinary differential equations and takes into account the partition of the comonomers between the different phases present in the system. Both copolymer composition and conversion were considered to be affected by experimental errors. The method was first checked by using simulated data that included random errors. The effect of the initial guess and level of errors on the values of the estimated reactivity ratios was investigated. Once the approach was checked, it was used to estimate the reactivity ratios of the styrene–acrylonitrile system based on data obtained in unseeded batch emulsion copolymerizations of these monomers.     

Optimal estimation of reactivity ratios for acrylamide/acrylic acid copolymerization

Reactivity ratios for the important acrylamide (AAm)/acrylic acid (AAc) copolymerization system exhibit considerable scatter in previously published literature, and therefore, there is a need for more definitive values for these reactivity ratios. An appropriate methodology, based on the error‐in‐variables‐model (EVM) framework along with a direct numerical integration procedure, is applied in order to determine reliable reactivity ratios. The reliability of the results is confirmed with extensive and independent replication. Furthermore, via an EVM‐based criterion for the design of experiments using mechanistic models, optimal feed compositions are calculated, and from these optimal reactivity ratios are estimated for the first time (r_AAm = 1.33 and r_AAc = 0.23) based on information from the full conversion range. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4819–4827     

Estimation of monomer reactivity ratios in free‐radical solution copolymerization of lauryl methacrylate–isobutyl methacrylate

Copolymers of isobutyl methacrylate (i‐BMA) and lauryl methacrylate (LMA) were prepared by free‐radical solution copolymerizations at 70 °C with azobisisobutyronitrile (AIBN) as an initiator. The synthesis of these copolymers was investigated over a wide composition range both at low and high conversion levels. Copolymer compositions were determined from the %C, %H, and %O contents of copolymer by elemental analysis. Monomer reactivity ratios were estimated by analyzing composition data with nonlinear least‐squares (NLLS) models based on Marquardt optimization and van Herk methods. The point estimates, 95% individual confidence intervals and 95% joint confidence intervals are obtained from differential and integral approaches. Even though no explicit integral form for penultimate unit model (PUM) is available, a numerical approach is developed for integral estimation of reactivity ratios from PUM. A simulator program was developed which upon coupling of experimental data, NLLS analysis, and D‐optimal criteria calculates the best optimized values of monomer reactivity ratios and monomer feed compositions in a sequential and iterative order for terminal and penultimate unit models. Moreover, the simulator has the capibilities to calculate all features of van Herk method, maximum compositional drift in each monomer feed composition, and data reconciliation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 112–129, 2004     

Reactivity ratios in conventional and nickel-mediated radical copolymerization of methyl methacrylate and functionalized methacrylate monomers

Copolymerization of an excess of methyl methacrylate (MMA) relative to 2-hydroxyethyl methacrylate (HEMA) was carried out in toluene at 80 °C according to both conventional and controlled Ni-mediated radical polymerizations. Reactivity ratios were derived from the copolymerization kinetics using the Jaacks method for MMA and integrated conversion equation for HEMA (r_MMA = 0.62 ± 0.04; r_HEMA = 2.03 ± 0.74). Poly(ethylene glycol) α-methyl ether, ω-methacrylate (PEGMA, M_n = 475 g mol⁻¹) was substituted for HEMA in the copolymerization experiments and reactivity ratios were also determined (r_MMA = 0.75 ± 0.07; r_PEGMA ∼ 1.33). Both the functionalized comonomers were consumed more rapidly than MMA indicating the preferred formation of heterogeneous bottle-brush copolymer structures with bristles constituted by the hydrophilic (macro)monomers. Reactivity ratios for nickel-mediated living radical polymerization were comparable with those obtained by conventional free radical copolymerization. Interactions between functional monomers and the catalyst (NiBr₂(PPh₃)₂) were observed by ¹H NMR spectroscopy.     

Analysis of the linear methods for determining copolymerization reactivity ratios. II. A critical reexamination of cationic monomer reactivity ratios

A thorough examination of some cationic copolymerization systems by a new method has shown that many published r values have to be corrected significantly and that some are erroneous and meaningless, because for these systems the conventional copolymer compositions equation does not hold. Available information in regard of cationic copolymerizations has been treated in terms of three classes: (a) Systems in which the conventional copolymer composition equation adequately describes the copolymerization mechanism and previous authors justifiably used the two parameter model to calculate reactivity ratios. Our results show that the discrepancy between published r values and the more precise values obtained in this work is about ±23%. (b) Systems in which the approximations implicit in the conventional copolymer composition equation do not hold and the calculated r values are erroneous and misleading. Monomer pairs comprising monomers of significantly different reactivities belong to this class indicating that in copolymerizations in general and in cationic copolymerizations in particular a strong cast system exists, i.e., copolymerization can readily occur within the cast (between monomers of similar reactivities); however, only with difficulty if at all between casts (between monomers of differing reactivities). (c) Systems in which the use of the copolymer composition equation is completely unjustified, the calculated r values are meaningless and in some cases the existence of true copolymers is questioned.     

Monomer reactivity ratios for the copolymerization of styrene with 1,2,4-trivinyl and p-divinylbenzenes

The copolymerization kinetics of 1,2,4-trivinylbenzene (TVB) with styrene do not clearly resemble those of o-, m-, or p-divinylbenzene (DVB), structural elements of which are present in TVB. A control determination of the reactivity ratios for the styrene-p-DVB pair under different conditions (70°C., pre-gel point conversion), run for comparison with the TVB data, show values (r₁ = 0.77; r₂ = 1.46) similar to those previously recorded (r₁ = 0.77; r₂ = 2.08).     

Miscibility of tetramethyl-hexafluoro copolycarbonates with styrene-methyl methacrylate copolymers

The compositions for which blends of copolycarbonates of tetramethyl bisphenol-A and hexafluoro bisphenol-A (TMPC-HFPC) with styrene-methyl methacrylate copolymers (SMMA) are miscible were determined experimentally. These copolymer compsition boundaries were compared to predictions based on the Flory-Huggins theory combined with the binary interaction model. The theoretical predictions employed interaction energies from the literature for the TMPC/PS, PS/PMMA, and TMPC/PMMA pairs, and values for the TMPC/HFPC, HFPC/PS, and HFPC/PMMA pairs were established or verified using independent experiments. The recommended set of interaction energies predicts that miscibility occurs in two separate regions of copolymer compositions. These predictions agree well with the experimental observations. The theoretical requirements for a single, continuous miscible region versus two disjointed miscible regions when the two limiting homopolymer pairs exhibit miscibility, that is, TMPC-PS and HFPC-PMMA in this example, are described. © 1994 John Wiley & Sons, Inc.     

Copolymers in dilute solution. I. Preliminary results for styrene-methyl methacrylate

The dilute solution properties of copolymers are briefly discussed in relation to those of the parent homopolymers. It is shown that copolymer molecules are usually more expanded in solution than would be expected from the averaged behavior of the pure polymers, because of repulsive interactions between the unlike monomer units. A thermodynamic parameter χAB characterizing these interactions can be derived from measurements of the dilute solution properties of copolymers. In favorable cases this parameter can be independently evaluated from studies of ternary systems composed of the two parent homopolymers and a solvent, thus allowing prediction of the behavior of the copolymer. Light scattering and viscosity measurements on fractions of approximately equimolal copolymers of styrene and methyl methacrylate are presented and analyzed. The values of χAB deduced from the results in two solvents agree satisfactorily with each other, but are somewhat larger than those earlier obtained from measurements on ternary systems.     

Monomer reactivity ratios for acrylonitrile–methyl acrylate free‐radical copolymerization

Nonlinear monomer reactivity ratios for the homogeneous free‐radical copolymerization of acrylonitrile and methyl acrylate were determined from ¹H NMR and real‐time Fourier transform infrared (FTIR) analyses. All ¹H NMR data were obtained on polymers isolated at low conversions (<10%), whereas the FTIR data were collected in situ. The copolymerizations were conducted in N,N‐dimethylformamide at 62 °C and were initiated with azobisisobutyronitrile. The real‐time FTIR technique allowed for many data points to be collected for each feed composition, which enabled the calculation of copolymer compositions (dM₁/dM₂) with better accuracy. Monomer reactivity ratios were estimated with the Mayo–Lewis method and then were refined via a nonlinear least‐squares analysis first suggested by Mortimer and Tidwell. Thus, monomer reactivity ratios at the 95% confidence level were determined to be 1.29 ± 0.2 and 0.96 ± 0.2 for acrylonitrile and methyl acrylate, respectively, which were valid under the specific system conditions (i.e., solvent and temperature) studied. The results are useful for the development of acrylonitrile (<90%) and methyl acrylate, melt‐processable copolymer fibers and films, including precursors for carbon fibers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2994–3001, 2004     

Statistical fluorinated copolymers from heterogeneous atom transfer radical copolymerization of styrene and 2,2,2‐trifluoroethyl methacrylate with similar reactivity ratios

Fluorinated copolymers with statistical structure of azeotropic or gradient composition were prepared from heterogeneous atom transfer radical copolymerizations of styrene (S) and 2,2,2‐trifluoroethyl methacrylate (T). The polymerization kinetic studies show that while the propagation rate constant of S increased with a decreasing S content in the comonomer feed ratio, the propagation rate of T decreased with decreases of the S content in the comonomer feed ratio. The polymerization rate and controllability of the heterogeneous ATRP of S and T were regulated by the solubility of Cu(II)/ligand in the reaction mixture, based on a mechanistic analysis and solubility tests of the Cu(II)/ligand system in the reaction media. The reactivity ratios of S and T were 0.22 and 0.35, as evaluated from kinetic analysis of monomer conversions higher than 35%. These statistical polymers self‐assembled in T to form giant vesicles GVs) with broad diameter distribution in the range of 1–10 μm. Unlike the methods normally used to prepare gradient copolymers by spontaneous controlling with feeding model or batch polymerization of comonomers with obvious differences in the reactivity ratio, in this contribution, we report a novel synthetic strategy for preparing gradient copolymers can also be prepared from both monomers with very similar reactivity ratio. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Monomer reactivity ratios for fluoroacrylate and butyl methacrylate in miniemulsion copolymerizations initiated by potassium persulphate

Miniemulsion copolymerization of butyl mathacrylate(BMA) with fluoroacrylate(HFMA,TFMA) was carried out at 70℃by employing potassium persulphate(KPS) as initiator.Copolymer compositions at low conversion levels were determined by ~1H NMR spectra techniques.The reactivity ratios were evaluated by employing Kellen-Tudos(K-T) methods,which yields the apparent reactivity ratios,r_(BMA)=0.74,r_(HFMA) = 0.87 and r_(BMA) = 0.73,r_(TFMA) = 0.75,respectively,and Q- and e-values of HFMA and TFMA were calculated by...     

A new method of estimating monomer reactivity ratios in copolymerization by linear regression methods

Sequential gas-liquid chromotographic analysis of the reaction mixture throughout a copolymerization reaction in conjuction with the improved curve-fitting I (integrated form) method, which accounts for measurements errors in both variables, allows accurate estimation of the monomer reactivity ratios. In this article an alternative method is presented for estimating r values in copolymerization with linear regression only, which is especially suited to cases in which one or two of the r values is close to 1. In these cases the improved curve-fitting I method tends to converge slowly because of the numerical instability of the integrated copolymerization equation. The use of the new method is illustrated for the estimation of the r values for ethylene and vinyl acatate in benzene at 35 kg/cm² and 62°C. The linear regression method was also tried on other copolymerizations and the results are compared with those obtained from the improved curve-fitting I method. The limits of the applicability of the linear regression method were determined by simulated sequential sampling experiments. It appears that the new method is applicable when the product of the r values is between 0.001 and 2, provided both monomer conversions are large enough compared with the measurements error.