First-order Markov Statistics Research Articles

Microphase Separation of Statistical Multiblock Copolymers

Random multiblock copolymers are characterized by a number of parameters, and their self-assembly is controlled, in particular, by correlations in monomer unit sequences. We investigate the microphase separation of random multiblock copolymers composed of A and B homo-oligomers (macromonomers) in melts. The copolymer synthesis and self-assembly are studied by computer simulations using the dissipative particle dynamics technique. The copolymers are formed by irreversible step-growth polymerization in an equimolar melt of end-functionalized macromonomers of length M up to a high conversion degree. Correlations between macromonomers of different types along the chains are controlled by the reaction probabilities. The molar mass and block mass distributions are described for linear macromolecules and for cycles. Macromonomer sequences in linear chains are well described by the first-order Markov statistics. With an increase in the Flory–Huggins parameter χ, microphase separation into a lamellar structure, for close-to-alternating block copolymers, and into irregularly arranged domains, for Bernoullian sequences of macromonomers, occurs. The transition χM values are approximately twice those obtained with weak segregation theory [Fredrickson, G. H. Macromolecules1992, 25, 6341−6354] and approximately half the values for which microphases were previously detected in the simulations of random copolymer melts [Gavrilov, A. A. J. Chem. Phys.2013, 139, 224901]. Microphase separation is described by the static structure factor and local composition, besides the block positions are monitored visually. The lamellar thickness H is always between the unperturbed sizes of one- and two-macromonomer blocks, and we characterize the separation as a moderate segregation regime. For the close-to-alternating block copolymers at a fixed χ, the thickness scales with the average block length approximately as H ∼ N̅bl2/3 that is in agreement with the theoretical description (Supporting Information) considering the elastic response of the shortest blocks only.

Investigation of poly(α-methyl styrene) tacticity synthesized by photo-polymerization

In this work, poly(α-methyl styrene) (PAS) was synthesized by free radical photo-polymerization. The tacticity and microstructure of PAS were studied by 13C nuclear magnetic resonance spectroscopy (13C NMR). Assignments of all stereo sequences were carried out at pentad and hexad levels of quaternary aliphatic, quaternary aromatic, and methylene carbons using 13C NMR in deuterated chloroform at 20 °C and 50 °C, respectively. It was found that by increasing the NMR acquisition temperature, higher resolution and higher splitting of the peaks were achieved for all mentioned carbons. Bernoullian and first-order Markov statistics were used for all carbons and the results were compared with experimental data by statistical method. It was shown that Bernoullian statics model fit slightly better than first-order Markov statics model for the assigned sequences. The results indicated that corresponding values of probability (Pm) was equal to 0.234, suggesting that the racemic addition was almost higher than the meso-one. The effect of the deuterated solvent on the peak resolution and the splitting of syndiotactic and isotactic sequences was investigated by replacing deuterated tetrahydrofuran with deuterated chloroform. It was observed that the peak resolution and the splitting in deuterated chloroform are much more than deuterated tetrahydrofuran.

Synthesis of ultrahigh-molecular-weight ethylene-1-hexene copolymers with high hexene content via living polymerization with fluorinated bis(phenoxy-imine) titanium(IV).

The fluorinated FI-Ti catalyst bis[N-(3-propylsalicylidene)-pentafluoroanilinato] titanium(IV) dichloride (PFI) combined with dried methylaluminoxane (dMAO) is investigated for ethylene/1-hexene copolymerization at 50 °C under atmospheric pressure. The reaction shows good livingness and has a high activity at high [H]/[E] molar ratios up to 14. Ultrahigh molecular weight (>1.4 × 10(6) g mol(-1) ) copolymers with high 1-hexene content (>25 mol%) are prepared. Kinetic parameters of the copolymerization with PFI are determined. The first-order Markov statistics applies and the product of the reactivity ratios r1 r2 is close to 1, giving random unit distributions.

Characterization of Backbone Structures in Poly(vinylidene fluoride-co-hexafluoropropylene) Copolymers by Multidimensional 19F NMR Spectroscopy

Advanced modern multidimensional solution NMR experiments have been used to deduce the sequence distribution in poly(VDF-co-HFP) copolymers. Assignment of 19F resonances from different monomer- and regio-sequences in poly(VDF-co-HFP) copolymer were identified. In addition to corroborating some assignments reported in earlier literature, this work provides assignments of some new resonances from the spectra of poly(VDF-co-HFP) copolymer, which resulted from better dispersion of the resonances. These assignments are used for the monomer sequence analyses of two polymers using first-order Markovian statistics, and the relative reactivities of the monomers during polymerization are discussed. The results from this study provide insight into the polymerization chemistry for this fluoropolymer.

Copolymerization of Ethylene with Norbornene Catalyzed by Cationic Rare-Earth Metal Half-Sandwich Complexes

We report on copolymerizations of ethylene with norbornene with half-sandwich rare-earth metal catalysts generated by activation of dialkyl complexes [Ln(η5-C5Me4SiMe2R)(η1-CH2SiMe3)2(THF)] (Ln = Sc, R = Me (1); Ln = Sc, R = C6F5 (2); Ln = Y, R = C6F5 (3); Ln = Lu, R = C6F5 (4)) with [Ph3C][B(C6F5)4]. Complexes 1 and 2 showed excellent activities, whereas complex 3 gave poor activity and 4 was practically inactive. Weak stabilization of metal center by bulkier silyl group of the tetramethylcyclopentadienyl ring in complexes 2 and 3 allows controlled copolymerization (Mw/Mn < 1.3). Mainly atactic alternating P(E-co-N) copolymers were obtained with the active catalytic systems. These copolymerizations were well described by first-order Markov statistics.

The effect of temperature on tacticity for bulk thermal polymerization of styrene

AbstractThree types of polystyrenes were prepared at different temperatures of 50, 150 and 250°C by bulk thermal polymerization of styrene below 20 percent of conversion. The assignment of all stereosequences at pentad level of quaternary aromatic carbon and hexad level of methylene carbon of the polystyrenes were done using 13C Liquid NMR in deuterated chloroform at similar conditions. Bernoullian and first-order Markov statistics were calculated and the results were compared with experimental NMR results. It is shown that first-order Markov statistics fit slightly better than Bernoullian statistics for the assigned carbons. The results indicated that by increasing polymerization temperature the probability of meso addition (Pm) in polystyrene chains was enhanced. Pm was calculated for polystyrenes prepared at 50, 150 and 250°C and corresponding values were 0.378, 0.398 and 0.402 respectively. It was shown that by increasing temperature the polymerization is directed toward the Bernoullian propagation. By increasing the NMR acquisition temperature from 20 to 65°C higher resolution especially in quaternary aromatic carbon was achieved and the related peak was splitted to 16 peaks corresponding to a heptad level compared to 10 peaks in 20°C.

Assignment of finely resolved 13C NMR spectra of poly(vinyl alcohol)

13C NMR spectra of three poly(vinyl alcohol)s differing in the stereoregularity (atactic, syndiotactic-rich and isotactic-rich) were determined in DMSO- d 6 and D 2O. The methylene and methine carbon absorptions including so far unassigned ones (mmmr heptad signals in mm-centered region and all heptad signals in mr-centered region) were completely assigned with hexads and heptads, respectively, and the assignments were quantitatively confirmed for atactic and syndiotactic-rich poly(vinyl alcohol)s. The isotactic-rich polymer showed a discrepancy between the observed and the calculated intensities, assuming the first-order Markov statistics, due to difficulty in determining its polymerization mechanism.

Microstructure of the Copolymer Chain Generated by Anionic Ring-Opening Polymerization of a Model Cyclotrisiloxane with Mixed Siloxane Units

Sequencing of siloxane units was studied in the copolymer chain formed by anionic polymerization of 2,2,4,4-tetramethyl-6,6-diphenylcyclotrisiloxane. The study involved three polymerization systems: lithium silanolate in THF, potassium silanolate complexed with 18-crown-6 in toluene, and tetramethylammonium silanolate in toluene. The sequencing proved to be a very good diagnostic tool for the studies of polymerization chemoselectivity. In all the three mentioned systems the chemoselectivity was high. In particular, processes leading to chain cleavage, such as backbiting and chain fragment interchange, occurred at a much lower rate than propagation, which allowed for quantitative studies of regioselectivity in polymerization. The pentad analysis, performed using the first-order Markov statistics, completed by the determination of the unit sequence at chain extremities, permitted the determination of the contributions from the monomer ring openings at three nonequivalent sites. The regioselectivity is poor...

General matrix formula for the weight-average molecular weights of crosslinked polymer systems

On the basis of the first-order Markovian statistics, we propose a general matrix formula for the weight-average molecular weight of crosslinked polymer systems, explicitly given by M w = M w.o + WX o (I - X) 1 S f This equation is valid for both step and chain-growth polymerizations, including those in a nonequilibrium state irrespective of the reactor types used. In the context of the present theory, the onset of gelation is simply stated as a point at which the largest eigenvalue of the matrix X reaches unity (i.e., det(I - X) = 0). The present theory provides a unified point of view for various types of gelling systems.

Microstructure and pressure—volume—temperature properties of ethene/1-octene random copolymers

Copolymers of ethene and 1-octene were synthesized covering the entire composition range by means of the methylalumoxane activated rac-Me 2 Si(2-MeBenz[e]Ind) 2 ZrCl 2 catalyst. 13 C-NMR spcctroscopy revealed first-order Markov statistics to be reasonably suited for the description of the copolymer sequence distribution. Characteristic parameters of ethene/1-octene copolymers were obtained by evaluation of pressure-volume-temperature data using the Flory-Orwoll-Vrij equation-of-state theory. The characteristic pressure could not be correlated with 1-octene comonomer incorporation when assuming validity of the mixing rules known for homopolymer blends, whereas the characteristic specific volume and characteristic temperature are independent of copolymer composition within experimental errors. A possible explanation is presented for why the attempts to predict the characteristic pressure of ethene/1-octene copolymers from the corresponding homopolymer parameters fail using Flory's mixing rules.

Synthesis of microsequential methylvinylsiloxane-dimethylsiloxane copolymers by nonequilibrium copolymerization

Nonequilibrium anionic ring-opening copolymerization of 1,3,5,7-tetramethyl-1,3,5,7-tetravinylcyclotetrasiloxane (V4) with hexamethylcyclotrisiloxane (D3) was examined as a route to methylvinyl–dimethylsiloxane microsequential copolymers. The copolymerization was carried out in toluene and was initiated with Me3SiCH2Li using DMSO as the promoter. Distribution of siloxane units obtained from kinetic analysis based on first-order Markovian statistics was compared with that found from analysis by 29Si NMR spectroscopy. Results showed that although chain transfer and back-biting play some role in this system, the kinetics of copolymerization may be described to a reasonable approximation by the first-order Markov model. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 137–145, 1998

NMR Sequence Analysis for Copolymers Made at High Conversions

Two analytical methodologies have been devised to treat the NMR sequence data of copolymers that are made at high conversions. The first approach is a computer simulation method whereby the copolymerization is simulated through a Monte Carlo process, and the copolymer sequences obtained are compared with the observed NMR data. In the second approach, the NMR triad data are directly analyzed through the first-order Markovian statistics with provision made for conversion. A simplex algorithm is used to optimize the parameters. The procedure has been automated. Examples are shown to illustrate the use of these approaches.

Influence of Indenyl Ligand Substitution Pattern on Metallocene-Catalyzed Ethene Copolymerization with 1-Octene

The influence of silylene-bridged bis(indenyl) ligand substitution, especially benzannelation and 2-methyl substitution, on methylaluminoxane-activated metallocene-catalyzed ethene/1-octene copolymerization in toluene at 40 °C was investigated. 2-Methyl substitution gave significantly higher molecular masses at the expense of catalyst activity, whereas benzannelation promoted 1-octene incorporation and randomness of the resulting poly(ethene-co-1-octene) copolymers. Force field calculations based on steric arguments were used to explain experimental copolymerization results. Activation energy differences between ethene and 1-octene insertion accounted for improved 1-octene incorporation in the case of benzannelated metallocenes. According to 13C-NMR microstructure analysis, copolymerization followed first-order Markov statistics.

Copolymers of N-vinylcarbazole and N,N-dimethylaminoethyl methacrylate

Copolymers of N-vinylcarbazole (NVC) and N,N-dimethylaminoethyl methacrylate (DMAEMA) were prepared by free-radical polymerization in a toluene solution at 60°C using 2,2′-azobisisobutyronitrile (AIBN) as an initiator. The reactivity ratios of both monomers were calculated using the extended Kelen-Tudős method and found to be r1 = 0.441 ± 0.052 and r2 = 1.632 ± 0.102. The microstructure of copolymer chains is described on the basis of first-order Markov statistics. The microstructure of copolymers was also studied by UV and 1H-NMR spectroscopy. Copolymers were characterized by viscocity and number-average molecular weight (M¯n) measurements. The glass transition temperatures (Tg) of the copolymers were determined calorimetrically and the variation of Tg with the copolymer composition is discussed. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 1815–1824, 1997

Microstructure of Ethylene−1-Butene Copolymers Produced by Zirconocene/Methylaluminoxane Catalysis

Low molecular weight (ca. 2000) ethylene−1-butene copolymers were synthesized at 90 °C using rac-(dimethylsilyl)bis(4,5,6,7-tetrahydro-1-indenyl)zirconium dichloride (I) catalyst and methylaluminoxane (MAO) cocatalyst. Comonomer composition, triad sequence distribution, and end groups were analyzed by 1H and 13C NMR. The average polymer molecule contains about one double bond and one saturated end group. The unsaturated end groups were formed almost exclusively by transfer from propagating chains containing 1-butene as the terminal unit. At least 98% of the unsaturated end groups are vinylidene and trisubstituted double bonds, which are present in the approximate ratio 3:1. Saturated end groups result from the initiation process. Both ethylene and 1-butene are involved in initiation, but ethylene more than 1-butene. The product is a random copolymer with very short blocks (no longer than 2−3 monomer units) of both ethylene and 1-butene. The comonomer sequence distributions determined by 13C NMR were fitted to first-order Markovian statistics, which allowed calculation of the monomer reactivity ratios. The results are discussed in terms of a reaction mechanism consisting of initiation, propagation, and chain transfer reactions.

Microstructure of Poly[(R,S)-.beta.-hydroxybutyrate] by 13C NMR

High-resolution 13 C NMR spectra were obtained for a wide tacticity range of racemic poly-[(R,S)-β-hydroxybutyrate] samples and interpreted with regard to several statistical models. None of the samples followed Bernoullian statistics, but the syndiotactic and atactic fractions essentially obeyed first-order Markov statistics, as derived for racemic monomer. Fitting to a second-order Markovian model confirmed previously-held theories regarding the blocky nature of the polymer. An enantiomorphic model described the more isotactic samples well but did not adequately describe the atactic and syndiotactic ones ; a two-site model involving enantiomorphic and first-order Markovian sites was therefore proposed, and the parameters necessary to describe each sample were calculated. Average isotactic and syndiotactic block lengths were also calculated and used in the interpretation of degradation and single-crystal results.

Preparation of heterotactic-rich poly(methyl methacrylate) with narrow molecular weight distribution bytert-butyllithium/bis(2,6-di-tert-butylphenoxy)methylaluminum

Polymerization of methyl methacrylate (MMA) withtert-butyllithium (t-C4H9Li) in toluene in the presence of aluminum alkoxides such as ethoxide,tert-butoxide and 2,6-di-tert-butylphenoxide, were examined at various Al/Li ratios. In the cases of ethoxide andtert-butoxide, predominantly isotactic polymers with broad molecular weight distribution were obtained. Combinations oft-C4H9Li and bis(2,6-ditert-butylphenoxy)methylaluminum [MeAl(ODBP)2] were found to be an efficient initiating system for heterotactic polymerization of MMA, which gives PMMA rich in heterotactic triads up to 68% with narrow molecular weight distribution (Mw/Mn=1.09−1.17). End group analysis by1H NMR indicated thatt-C4H9Li initiates the polymerization and MeAl(ODBP)2 works as a stereospecific modifier. From stereosequence analysis of the heterotactic PMMA by13C NMR, it was found that the calculated pentad fractions from the first-order Markovian statistics (Pm/r=0.742, Pr/m=0.627) fitted the observed ones better than those from Bernoullian statistics. The glass transition temperature of the heterotactic PMMA was 13°C lower than that of syndiotactic PMMA, and the intrinsic viscosity in tetrahydrofuran was close to that of isotactic PMMA with a similar molecular weight but higher than that of syndiotactic PMMA.

Free radical copolymerization of furfuryl methacrylate and N-vinylpyrrolidone

Copolymers of furfuryl methacrylate (F) and N-vinylpyrrolidone (P) were prepared by free radical polymerization in N, N-dimethylformamide solution at 50°C, using 2,2′-azobisisobutyronitrile as initiator. The reactivity ratios of both monomers were calculated according to the general copolymerization equation using the Fineman-Ross and Kelen-Tüdös linearization methods, as well as the Tidwell and Mortimer non-linear least-squares treatment. The reactivity ratios obtained were r F = 3.92 and r P = 0.004. The microstructure of the copolymer chains is described on the basis of first-order Markov statistics, and the copolymer glass transition temperatures ( T gs) were determined calorimetrically. The variation of T g with copolymer composition is discussed according to modern methods, considering the sequence distribution of monomeric units along the copolymer chains. Also the T g of the corresponding homopolymers was determined giving the values T g(F) = 392 K and T g(P) = 358 K, whereas the T g of the corresponding alternating diad has an average value of T gFP = 347 K.

Solution properties of poly(vinylidene fluoride): 2. Relation between microgel formation and microstructure

In contrast to type I poly(vinylidene fluoride) (PVDF), solutions of type II PVDF contain, even in good solvents, a fraction of microgel that cannot be fully eliminated for characterization by light scattering. Intrinsic viscosity and size exclusion chromatography reveal that the soluble fraction has a molecular mass in the same range as type I samples, which are fully soluble in the same solvents. The shear moduli in the molten state reveal that the microgel fraction does not contain a high enough molecular mass to explain microgel formation by phase separation. From an analysis of the 19F nuclear magnetic resonance spectra of both suspension- and emulsion-polymerized PVDF samples, with first-order Markov statistics, microgel formation is attributed to differences in microstructure, involving sequences with two reversed additions in a row.

Sequence determination in MMA-EMA copolymers by 13C NMR

The 13C nuclear magnetic resonance spectra of MMA-EMA copolymers have been recorded and analyzed. The carbonyl carbon resonance region contains six resonating peaks due to its sensitivity to triad concentrations. From these signals, triad concentrations were determined and compared with calculated values based on Bernoullian and first-order Markovian statistics. Molecular weights were determined by viscosity measurement method.