MOLECULAR WEIGHT DISTRIBUTION OFAB, B TYPE CONDENSATION POLYMERS OBTAINED BY ADDING AB MONOMERS IN BATCHES

The molecular weight distribution function (MWD) of AB, B type condensation polymers obtained by adding AB monomers in batches has been derived by statisticaland kinetic methods. Calculations show that the MWD of condensation polymers obtained by this process is much narrower than the Flory distribution and agrees with the Monte Carlo results very well.     

Narrow molecular weight distribution of condensation polymers achieved by adding monomers in many batches

The Z transform method has been used to calculate the molecular weight distribution (MWD) of condensation polymers. The MWD obtained by using Z transform is explicitly discrete. The method is illustrated for two cases: (1) further polycondensation of AB prepolymers with certain initial MWD, and (2) polycondensation of AB and Ar (r is the number of A type functional groups) monomers where AB monomers are added in several batches. In the latter case, it is found that the resulting MWD is much narrower than that of one-batch polycondensation. The trick of producing narrow MWDs of condensation polymers is merely a consequence of keeping AB monomer concentration as low as possible during the reaction in order to suppress the condensation reaction between monomeric AB molecules. The theoretical prediction has been confirmed by Monte Carlo simulation. Therefore, it provides a new possible technique for obtaining narrow MWD polymers through polycondensation reactions.     

Af+AB星型聚合体系的统计热力学

应用统计力学和热力学原理研究了 A_f+AB星型聚合体系的性质. 首先从两种不同的角度给出了与聚合反应相应的配分函数, 并据此得到反应体系的平衡自由能、质量作用定律及数量分布函数, 进而得到了体系的平衡状态方程和比热. 在此基础上, 以反应体系的回转半径为例研究了溶剂效应对星型高分子空间尺度的影响.     

Molecular weight distributions of linear polymers: Detailed analysis from GPC data

The GPC method is used widely to measure molecular weights of linear polymers. High-quality GPC data contains detailed information on many aspects of the polymer's molecular weight distribution (MWD). This information can be extracted from the data using computer analysis. Equations have been derived for the two simplest MWD functions in the GPC coordinates: the Flory function (one growing polymer chain produces one polymer molecule), and for the case when two polymer radicals combine into one polymer molecule. The equations were used to analyze MWD of two classes of polymers. The first class includes polymers with narrow MWD: polyethylene, ethylene-propylene and ethylene-hexene copolymers, syndiotactic polystyrene, and radical polystyrene. The second class includes polymers with broad MWD: ethylene copolymers and polypropylene produced with heterogeneous, Ti-based catalysts. The examples demonstrate that the resolution of complex GPC curves into their constitutents serve as an important source of information about kinetics of polymerization reactions. © 1995 John Wiley & Sons, Inc.     

Synthesis and physical properties of highly branched perfluorinated polymers from AB and AB2 monomers

Highly branched perfluorinated aromatic polyether copolymers were prepared from the polycondensation of the AB₂ monomer, 3,5‐bis[(pentafluorobenzyl)oxy]benzyl alcohol with a variety of fluoroaryl and alkyl bromide AB comonomers. The structures and comonomer distribution of the resulting polymers were characterized in detail. ¹H NMR data from kinetic trials illustrated that perfluoroaryl AB comonomer distribution correlated to AB comonomer sterics. ¹⁹F NMR data revealed that fluorinated AB monomers and 3‐bromo‐1‐propanol AB monomers were distributed within the AB₂ polymer backbone, while longer alkyl bromide AB monomers, 6‐bromo‐1‐hexanol, were mostly distributed along hyperbranched polymer chain ends. In general, as AB comonomer incorporation increased for nonsterically hindered copolymers, thermal decomposition onset increased and glass transition temperatures decreased. The combined data demonstrated the effect of comonomer distribution and sterics on physical properties of AB₂‐based polymer systems. The resulting materials were used to cast thin polymer films for measurement of contact angle, which were shown to be directly related to comonomer content. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1880–1894     

Simulation of reversible polycondensations with monomer having reactivity different from that of higher homologs

Reversible AB-type polycondensations have been simulated in a batch reactor where the monomer reacts with itself or any higher oligomer with a rate constant R times that for higher mers. Similarly, the rate of reaction of the condensation product with an ? AB? group at the end of a polymer chain has been assumed to be R' times that with an “internal” ? ? AB? ? group. The variation of the number-average chain length μ_n with time (until equilibrium is reached) has been obtained. μ_n is found to be lower and the polydispersity index higher in the presence of the reverse reactions. Where the equilibrium conversions are high enough, a split in the molecular-weight distribution (MWD) curves is observed for even- and odd-order homologs for R < 1, though this effect is considerably diminished as compared with that in similar irreversible polycondensations. It is also found that the most probable distribution does not adequately represent the MWD when the functional groups violate the equal-reactivity hypothesis and number-average chain lengths are relatively small.     

Ethylene Polymerization over Supported Titanium-Magnesium Catalysts: Heterogeneity of Active Centers and Effect of Catalyst Composition on the Molecular Mass Distribution of Polymer

New experimental approach was used for analysis of molecular weight distribution (MWD) of polymers produced over titanium-magnesium catalysts (TMC). Polymers were fractionated on to fractions with narrow MWD (polydispersity (PD) values Mw/Mn ≤ 2). Then some of these fractions were combined to get the minimal quantity of fractions with PD values close to 2 (Flory components). It was found that three fractions corresponding to three groups of active centers are sufficient for proper fitting experimental MWD curve for PE obtained over TMC with different Ti content and with different hydrogen concentration in polymerization.     

KINETIC ANALYSIS OF CO-CONDENSATION POLYMERIZATION OF AB2 AND AB MONOMERS

This work deals with the kinetics of co-condensation polymerization of AB2 and AB monomers, giving expressions of the two-dimensional molecular weight distribution function and the number/weight average molecular weights of the resulting copolymers. The two-dimensional molecular weight distribution depends on two indices, n and l, which are the respective numbers of AB2 and AB units in a copolymer species. The evolution of the two-dimensional weight and z distributions during the co-condensation polymerization has been evaluated systematically. Finally, the two-dimensional distribution was transformed into a one-dimensional molecular weight distribution with only one variable (the molecular weight of the products instead of the degree of polymerization). The calculated results show that the highly branched copolymer has a very broad molecular weight distribution when the co-condensation polymerization approaches completion.     

The effect of direct interchange reactions on the MWD of condensation polymers

In this theoretical study, a relationship has been developed for the transient molecular-weight distribution (MWD) of a condensation polymer undergoing a direct interchange reaction. Direct interchange is one of several reactions which can take place in condensation polymers in the melt. When compared to the more well-known reactions of polycondensation, degradation, and interchange of an end-group with a condensation linkage, direct interchange has a more complex statistical effect on the MWD and is less commonly observed. However, these types of reactions can be quite important in some polymeric systems, such as in the reaction of poly (butylene terephthalate) with polycarbonate. The MWD relationship was developed from the species balance: The rate of accumulation of chains of a given molecular weight is equal to their rate of generation minus their rate of consumption. For this reaction, development of the generation term is quite complex; it is approached here by describing five probability situations which are determined by each possible combination of reactant and product chains. Example distributions computed from these equations show that different transient paths are followed under direct and end-group interchange, but that both reactions lead to the equilibrium most-probable distribution.     

Monte Carlo simulation of size exclusion chromatography for randomly branched and crosslinked polymers

The elution curves of size exclusion chromatography for nonlinear polymers formed through random branching and crosslinking of long polymer chains were simulated with a Monte Carlo method. We considered two types of measured molecular weight distributions (MWDs): (1) the MWD calibrated relative to standard linear polymers and (2) the MWD obtained with a light scattering (LS) photometer in which the weight‐average molecular weight of polymers within the elution volume is determined directly. The calibrated MWDs clearly underestimate the molecular weights for both randomly branched and crosslinked polymers, and this technique can be used to assess the degree of deviation from the true MWD. When the primary chains conform to the most probable distribution, the calibrated MWD can be estimated reasonably well with the Zimm–Stockmayer equation for the g factor with the help of the relationship between the average number of branch points per molecule and the degree of polymerization. However, the LS method gives good estimates of the true MWD for both randomly branched and crosslinked polymers, although the agreement is better for the branched ones. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2009–2018, 2000     

Manipulation of Molecular Weight Distribution Shape as a New Strategy to Control Processing Parameters

Molecular weight and dispersity (Ð ) influence physical and rheological properties of polymers, which are of significant importance in polymer processing technologies. However, these parameters provide only partial information about the precise composition of polymers, which is reflected by the shape and symmetry of molecular weight distribution (MWD). In this work, the effect of MWD symmetry on thermal and rheological properties of polymers with identical molecular weights and Ð is demonstrated. Remarkably, when the MWD is skewed to higher molecular weight, a higher glass transition temperature (T _g), increased stiffness, increased thermal stability, and higher apparent viscosities are observed. These observed differences are attributed to the chain length composition of the polymers, easily controlled by the synthetic strategy. This work demonstrates a versatile approach to engineer the properties of polymers using controlled synthesis to skew the shape of MWD.     

AB交联聚合物的形态

以低分子量的端乙烯基聚氨酯预聚物同乙烯类单体共聚制得的AB交联聚合物(ABCP)呈现出两相形态结构,聚氨酯相形成分散相,塑料组份形成连续相。形态结构最显著特点是分散相区呈现出多分散性;其次,分散相区的形状不规则。这些特征不同于线型AB、ABA嵌段共聚物及A_2B接枝共聚物,这是由于ABCP中,A和B两组份间存在着化学交联。交联密度,预聚物的分子量对两组份的相容性,形态结构有显著影响。     

Polymer Distribution Change During Irreversible Depolymerization by Chain‐End Scission

The change in polymer distribution during depolymerization in which monomer molecules are severed one by one from the chain ends, is considered. Assuming irreversible depolymerization and equal reactivity of all the chain ends, a general formula to calculate the MWD is proposed. After the removal of monomers severed from the chains, the MWDs of depolymerized polymers always approach the most probable distribution whose PDI is practically equal to 2. It may appear to be counterintuitive, but the average MWs of polymers may increase during chain scission when the initial distribution is broader than the most probable (PDI > 2). The interpretation of the MWD data of polymers during depolymerization, such as those obtained by GPC, are not straightforward especially for the initial broad MWDs.

     

Molecular‐Weight Multimodality of Multiple Flory Distributions

It is well‐known that the final end‐use properties of polymer resins depend on the shape of the molecular‐weight distribution (MWD) very strongly. Particularly, polymer resins with bimodal MWDs are required for certain special applications, as they may simultaneously present enhanced mechanical and flow properties. A theoretical framework for the characterization of bimodality (or multimodality) of MWDs of polymers produced through linear polymerizations at steady‐state or quasi‐steady‐state conditions is developed and presented here. Conditions for the development of bimodality in generalized NS‐Schulz–Flory distributions are characterized for different forms of presentation of the MWDs. It is shown that the bimodal character of the MWD depends on the particular form used to represent it, which can then be used to generate an index of bimodality of the MWD. The theoretical results are finally used to compute the index of bimodality of actual polymer materials obtained at plant site.     

Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

In free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s²〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s²〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001     

Thermosensitive diblock copolymers with designed molecular weight distribution: Synthesis by continuous living cationic polymerization and micellization behavior

The synthesis of diblock copolymers with designed molecular weight distributions (MWDs) was successfully demonstrated in a continuous living cationic polymerization system using simple equipment. The control of MWDs was achieved by gradually feeding a polymerization reaction mixture into a terminating agent. As thermosensitive diblock copolymers, poly(vinyl ethers) containing a thermosensitive segment with oxyethylene side chains and a hydrophilic segment were prepared. The polymerization was carried out in a gas‐tight microsyringe, and the polymerization mixture was added continuously into methanol during the second‐stage polymerization. The self‐association behavior of the resulting diblock copolymers was evaluated by dynamic light scattering in water. MWD‐designed polymers with thermosensitive segments that varied continuously in length and hydrophilic segments of nearly uniform lengths formed micelles with a broad size distribution. Conversely, polymers with nearly uniform thermosensitive segments and hydrophilic segments of different lengths formed micelles with a narrow size distribution, as observed with conventional narrow MWD diblock copolymers. Thus, the MWD of the thermosensitive segment proved a decisive factor in achieving fine control of self‐association. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2212–2221, 2008     

线型高聚物分子量分布函数的另一种推导方法

针对自由基聚合歧化终止和偶合终止两类机理生成的线型高聚物,应用统计物理的基本原理,对其分子量分布重新进行了理论推导,其方法简洁清晰,无须任何附加假定,导出FlorySchulz分布.结果有助于从另一方面理解FlorySchulz分布的物理学基础.     

Monte Carlo simulation of size exclusion chromatography for branched polymers formed through free‐radical polymerization with chain transfer to polymer

The elution curves of size exclusion chromatography (SEC) for branched polymers formed through free‐radical polymerization that involves chain transfer to polymer were theoretically investigated by using a Monte Carlo method. We considered two types of measured molecular weight distribution (MWD), (1) the calibrated MWD relative to standard linear polymers, and (2) the MWD obtained by using a light scattering photometer (LS) in which the weight‐average molecular weight of polymers within the elution volume is determined directly. It was found that the calibrated MWD clearly underestimates the high molecular weight tail, and the measured distributions are narrower than the true MWD. On the other hand, the present simulation results showed that the LS method gives reasonable estimates of the true MWDs. The mean square radius of gyration of the polymer molecules having the same molecular weight was also investigated. The radii of gyration showed clear deviation from the Zimm‐Stockmayer equation^[1] because of the non‐random nature of branched structure and the difference in the primary chain length distribution.     

Study of Multi-Site Nature of Supported Ziegler-Natta Catalysts in Ethylene-Hexene-1 Copolymerization

Summary: Heterogeneity of active centers (AC) of titanium-magnesium catalysts (TMC) and vanadium-magnesium catalyst (VMC) in ethylene-hexene-1 copolymerization has been studied on the base of data of polymer molecular weight distribution (MWD) deconvolution technique and copolymer fractionation onto narrow fractions. It was found that 3 and 4 Flory components (groups of active centers) are required to describe experimental MWD curves of copolymers produced over TMC with different Ti content. In the case of VMC MWD of homopolymer and copolymer are characterized by set of 5 Flory components (5 groups of AC). Different character of inter-relationship between MW and short chain branching (SCB) was found for ethylene-hexene-1 copolymers produced over different catalysts: heterogeneous type in the case of TMC and more uniform for copolymer prepared over VMC. The content of Ti affects on the slope of that profile in copolymers produced over TMC. The results indicated that TMC and VMC are different greatly on the heterogeneity of active centers to the formation of polymers with different molecular weights and to formation of copolymers with different inter-relationship between MW and short chain branching. TMC produces polymers with more narrow MWD but it contains highly heterogeneous centers regarding comonomer reactivity ratios. VMC produces polymers with broad and bimodal MWD but it contains more homogeneous centers regarding comonomer reactivity ratios.     

Controlling molecular weight distributions of polyethylene by combining soluble metallocene/MAO catalysts

A critical look at the possibility of controlling the molecular weight distribution (MWD) of polyolefins by combining metallocene/methylalumoxane (MAO) catalysts is offered. Catalysts investigated were bis(cyclopentadienyl)zirconium dichloride (Cp₂ZrCl₂), its titanium and hafnium analogues (Cp₂TiCl₂ and Cp₂HfCl₂), as well as rac-ethylenebis(indenyl)zirconium dichloride (Et(Ind)₂ZrCl₂). As observed by other researchers, the MWD of polyethylene can be manipulated by combining soluble catalysts, which on their own produce polymer with narrow MWD but with different average molecular weights. Combined in slurry polymerization reactors, the catalysts in consideration produce ethylene homopolymer just as they would independently. Unimodal or bimodal MWDs can be obtained. This effect can be mimicked by blending polymers produced by the individual catalysts. We demonstrate how a variability in catalyst activity translates into a variability in MWD when mixing soluble catalysts in polymerization. Such a variability in MWD must be considered when setting goals for MWD control. We introduce a more quantitative approach to controlling the MWD using this method. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 831–840, 1998