Static and Dynamic Scaling Close to Gelation in Chain‐Polymerization: Effect of Reactor Type

Because of the familiarity of gelation theories in polycondensation reaction of multifunctional groups, often the gel‐point is defined as the point of diverging weight averaged molar mass. The authors present an industrially relevant counter‐example to this common perception. Chain‐growth polymerization in realistic reactors introduces history dependent crosslinking probability. For copolymerization of a two functional monomer (ethylene) with a four functional comonomer (nonconjugated diene), the authors show from a Monte Carlo scheme that standard gelation scaling exponents remain valid for a semibatch reactor. However, for syntheses in a continuous stirred tank reactor (CSTR), all commonly measured molar mass moments (number, weight and “z ”‐averaged moment) remain finite at the gel‐point; the first moment to diverge is the fourth moment. Hence, identification of the gel point from experimental observations is difficult, and cannot be achieved through monitoring of the weight averaged molar mass. The authors use a numerical scheme based on the tube model of polymer melts to predict the rheology of the generated molecules. Stress relaxation follows a power‐law decay, but due to dynamic dilution effects the CSTR resins exhibit much slower increase in the zero shear viscosity as the gel point is approached as compared to the semibatch reactor resins.

     

Reconstruction of the Chain Length Distribution for Vinyl‐Divinyl Copolymerization Using the Numerical Fractionation Technique

A proposed theory for evaluating the chain length distribution (CLD) using the numerical fractionation (NF) technique was extended to the vinyl‐divinyl (VDV) copolymerization. The CLD is reconstructed for this system, in which pendant double bond propagation leads to crosslinking and gel formation. The method was earlier developed for a non‐linear free‐radical polymerization scheme where chain transfer to polymer and termination by combination resulted in gel formation. The VDV study presented indicates that the proposed method of weighted summation (WS) accurately predicts the resulting CLDs evaluated using NF.

Comparison of the overall polymer NF and the direct solution CLDs near the gel point.     

Single‐electron transfer‐living radical copolymerization of butyl methacrylate and divinylbenzene for preparation of oil‐absorbing gel

Crosslinking copolymerization of butyl methacrylate with a small amount of divinylbenzene (DVB) was carried out using single‐electron transfer‐living radical polymerization initiated with carbon tetrachloride (CCl₄) and catalyzed by Cu(0)/N‐ligand in N,N‐dimethylformamide to produce a highly oil‐absorbing gel. The polymerization, gelation process, and oil‐absorbing properties were studied in detail. Analysis of monomer conversion with reaction time showed that the polymerization followed first‐order kinetics for both linear and crosslinking polymerization before gelation. Higher levels of DVB led to earlier gelation and the influence of N‐ligand on gelation was also significant. Under optimal conditions, oil absorption of the prepared gel to chloroform could reach 42.1 g·g^?1. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3233–3239     

Molecular Weight Development during Simultaneous Chain Scission,Long‐Chain Branching and Crosslinking, 1

A general matrix formula is proposed for the weight‐average molecular weights of the polymer systems formed through simultaneous scission, branching and crosslinking of N types of chains, assuming the chain connection statistics are Markovian. For the polymerization systems in which chains are generated consecutively, such as for free‐radical polymerization, the present theory can be applied by increasing the number of chain types N to infinity, by considering the chains formed at different times as different types of chains. The gel point determination reduces to the eigenvalue problem and the present theory extends the classical gelation theory to non‐random, history‐dependent reaction systems. From the mathematical point of view, this theory is capable of describing complex molecular build‐up processes through end‐linking, T‐ and H‐shaped chain connections, irrespective of reaction/reactor types used.

Schematic representation of the 0^th generation segment and the connection to the 1^st generation segments.     

Stimuli‐Responsive Polypeptide‐Based Supramolecular Hydrogels Mediated by Ca2+ Ion Cross‐Linking

Hydrogels cross‐linked with metal ions (e.g., Ca²⁺) represent a promising class of bioinspired materials for a wide range of biomedical applications. Herein, we report a facile approach to obtain cross‐linked stimuli‐responsive supramolecular polypeptide hydrogels. The hydrogel is prepared by statistical/block copoly(L‐glutamate)s based copolymers cross‐linked with calcium ions. The incorporation of both oligo(ethylene glycol) (OEG) and glutamic acid residues in the polymer offers thermal‐responsive property and cooperative binding sites with Ca²⁺ ions simultaneously. We present a systematic study of the influence of calcium ions on the gelation behaviors of these copolymers. It is observed that the addition of calcium ions induces the formation of hydrogels. Increasing the concentration of Ca²⁺ ions can significantly enhance the gelation ability of the samples as indicated by increased storage modulus and decreased sol‐to‐gel transition temperature (T_sol‐gel). We further demonstrate that the influence of monomer distribution on the gelation behavior is trivial, which is possibly due to similar morphology of the self‐assemblies. The obtained hydrogels exhibit thermal‐responsive gelation behavior mediated by ion cross‐linking, which enables them to be ideal smart hydrogel system for many applications.     

Chain Length Distributions of Polyolefins Made with Coordination Catalysts at Very Short Polymerization Times – Analytical Solution and Monte Carlo Simulation

We developed an analytical solution to describe how the CLD of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerization times before the CLD becomes completely developed. We compared the analytical solution with a dynamic Monte Carlo model for validation, obtaining excellent agreement. Our analytical solution can be used to determine when the steady‐state hypothesis, commonly used in polymerization models, becomes valid as a function of polymer chain length. We also extended our model to describe polymerization with multiple‐site‐type catalysts. Depending on the polymerization kinetic parameters of the different site types on the catalyst, the fully developed CLD is reached through very different intermediate CLDs. This modeling approach, although rather simplified, can be used to interpret results from short polymerization time experiments such as the ones done in stopped‐flow reactors.

     

Side Reactions in Aqueous Phase Polymerization of N‐Vinyl‐Pyrrolidone as Possible Source for Fouling

An improved kinetic model for the radical polymerization of N‐vinyl‐pyrrolidone (NVP) in aqueous medium is developed. Quantum chemical simulations reveal that the transfer to polymer is of minor importance whereas the transfer to monomer by hydrogen abstraction in 3‐position of the pyrrolidone ring leads to a radical with a double bond which initiates a new chain bearing a terminal double bond (TDB). The resulting dead chains with one, two, or more TDB are the main source for a strong increase of molar mass in batch reactors at high conversion due to long chain branching and crosslinking. This can be a source for gel formation and fouling in continuous reactors.     

Calculation of CLD Using Population Balance Equations of Generating Functions: Linear and Non‐Linear Ideal Controlled Radical Polymerization

Population balance equations in terms of generating functions (GF) are used to predict chain length distributions (CLD) of linear and non‐linear ideal controlled radical polymerization (CRP) systems. It is here shown that under simplified conditions analytical solutions for the CLD can be found and moreover the fundamental CLD derived by H. Tobita in 2006 is a limiting case of the more general solutions here presented. In order to deal with more complex CRP systems, solutions based upon the numerical inversion of GF are presented. These studies are also extended to the non‐linear CRP of vinyl/divinyl monomers where multimodal CLDs are predicted to occur.

     

Transient Behavior and Gelation of Free Radical Polymerizations in Continuous Stirred Tank Reactors

Summary: Using the authors' previously developed method for the general kinetic analysis of non‐linear irreversible polymerizations, the simulation of free radical homogeneous polymerization systems with terminal branching and chain transfer to polymer has been carried out for continuous stirred tank reactors. Its improved accuracy on the numerical evaluation of generating functions has been exploited in order to perform their numerical inversion and chain length distributions could also be estimated with or without the presence of gel. A comparison with alternative techniques emphasizing the effect of their simplifying assumptions on the accuracy of calculations is also presented.

Predicted CLD before gelation (t = 1 h), after gelation (t = 15 h, steady state), and close to gel point for a free radical polymerization with transfer to polymer in a CSTR with τ = 60 min.     

Ab initio RAFT emulsion polymerization of butadiene using the amphiphilic poly(acrylic acid‐b‐styrene) trithiocarbonate as both surfactant and mediator

Ab initio reversible addition fragmentation chain transfer (RAFT) emulsion polymerization of butadiene was investigated by using the amphiphilic poly(acrylic acid_n‐b‐styrene₅) trithiocarbonate as both surfactant and mediator. The neutralization on acrylic acid (AA) units played significant influence on the gelation. When half of the AA units were neutralized, the gelation occurred in the early stage of the polymerization so that the highest accessible molecular weight of polybutadiene was as low as 5 kg mol^?1. In the non‐neutralized conditions, the gelation was much retarded so that the highest accessible molecular weight was increased up to 23 kg mol^?1. In the non‐neutralized conditions, potassium persulfate could not initiate the polymerization. When azobisisobutyronitrile was used as initiator, the polymerization mediated by poly(acrylic acid₂₇‐b‐styrene₅) trithiocarbonate could proceed much faster than the solution polymerization did. The latex was stable. Before the gel point, molecular weight agreed well with the theoretical prediction while PDI was relatively high due to the branching reaction. The poly(butadiene‐b‐styrene) core/shell particles could obtained by extending polybutadiene. When the n value in poly (acrylic acid_n‐b‐styrene₅) trithiocarbonate was lower than 20, the coalescence would occur, leading to the formation of some coagulum. On the other hand, when n value was as high as 60, the molecular weight was out of control. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Chain‐length dependent termination in rotating sector polymerization, 1. The evaluation of the rate constant of chain propagation kp

The chain‐length distributions (CLDs) of polymers prepared by rotating‐sector (RS) techniques under pseudostationary conditions were simulated for the case of chain‐length dependent termination and analysed for their suitability of determining the rate constant of chain propagation k_p from the positions of their points of inflection. The tendency to underestimate k_p is a little more pronounced than in pulsed‐laser polymerization (PLP) but, interestingly, the situation improves in the presence of chain‐length dependent termination. The estimates also were found to be more precise a) for smaller rates of initiation, b) for higher order points of inflection, c) if termination is by combination, d) if the role played by the shorter one of the two chains becomes less dominant. Taken in all, the determination of k_p from the points of inflection in the CLD of RS‐prepared polymers may well compete with the more famous PLP method, especially if some care is taken with respect to the choice of experimental conditions.     

The Nature of Crosslinking in N‐Vinylformamide Free‐Radical Polymerization

N‐Vinylformamide (NVF) free‐radical polymerization was found to form polymer gels at high conversions both in bulk and in solution. The polymerization was conducted at different temperatures, monomer and initiator concentrations to show the gelation conditions. Gel fractions and gel swelling ratios were also measured after separating the gel from the polymer samples. In order to confirm the crosslinking unit, a series of hydrolysis experiments were conducted on the gel samples. The hydrolysis results showed that the crosslinks in PNVF gels could be destroyed by alkaline hydrolysis. The most appropriate explanation to this fact is that crosslinking takes place via the amide group.     

Free‐radical crosslinking copolymerization of 2,2′‐azobis[N‐(2‐propenyl)‐2‐methylpropionamide] with vinyl benzoate resulting in polymeric azo initiators

2,2′‐Azobis[N‐(2‐propenyl)‐2‐methylpropionamide] (APMPA) with two carbon–carbon double bonds and an azo group was copolymerized with vinyl benzoate (VBz) at 60 °C, resulting in azo groups containing VBz/APMPA prepolymers and crosslinked polymers as soluble and insoluble polymeric azo initiators, respectively. The polymerization characteristics of APMPA as a novel diallyl monomer were clarified with the rate and degree of polymerization and the monomer reactivity ratios. The gelation behaviors in VBz/APMPA crosslinking copolymerizations were examined in detail with a comparison of the actual gel point and the theoretical gel point calculated according to Stockmayer's equation with the tentative assumption of equal reactivity for both vinyl groups belonging to VBz and APMPA. The effectiveness of the resulting branched or crosslinked poly(VBz‐co‐APMPA)s as soluble or insoluble polymeric azo initiators, respectively, at providing graft polymers through the cleavage of azo groups at an elevated temperature was examined by the polymerization of allyl benzoate at 120 °C. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 317–325, 2002     

Crosslinking polymerization leading to interpenetrating polymer network formation. II. Polyaddition crosslinking reactions of poly(methyl methacrylate‐co‐2‐methacryloyloxyethyl isocyanate) with various diols

As part of our continuing studies concerned with the elucidation of the crosslinking polymerization mechanism leading to interpenetrating polymer network (IPN) formation, in which IPNs consist of both polymethacrylates and polyurethane (PU) networks, this article explores the polyaddition crosslinking reactions of multifunctional poly(methyl methacrylate‐co‐2‐methacryloyloxyethyl isocyanate) [poly(MMA‐co‐MOI)] [MMA/MOI = 90/10] with various diols leading to PU network formation. Thus, the equimolar polyaddition crosslinking reactions of poly(MMA‐co‐MOI) with ethylene glycol (EG), 1,6‐hexane diol, and 1,10‐decane diol (DD) were carried out in N‐methyl pyrrolidone at a 0.25 mol/L isocyanate group concentration at 80 °C. The second‐order rate constants decreased from EG to DD. The deviation of the actual gel point from the theoretical one was smaller from EG to DD. The intrinsic viscosity of resulting prepolymer demonstrated almost no variation with progressing polymerization for the EG system, whereas it gradually increased with conversion for the DD system. Close to the gel point conversion it increased rather drastically for both systems. The swelling ratio of resulting gel was higher from EG to DD. These are discussed mechanistically in terms of the significant occurrence of intramolecular cyclization and intramolecular crosslinking reactions leading to shrinkage of the molecular size. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3243–3248, 2003     

Photoregulated Sol‐Gel Transition of Novel Azobenzene‐Functionalized Hydroxypropyl Methylcellulose and Its α‐Cyclodextrin Complexes

Summary: Novel azobenzene‐functionalized hydroxypropyl methylcellulose (AZO‐HPMC) polymers and their α‐cyclodextrin (α‐CD) complexes have been prepared. These polymers show interesting sol‐gel transition behavior in aqueous solutions. In the absence of α‐CD, the gelation temperature increases after UV irradiation, while in the presence of α‐CD, the gelation temperature decreases after UV irradiation. The difference in the gelation temperatures between the trans and cis samples of AZO‐HPMC opens a wide operating window for reversible regulation of the sol‐gel transition behavior by photoirradiation.

The UV‐induced cis/trans isomerism of azobenzene‐functionalized hydroxypropyl methylcellulose and its α‐cyclodextrin complexes.     

Preparation of l‐phenylalanine‐imprinted solid‐phase extraction sorbent by Pickering emulsion polymerization and the selective enrichment of l‐phenylalanine from human urine

A novel l‐ phenylalanine molecularly imprinted solid‐phase extraction sorbent was synthesized by the combination of Pickering emulsion polymerization and ion‐pair dummy template imprinting. Compared to other polymerization methods, the molecularly imprinted polymers thus prepared exhibit a high specific surface, large pore diameter, and appropriate particle size. The key parameters for solid‐phase extraction were optimized, and the result indicated that the molecularly imprinted polymer thus prepared exhibits a good recovery of 98.9% for l‐ phenylalanine. Under the optimized conditions of the procedure, an analytical method for l‐ phenylalanine was well established. By comparing the performance of the molecularly imprinted polymer and a commercial reverse‐phase silica gel, the obtained molecularly imprinted polymer as an solid‐phase extraction sorbent is more suitable, exhibiting high precision (relative standard deviation 3.2%, n = 4) and a low limit of detection (60.0 ± 1.9 nmol·L^?1) for the isolation of l‐ phenylalanine. Based on these results, the combination of the Pickering emulsion polymerization and ion‐pair dummy template imprinting is effective for preparing selective solid‐phase extraction sorbents for the separation of amino acids and organic acids from complex biological samples.     

Discussion of substantially identical gel points among multiallyl monomers based on characterization of resultant network polymer precursors consisting of oligomeric primary polymer chains

No difference in the actual gel points was substantially observed among three isomeric diallyl phthalates such as diallyl phthalate (DAP), diallyl isophthalate, and diallyl terephthalate (DAT); this interesting gelation behavior was discussed further in terms of the correlation between gelation and the difference in cyclization modes, and also, the difference in reactivity between the uncyclized and cyclized radicals for cross‐linking. In the present work, we tried to extend the preceding discussion to the polymerization of triallyl trimellitate (TAT) because the molecular structure of TAT is presumed to essentially involve the characteristics of three isomeric diallyl phthalates and, therefore, the enhanced gelation was expected in TAT polymerization. However, no enhancement of gelation was observed. For a full understanding of the gelation in multiallyl cross‐linking polymerization, we explored further the polymerizations of DAP, DAT, and TAT, especially focusing on the characterization of resultant network polymer precursors (NPPs) using SEC‐MALLS‐viscometry providing the correlation of [η] versus M_w of fractionated samples. Notably, the structure of NPP consisting of oligomeric primary polymer chains generated from specific allyl polymerization would become core‐shell type dendritic with the progress of polymerization. The correlation between delayed gelation and decreased reactivity of dendritic NPP for intermolecular cross‐linking is discussed. Conclusively, the reactivity for intermolecular cross‐linking between NPPs decreased with the progress of polymerization leading to a delayed gelation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2871–2881, 2009     

Temperature‐dependent self‐assembly and rheological behavior of a thermoreversible pmma–PnBA–PMMA triblock copolymer gel

Self‐assembly and mechanical properties of triblock copolymers in a mid‐block selective solvent are of interest in many applications. Herein, we report physical assembly of an ABA triblock copolymer, [PMMA–Pn BA–PMMA] in two different mid‐block selective solvents, n‐butanol and 2‐ethyl‐1‐hexanol. Gel formation resulting from end‐block associations and the corresponding changes in mechanical properties have been investigated over a temperature range of ?80 °C to 60 °C, from near the solvent melting points to above the gelation temperature. Shear‐rheometry, thermal analysis, and small‐angle neutron scattering data reveal formation and transition of structure in these systems from a liquid state to a gel state to a percolated cluster network with decrease in temperature. The aggregated PMMA end‐blocks display a glass transition temperature. Our results provide new understanding into the structural changes of a self‐assembled triblock copolymer gel over a large length scale and wide temperature range. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 877–887     

A Semi‐Microscopic Modeling for Polymer Flow Reactors

Summary: A nonisothermal plug‐flow reactor for ethylene polymerization is reexamined so as to illustrate the principle and effect of a refined, semi‐microscopic modeling. The novel feature of the current simulation is the application of a Monte Carlo scheme to exactly solve the free‐radical polymerization involved, whereas a reptation‐based molecular theory is introduced in a self‐consistent manner to simulate more accurately the reactant fluid viscosity during polymerization. The simulation is shown to capture some in‐depth consequences of reaction‐transport coupling that cannot be revealed by a traditional, macroscopic type of modeling. The principle of a future extension for dealing with more complex flow reactors is briefly discussed.

Comparison of the predicted temperature profile between Monte Carlo‐based simulation and the ones using moment equations together with two different weight distributions is shown with experimental data for LDPE.     

Effect of Microstructures on the Phase Transition Behavior of P(CL‐GL)‐PEG‐P(CL‐GL) Triblock Copolymer Aqueous Solutions

Amphiphilic poly[(ε‐caprolactone)‐co‐glycolide]‐block‐poly(ethylene glycol)‐block‐poly[(ε‐caprolactone)‐co‐glycolide) [P(CL‐GL)‐PEG‐P(CL‐GL)] triblock copolymers with different average lengths of caproyl sequences (L_CL) were synthesized by ring‐opening polymerization at different temperatures. A 25% aqueous solution of the copolymer with L_CL = 11.0 formed a gel, owing to strong crystallinity‐induced hydrophobicity at low temperature, and underwent a gel‐sol transition (UCST behavior) when the temperature was increased to 40 °C. In contrast, the solution of copolymer with L_CL = 6.7 underwent a sol‐gel transition (LCST behavior) due to micelle aggregation. However, a clear sol‐turbid sol phase transition was observed for the copolymer with more random microstructures (L_CL = 5.2).