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     

Mechanistic discussion of cationic crosslinking copolymerizations of 1,2‐epoxycyclohexane with diepoxide crosslinkers accompanied by intramolecular and intermolecular chain transfer reactions

Our previous mechanistic discussion of the free‐radical crosslinking monoallyl/diallyl copolymerizations was extended to the cationic crosslinking monoepoxide/diepoxide copolymerizations, typically including 1,2‐epoxycyclohexane (ECH) as a monoepoxide and bis[3,4‐epoxycyclohexylmethyl] adipate (BECHMA) as a diepoxide crosslinker. In the cationic polymerization, oligomer is usually obtained because of the occurrence of characteristic chain‐forming reactions. Therefore, cationic crosslinking monoepoxide/diepoxide copolymerizations could be in the category of the network formation through free‐radical crosslinking monoallyl/diallyl copolymerizations. Thus, the gelation behavior was discussed by comparing the actual gel points with the theoretical ones; the greatly delayed gelation from theory was observed. Then, the resulting network polymer precursors (NPPs) were characterized by SEC‐MALLS‐viscometry to clarify the cationic crosslinking ECH/BECHMA copolymerization mechanism. Notably, the correlation lines of molecular weight versus elution volume were specific for the NPPs obtained at a high conversion close to the gel point as compared with those obtained by the free‐radical crosslinking monoallyl/diallyl copolymerization. This may be ascribed to the occurrence of intramolecular and intermolecular chain transfer reactions characteristic of cationic polymerization; the chain transfer reactions involve the intramolecular and intermolecular nucleophilic attack of ether oxygen or terminal hydroxyl oxygen in the NPPs to a terminal growing cation that leads to the formation of not only the loop‐ but also the crosslink‐structures containing NPPs, providing fragile ultrahigh‐molecular‐weight NPP in the SEC columns. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Skewered reactions in free‐radical crosslinking (co)polymerizations of liquid polybutadiene as internal olefinic multivinyl crosslinker

As an extension of our continuing studies concerned with the mechanistic discussion of network formation in the free‐radical crosslinking (co)polymerization of multivinyl monomers, this work refers to the skewered reactions in the crosslinking (co)polymerizations of liquid polybutadiene rubber (LBR) as an internal olefinic multivinyl monomer or crosslinker, especially focused on the competitive occurrence of both addition or skewered reaction to internal carbon–carbon (CC) double bonds and abstraction reaction of allylic hydrogens in LBR by growing polymer radical. Thus, LBR is regarded as an internal olefinic multiallyl monomer‐linked allyl groups (? CH?CH? CH₂? ) with methylene units (? CH₂? ). First, gelation in the polymerization of LBR was explored in detail, especially at elevated temperatures. The occurrence of intermolecular crosslinking was easier in the order LBR > LBR containing 20 mol % of 1,2‐structural units > liquid polyisoprene rubber. Then, we pursued the polymerization of LBR using dicumyl peroxide (DCPO) as typical organic peroxide used at elevated temperatures. The primary cumyloxy radical generated by the thermal decomposition of DCPO may add to CC double bond or abstract allylic hydrogen or undergo β‐scission to generate a secondary methyl radical. The initiation by the cumyloxy radical was omitted. The ratio of allylic hydrogen abstraction to β‐scission reaction was estimated; thus, only 39% of cumyloxy radical was used for the allylic hydrogen abstraction reaction. The addition of methyl radical to CC double bond was clearly observed. Finally, we pursued the intermolecular and intramolecular skewered reactions in free‐radical crosslinking LBR/vinyl pivalate copolymerizations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

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     

UV‐induced crosslinking of ring opening metathesis block copolymer micelles

Statistical and amphiphilic block copolymers bearing cinnamoyl groups were prepared by ring opening metathesis polymerization (ROMP). The UV‐induced [2 + 2] cycloaddition reaction of polymer bound cinnamic acid groups was studied in polymer thin films as well as in block copolymer micelles. In both cases, exposure to UV‐light for 10 min led to a crosslinking conversion of about 60%, as determined by FT‐IR spectroscopy and UV–vis absorption measurements. Time based IR‐spectroscopy revealed a maximum conversion of 78% reached after an irradiation time of about 16 min. For micelles obtained from polymers bearing 5 mol % or more cinnamoyl groups, the crosslinking reaction proceeded smoothly, yielding in crosslinked particles which were stable in a non‐selective solvent (CHCl₃). Diameters determined by dynamic light scattering in the selective solvent (MeOH) were similar for both, non‐crosslinked and crosslinked micelles, whereas diameters of crosslinked micelles in the non‐selective solvent (CHCl₃) were significantly larger compared to MeOH samples. This strategy of direct self assembly of block‐copolymers in a selective solvent followed by “clean” crosslinking, without the need for additional crosslinking reagents or crosslinking initiators, provides a straight forward approach toward ROMP‐based polymeric nano‐particles. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2402–2413, 2008     

The delayed crosslinking amphiphilic polymer gel system based on multiple emulsion for in-depth profile control

Delayed crosslinking polymer gel systems are widely used in-depth profile control technology for water production control. In this paper, an amphiphilic polymer P(AM-NaA-DDAM) was synthesized by a free radical micellar polymerization method and a delayed crosslinking amphiphilic polymer gel system was prepared based on multiple emulsion of W₁/O/W₂ emulsion which was prepared by a two-step emulsification method. The optimized formulation of amphiphilic polymer gel systems is: 0.15% P(AM-NaA-DDAM), 0.3% methenamine, 0.02% resorcinol, and 0.3% citric acid. The delayed gelation time of the delayed crosslinking amphiphilic polymer gel system is closely related to the stability of the W₁/O emulsion. By using multiple emulsion delayed crosslinking method, the delayed crosslinking amphiphilic polymer gel system with diesel as the oil phase can delay the gelation time up to 168 hours.     

Metallocene‐mediated cationic ring‐opening polymerization of 2‐methyl‐ and 2‐phenyl‐oxazoline

The cationic ring‐opening polymerization of 2‐methyl‐2‐oxazoline and 2‐phenyl‐2‐oxazoline was efficiently used using bis(η⁵‐cyclopentadienyl)dimethyl zirconium, Cp₂ZrMe₂, or bis(η⁵‐tert‐butyl‐cyclopentadienyl)dimethyl hafnium in combination with either tris(pentafluorophenyl)borate or tetrakis(pentafluorophenyl)borate dimethylanilinum salt as initiation systems. The evolution of polymer yield, molecular weight, and molecular weight distribution with time was examined. In addition, the influence of the initiation system and the monomer on the control of the polymerization was studied. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 000: 000–000, 2011     

Large electro‐optic activity and enhanced temporal stability of methacrylate‐based crosslinking hyperbranched nonlinear optical polymer

A methacrylate‐based crosslinking hyperbranced polymers have been synthesized through initiator‐fragment incorporation radical polymerization and used for the temperature stable electro‐optic (EO) polymer application. This polymer consists of methyl methacrylate, 2‐metacryloxyethyl isocyanate, and ethylene glycol dimethacrylate (EGDMA) monomers. The use of EGDMA as a bifunctional unit resulted in the solvent‐soluble crosslinking hyperbranched chain, so that the EO polymer enhanced glass transition temperatures. A phenyl vinylene thiophene vinylene bridge nonlinear optical chromophore was attached to the polymer backbone as the side‐chain by a post‐functionalization reaction. The loading concentration of the chromophore was varied between 30 and 50 wt % by simply changing the mixing ratio of the precursor polymer to the chromophore. The synthesized EO polymers produced optical quality films with a light propagation loss of 0.61 dB/cm in a slab waveguide at 1.31 μm. The electrically poled film had an EO coefficient (r₃₃) of 139 pm/V at 1.31 μm. The EO crosslinking hyperbranced polymer had a high‐glass transition temperature of 170 °C, and exhibited excellent temporal stability of the EO activity at 85 °C for 500 h. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Basic study of the gelation of dimethacrylate‐type crosslinking agents

An investigation was made of the gelation of dimethacrylate‐type crosslinking agents in view of an application for separation media. The study mainly centered on a crosslinking agent, glycerol dimethacrylate (GDMA), which is relatively hydrophilic because of a hydroxyl group in the middle of its structure. The gelation of GDMA was compared with that of other hydrophobic crosslinking agents such as ethylene glycol dimethacrylate and 1,6‐hexanediol dimethacrylate. The diluents used in the study were toluene, toluene with methanol, and cyclohexanol. The gelation was observed in real time with a charge coupled device camera and dynamic light scattering (DLS). Also, the separated dry gels were extensively characterized with scanning electron microscopy, BET (N₂ absorption and desorption isotherm), and Fourier transform infrared. DLS analysis showed a stronger molecular interaction of GDMA gelation in toluene, whereas this interaction was much weaker in an alcoholic solvent such as toluene with methanol or cyclohexanol. This indicated that GDMA gelation might proceed through hydrogen bonding as well as a crosslinking reaction of vinyl groups. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 949–958, 2006     

Copolymerization behavior of direct polycondensation of AB2 and AB monomers that forms hyperbranched aromatic polyamide copolymers

The copolymerization behavior of the one‐step direct polycondensation of 3,5‐bis‐(4‐aminophenoxy)benzoic acid (AB₂ monomer) and 3‐(4‐aminophenoxy)benzoic acid (AB monomer) was investigated by IR and ¹³C NMR measurements. IR measurements revealed that the content of the AB₂ units in the polymer was higher in the early stages of polymerization. ¹³C NMR spectra of the polymers indicated that the number of dendritic units increased slowly with increasing reaction time. The stepwise copolymerization of the AB₂ and AB monomers was also carried out, and the structure was analyzed by ¹³C NMR measurements. Copolymer synthesized stepwise by adding AB₂ monomer first (polymer II ) had more dendritic units and less terminal units as compared with the one‐step copolymer (polymer I ). Copolymer synthesized stepwise by adding AB monomer first gave a resulting copolymer (polymer III ) composed of long AB chains. The solubility of the stepwise copolymers was low, and the inherent viscosity was high in comparison with the one‐step copolymer as a result of the difference in architecture of the copolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3304–3310, 2001     

Thermoreversible gelation of helical polypeptide/single‐walled carbon nanotubes and their solid‐state structures

Single‐walled carbon nanotubes (SWCNTs) have been functionalized with poly(γ‐benzyl‐L ‐glutamate)s (PBLGs) having well‐defined polymer molecular weight (M_n = 7.5–21.1 kg·mol^?1) and molecular weight distribution (PDI = 1.05–1.20) by a graft‐to method. Toluene solutions containing 5 wt % free PBLG and variable amounts of PBLG‐functionalized SWCNTs (PBLG‐SWCNTs) form gels at room temperature. Differential scanning calorimetry (DSC) analysis reveals that the gelation occurs thermoreversibly, in accord with previous studies on the pristine PBLG/toluene gels. The heat of gel melting (ΔH_m) is slightly elevated for the composite gels compared with the pristine gel, which suggests enhanced interactions between PBLGs in the former. But the gelation temperatures of the composites are unaffected by the presence of PBLG‐SWCNTs. Small‐angle X‐ray scattering (SAXS) analysis of the composite and pristine gels at different temperatures by the Guinier method suggests that PBLG‐SWCNTs promote interactions between PBLG rods, as indicated by the larger PBLG bundle size with increasing PBLG‐SWCNT content in the gel and the melt state. W/SAXS analysis of the dry gels reveals that PBLG‐SWCNTs induce significant changes in the PBLG packing order, resulting in a nematic phase, in contrast to a weakly ordered smectic C phase containing tilted PBLG rods that is observed in the pristine gel. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

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.     

Synthesis of polyarylacetylenes by γ‐ray‐induced polymerization of terminal alkynes. Nanostructures of ortho‐substituted derivatives

Terminal aryl alkynes RC₆H₄C?CH with substituents of different electronic properties and ring position (R = H, 4‐CF₃, 4‐OMe, 2‐CF₃, 2‐OMe, 2‐Me) were exposed to γ‐radiation (50–400 kGy) in organic solvents (hexane, 1,4‐dioxane, ethylacetate, methanol, tetrahydrofuran), at room temperature. The effects arising from substituent, solvent, dilution, and radiation dose allowed to define the conditions suitable for polymerization, which was favored in methanol at increasing dilution of the alkyne. Ortho‐substitution represented the key structural element in the substrate, and the derived polyarylacetylenes were characterized in detail, including gel permeation chromatography, thermal analysis, infrared, NMR, UV–vis, fluorescence, and scanning electron microscope spectroscopy. The results are consistent with the formation of irregular polymers mainly composed of trans‐transoid chains. Controlled aggregation of the polymers by means of an osmosis‐based procedure in solvent/non‐solvent mixtures allowed the formation of nanostructured materials, in particular of hollow nanospheres from THF/water. The methodology sets the basis for the development of γ‐rays‐induced polymerization of alkynes, in a transition metal catalyst‐free environment. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Syntheses of amphiphilic block copolymers by living cationic polymerization of vinyl ethers and their selective solvent‐induced physical gelation

Amphiphilic diblock copolymers were prepared by the living cationic polymerization of vinyl ethers in the presence of added bases, and their selective solvent‐induced physical gelation behavior was investigated. The block copolymerization of 2‐phenoxyethyl vinyl ether (PhOVE) and 2‐methoxyethyl vinyl ether (MOVE) was carried out in the presence of ethyl acetate with Et_1.5AlCl_1.5 in toluene at 0 °C. Despite the rate difference, diblock copolymers with a very narrow molecular weight distribution were obtained, quantitatively. By adding the selective solvent, water, to the acetone solution of the diblock copolymer, PhOVE₂₀₀‐b‐MOVE₄₀₀, physical gelation occurred suddenly and the system ceased to flow, maintaining transparency. Viscoelastic measurements and transmission electron microscopic observations were performed to examine the characteristic gelation behavior and structure of the obtained gels. Various gelation conditions and physical gelation by other amphiphilic block copolymers were also designed on the basis of the solubility of each block segment. Further, new forms of physical gelation, accompanied by the solubilization of immiscible organic compounds, were achieved using similar diblock copolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3190–3197, 2001     

Control of porosity in hierarchically porous polymers derived from hyper‐crosslinked block polymer precursors

We report an approach to control the pore characteristics of hierarchically porous polymers (HPPs) containing micropores in a well‐defined 3D continuous mesoporous framework, by the hyper‐crosslinking reaction of a crosslinked block polymer precursor polylactide‐b‐poly(vinylbenzyl chloride‐co‐styrene‐co‐divinylbenzene) (PLA‐b‐P(VBzCl‐co‐S‐co‐DVB)) consisting of bicontinuous PLA and P(VBzCl‐co‐S‐co‐DVB) microdomains. We investigated the hyper‐crosslinking reaction of P(VBzCl‐co‐S‐co‐DVB)s synthesized by reversible addition‐fragmentation chain transfer (RAFT) copolymerization, and then examined the effect of VBzCl, S, DVB, and polylactide macrochain transfer agent (PLA‐CTA) contents in the polymerization mixture on the pore characteristics of the HPPs. We demonstrate that while the VBzCl content responsible for the hyper‐crosslinking reaction primarily governs microporosity, the DVB content has a strong influence on the mesopore structure, as it determines the onset of the gelation of the polymerization mixture, which arrests the emerging disordered bicontinuous morphology induced by the polymerization‐induced microphase separation process. Because the PLA microdomains template the percolating mesoporous space, mesoporosity was mainly controlled by the PLA‐CTA contents. The synergistic combination of hyper‐crosslinking and block polymer self‐assembly in the HPP formation provided a highly reinforced mesoporous framework, stable against pore collapse, and interconnected mesopores. These facilitated diffusion to the microporous surfaces, suggesting its utility for advanced absorbents and catalytic supports. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 900–913     

Multiarm star poly(glycidol)‐block‐poly(ε‐caprolactone) of different arm lengths and their use as modifiers of diglycidylether of bisphenol a thermosets

Well‐defined multiarm star copolymers, hyperbranched poly(glycidol)‐b‐poly(ε‐caprolactone), with an average of 100–110 arms per molecule and a molecular weight of arms of 3000 g/mol (PGOH‐b‐PCL₃₀) and 1000 g/mol (PGOH‐b‐PCL₁₀) were synthesized by cationic ring‐opening polymerization of ε‐caprolactone from a poly(glycidol) core and used to modify diglycidylether of bisphenol A formulations. The curing process, studied by dynamic scanning calorimetry, was only slightly retarded when PGOH‐b‐PCL_x were added to the formulation. By rheometry, the effect of this new topology and the arm length on the complex viscosity (η*) and gelation of the reactive mixture was analyzed in detail. The addition of these new reactive modifiers decreases the global shrinkage and increases the conversion at gelation. In addition, the modified thermosets have an improved reworkability. The homogeneity of pure DGEBA and modified thermosets was proved by dynamic thermomechanical analysis and electronic microscopy (FESEM). Addition of star‐like structures led to a more toughened fracture of the thermoset in comparison to pure DGEBA. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Synthesis of polymers bearing 1,3‐benzoxazine moiety in the side chains from poly(allylamine) and their crosslinking behaviors

A polymer bearing 1,3‐benzoxazine moiety in the side chain was synthesized successfully from poly(allylamine) based on a stepwise strategy consisted of three steps: (1) treatment of poly(allylamine) with salicylaldehyde to convert the amino group in the side chain into the corresponding o‐(iminomethyl)phenol moiety, (2) reduction of the o‐(iminomethyl)phenol to obtain the corresponding o‐(aminomethyl)phenol moiety, and (3) formation of 1,3‐benzoxazine moiety by the reaction of the o‐(aminomethyl)phenol with formaldehyde. The content ratio of benzoxazine moieties and o‐(aminomethyl)phenol moieties in the polymer were tunable by varying amount of formaldehyde. The presence of o‐(aminomethyl)phenol moieties exhibited a significant promoting effect on the crosslinking reaction. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Novel polymer monolith prepared from a water‐soluble crosslinking agent

In this study, we described the fundamental properties of novel polymer monoliths that were prepared from a water‐soluble crosslinking agent. Each monolith was evaluated by scanning electron microscope (SEM) and scanning probe microscope (SPM) to observe the monolithic structure, and the polymer films that were prepared from several monomers were evaluated by the contact angle of water. As results of evaluations, the polymer prepared from a water‐soluble crosslinking agent had high hydrophilicity. Furthermore, SEM evaluations suggested that polymer porogenic solvent (PEG) was contributed to the construction of monolithic structure, and the polymerization degree of PEG was also taken effect of the structural changing by the variation of phase separation. Additionally, the results of SPM evaluations and the differences of monolithic structure were also reflected under water condition although the swelling of polymer was observed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3811–3817, 2007     

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     

Postgel properties in the statistical crosslinking of heterochains. I. Systems with N types of chains

The heterochain crosslinking model describes nonrandom crosslinking of polymer chains and is an extension of the classical Flory/Stockmayer gelation theory. We consider the postgelation relationship for the system consisting of N types of polymer chains, in which the probability that a crosslink point on an i‐type chain is connected to a j‐type chain is explicitly given by p_ij. The analytical solutions for the weight fraction of the sol, the number‐average and weight‐average molecular weights within the sol fraction, and the crosslinking density within the sol and gel fractions are derived for the systems, with each type of chain conforming to the Schulz–Zimm distribution. Illustrative calculations are shown for the systems consisting of two and three types of chains, and the obtained results agree with those from the Monte Carlo method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2333–2341, 2000