The effects of monophenol chain terminators on the structure–property relationships of controlled epoxy networks

Five families of new controlled epoxy thermosets (CENs) using three monophenol chain terminators were prepared to study systematic changes in the structure and amount of the monophenol and the initial molecular weight between crosslinks (M_c,i) on the properties of epoxy thermosets. Glass transition temperature (T_g) decreases with monophenol mole fraction (χ) in proportion to both the concentration and flexibility of the chain terminator. Distinct serial relations for T_g depression were observed for the three M_c,i families. Dynamic mechanical analysis (DMA) shows significant perturbations of the relaxation behavior with added terminator as evidenced by decrease in peak tan δ and in post T_g damping. The rubbery coefficients of thermal expansion (CTE) increases with monophenol concentration only at χ > 0.05 and shows distinct curvature versus temperature, but is largely invariant with monophenol flexibility. The thermal stability of terminated CENs decreases only slightly with χ and little difference was found with monophenol structure. Most surprisingly, fracture toughness decreases markedly and discontinuously with χ depending on M_c,i. The values of the critical monophenol concentration at which fracture toughness markedly decreases (χ_c) are inversely proportional to M_c,i but are independent of monophenol flexibility. No correlation of χ_c with any of the calculated network structure parameters was apparent. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1632–1640, 2008     

The effect of network architecture on the thermal and mechanical behavior of epoxy resins

The effects of crosslink functionality (f_c), molecular weight between crosslinks (M_c), and chain stiffness display on the thermal and mechanical behavior of epoxy networks are determined. Both f_c and M_c are controlled by blending different functionality amines with a difunctional epoxy resin. Chain stiffness is controlled by changing the chemical structure of the various amines. In agreement with rubber elasticity theory, the rubbery moduli are dependent on f_c and M_c, but independent of chain stiffness. The glassy moduli and secondary relaxations of these networks are relatively independent of f_c, M_c, and chain stiffness. However, the glass transition temperatures (T_g) of these networks are dependent on all three structural variables. This trend is consistent with free volume theory and entropic theories of T_g. f_c, M_c, and chain stiffness control the yield strength of these networks in a manner similar to that of T_g and is the result that both properties involve flow or relaxation processes. Fracture toughness, as measured by the critical stress intensity factor (K_Ic), revealed that f_c and M_c are both critical parameters. The fracture behavior is the result of the fracture toughness being controlled by the ability of the network to yield in front of the crack tip. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1371–1382, 1998     

Structure and property relationships in model diglycidyl ether of bisphenol‐a and diglycidyl ether of tetramethyl bisphenol‐a epoxy systems. I. Mechanical property characterizations

Model epoxy networks, with variations in crosslink density and in epoxy monomer rigidity, were prepared to study how the network structure affects modulus, T_g, and toughness/toughenability of epoxy resins. Diglycidyl ether of bisphenol‐A and diglycidyl ether of tetramethyl‐bisphenol‐A, along with the corresponding chain extenders, were chosen to study how monomer backbone rigidity and crosslink density affect physical and mechanical properties of epoxies. The present study indicates that, as expected, the backbone rigidity of the epoxy network, not the crosslink density alone, will strongly influence modulus and T_g of epoxy resins. Upon rubber toughening, it is found that the rigidity of the epoxy backbone and/or the nature of the crosslinking agent utilized are most critical to the toughenability of the epoxy. That is, the well‐known correlation between toughenability and the average molecular weight between crosslinks (M_c) does not necessarily hold true when the nature of epoxy backbone molecular mobility is altered. The potential significance of the present findings for a better design of toughened thermosets for structural applications is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2137–2149, 1999     

Synthesis of hydroxyl‐terminated poly(ether ether ketone) with pendent tert‐butyl groups and its use as a toughener for epoxy resins

Hydroxyl‐terminated poly(ether ether ketone) with pendent tert‐butyl groups (PEEKTOH) was synthesized by the nucleophilic substitution reaction of 4,4′‐difluorobenzophenone with tert‐butyl hydroquinone with potassium carbonate as a catalyst and N‐methyl‐2‐pyrrolidone as a solvent. Diglycidyl ether of bisphenol A epoxy resin was toughened with PEEKTOHs having different molecular weights. The melt‐mixed binary blends were homogeneous and showed a single composition‐dependent glass‐transition temperature (T_g). Kelley–Bueche and Gordon–Taylor equations gave good correlation with the experimental T_g. Scanning electron microscopy studies of the cured blends revealed a two‐phase morphology. A sea‐island morphology in which the thermoplastic was dispersed in a continuous matrix of epoxy resin was observed. Phase separation occurred by a nucleation and growth mechanism. The dynamic mechanical spectrum of the blends gave two peaks corresponding to epoxy‐rich and thermoplastic‐rich phases. The T_g of the epoxy‐rich phase was lower than that of the unmodified epoxy resin, indicating the presence of dissolved PEEKTOH in the epoxy matrix. There was an increase in the tensile strength with the addition of PEEKTOH. The fracture toughness increased by 135% with the addition of high‐molecular‐weight PEEKTOH. The improvement in the fracture toughness was dependent on the molecular weight and concentration of the oligomers present in the blend. Fracture mechanisms such as crack path deflection, ductile tearing of the thermoplastic, and local plastic deformation of the matrix occurred in the blends. The thermal stability of the blends was not affected by blending with PEEKTOH. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 541–556, 2006     

Divinylsiloxane‐bisbenzocyclobutene‐based polymer modified with polystyrene–polybutadiene–polystyrene triblock copolymers

Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high T_g and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006     

Influence of carboxyl‐terminated (butadiene‐co‐acrylonitrile) loading on the mechanical and thermal properties of cured epoxy blends

A mixture of epoxy with liquid nitrile rubber, carboxyl‐terminated (butadiene‐co‐acrylonitrile) (CTBN) was cured under various temperatures. The cured resin was a two‐phase system, where spherical rubber domains were dispersed in the matrix of epoxy. The morphology development during cure was investigated by scanning electron microscope (SEM). There was slight reduction in the glass transition temperature of the epoxy matrix (T_g) on the addition of CTBN. It was observed that, for a particular CTBN content, T_g was found to be unaffected by the cure temperature. Bimodal distribution of particles was noted by SEM analysis. The increase in the size of rubber domains with CTBN content is due probably to the coalescence of the rubber particles. The mechanical properties of the cured resin were thoroughly investigated. Although there was a slight reduction in tensile strength and young's modulus, appreciable improvements in impact strength, fracture energy, and fracture toughness were observed. Addition of nitrile rubber above 20 parts per hundred parts of resin (phr) made the epoxy network more flexible. The volume fraction of dispersed rubbery phase and interfacial area were increased with the addition of more CTBN. A two‐phase morphology was further established by dynamic mechanical analysis (DMA). © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2531–2544, 2004     

Effects of water on epoxy cure kinetics and glass transition temperature utilizing molecular dynamics simulations

Effects of water on epoxy cure kinetics are investigated. Experimental tests show that absorbed water in an uncured bisphenol‐F/diethyl‐toluene‐diamine epoxy system causes an increase in cure rate at low degrees of cure and a decrease in cure rate at high degrees of cure. Molecular simulations of the same epoxy system indicate that the initial increase in cure rate is due to an increase in molecular self‐diffusion of the epoxy molecules in the presence of water. Effects of water on the glass transition temperature (T_g) of the crosslinked thermoset are also studied. Both experiments and simulations show that water decreases T_g. Both types of results indicate that T_g effects are small below 1% water by weight, but that T_g depression occurs much quickly with increasing water content above 1%. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1150–1159     

Engineering superior toughness in commercially viable block copolymer modified epoxy resin

The microstructure and mechanical properties of a block copolymer modified commercial thermoset plastic formed from a bisphenol-A based epoxy and a bio-derived amine hardener (Cardolite^® NC-541LV) were investigated. A series of poly(ethylene oxide)-b-poly(butylene oxide) (PEO-PBO) diblock copolymers was synthesized at fixed composition (31 ± 1% by volume PEO) and varying molecular weight expanding on a commercially available PEO-PBO compound marketed by the Dow Chemical Company under the trade name FORTEGRA™ 100; direct application of any of these block copolymers resulted in little improvement of the poor fracture toughness of the cured material. Modification of the resin formulation and curing protocol led to the development of well-defined spherical and branched worm-like micelles containing a PBO core and PEO corona in the cross-linked products as evidenced by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) measurements. Maximum fracture toughness (K_1c) and a ninefold increase in the critical strain energy release rate (G_1c) over the unmodified neat epoxy was achieved at 5 wt % loading of intermediate molecular weight PEO-PBO, without measureable reductions in modulus, glass transition temperature or transparency. This study provides new strategies for engineering improved performance in thermoset materials using block copolymer additives that exhibit challenging mixing thermodynamic characteristics with the component monomers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 189–204     

The temperature‐dependent ballistic performance and the ductile‐to‐brittle transition in polymer networks

The temperature dependence of the ballistic impact performance of a series of transparent polymer networks is evaluated. A systematic series of homogeneous epoxy/propylene‐oxide‐based thermosets, a nanoscale phase‐separated epoxy/dual amine thermoset, and two homogeneous, completely aliphatic materials synthesized via ring‐opening metathesis polymerization are examined. The Vogel temperature (T_o) and the Kauzmann temperature (T_K) are critical parameters for scaling the temperature‐dependent ballistic impact performance of each class of materials. The ductile‐to‐brittle transition temperature in a series of propylene‐oxide amine‐cured epoxies occurs at the material T_K, corresponding to a sharp drop in fracture toughness and ballistic impact performance. Two aliphatic, ring‐opening metathesis polymerized materials are found to exhibit no clear transition from purely ductile to purely brittle behavior, but the temperature dependence is still scaled to a single curve when normalized by T_o. The cooperatively rearranging region (CRR) or the volume of this region is related to the breadth of temperatures over which these materials exhibit purely ductile deformation both quasi‐statically and at higher rates. The temperature‐dependent performance is discussed in the context of the configurational entropy. The breadth of the ductility window is related to the size of the CRR, calculated from calorimetric measurements at the resin T_g. Published 2019. This article is a U.S. Government work and is in the public domainin the USA. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 511–523     

Effect of end group chemistry on surface molecular motion of monodisperse polystyrene films

The surface molecular motion of monodisperse polystyrene (PS) with various chain end groups was investigated on the basis of temperature‐dependent scanning viscoelasticity microscope (TDSVM). The surface glass transition temperatures, T_g^ss for the proton‐terminated PS (PS‐H) films with number‐average molecular weight, M_n of 4.9k–1,450k measured by TDSVM measurement were smaller than those for the bulk one, with corresponding M_ns, and the T_g^ss for M_n smaller than ca. 50k were lower than room temperature (293 K). In the case of M_n = ca. 50k, the T_g^ss for the α,ω‐diamino‐terminated PS (α,ω‐PS(NH₂)₂) and α,ω‐dicarboxy‐terminated PS (α,ω‐PS(COOH)₂) films were higher than that of the PS‐H film. On the other hand, the T_g^s for the α,ω‐perfluoroalkylsilyl‐terminated PS (α,ω‐PS(SiC₂C^F₆)₂) film with the same M_n was much lower than those for the PS films with all other chain ends. The change of T_g^s for the PS film with various chain end groups can be explained in terms of the depth distribution of chain end groups at the surface region.     

Phase behavior and some calorimetric and physical properties of diurethanes from perfluoropolyether macromonomers

Density and calorimetric measurements have been carried out on copolymeric perfluoropolyethers of molecular weight ranging between 500 and 4700, terminated at both chain ends either with  CH₂OH or ethylurethane groups. Samples of the second series are models for perfluoropolyethers based polyurethanes. Density measurements point out that the terminal alcoholic group brings about a negative excess volume, which increases with decreasing the molecular weight; a lower excess volume is found for urethane‐terminated molecules. Calorimetric traces, T_g, and Δc_p at T_g show that alcoholic‐terminated molecules are amorphous and one phase systems, while urethane‐terminated compounds are crystalline; phase separation is observed for this last series when the molecular weight of the fluorinated segment is larger than 1000. The trend of T_g with molecular weight is discussed for one‐ and two‐phase systems in the light of current theories for the glass transition. The decrease of the melting point with increasing the molecular weight for the urethane series can be described by the Flory equation for random copolymers. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1609–1622, 1999     

Thermal properties and toughness performance of hyperbranched‐polyimide‐modified epoxy resins

An amine‐terminated hyperbranched polyimide (HBPI) was prepared by the condensation polymerization of a commercially available triamine monomer with a dianhydride monomer. The effects of the HBPI content on the thermal and mechanical interfacial properties of diglycidyl ether of bisphenol A (DGEBA) epoxy resins were investigated with several techniques. The thermogravimetric analysis results showed that the thermal stability of the DGEBA/HBPI blends did not obviously change as the HBPI content increased. The glass‐transition temperature (T_g) of the DGEBA/HBPI blends increased with the addition of HBPI. Improvements in the critical stress intensity factor (K_IC) and impact strength of the blends were observed with the addition of HBPI. The K_IC value and impact strength were 2.5 and 2 times the values of the neat epoxy resins with only 4 wt % HBPI. The fractured surfaces were studied with scanning electron microscopy to investigate the morphology of the blends, and they showed that shear deformation occurred to prevent the propagation of cracks in the DGEBA/HBPI blends. These results indicated that a toughness improvement was achieved without a decrease in the thermal stability or T_g. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3348–3356, 2006     

Synthesis and characterization of polytulipalin‐g‐polylactide copolymers

Graft copolymers of poly(tulipalin A) (PT) and poly(DL‐lactide) (PDLLA) (PT‐g‐PDLLA) having various graft lengths and ratios were synthesized by free‐radical copolymerization of α‐methylene‐γ‐butyrolactone (MBL) and PDLLA macromonomers (HEMA‐PDLLA) terminated by 2‐hydroxyethyl methacrylate (HEMA)‐terminated. HEMA‐PDLLA were synthesized by ring opening polymerization (ROP) of DL‐lactide in the presence of HEMA. Both HEMA‐PDLLA and the copolymers were characterized by NMR spectroscopy and gel permeation chromatography (GPC). The thermal properties of the graft copolymers were found to depend on the graft length and the ratio. The copolymers consisting of PDLLA side chains of M_n = 500 Da showed a single T_g between T_gs of the two component polymers, suggesting a miscible state of PT and PDLLA. In contrast, the copolymers consisting of PDLLA side chains of M_n = 1100, 2000, and 7000 Da showed two isolated T_g, suggesting two segregated domains. The AFM phase images of the copolymers supported the single and phase‐separated morphologies for the former and latter systems, respectively. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Morphology,tensile properties,and fracture toughness of epoxy/Al2O3 nanocomposites

Epoxy/Al₂O₃ nanocomposites were prepared using an epoxy resin, diglycidyl ether of bisphenol A, and cured with a polyoxypropylene diamine (Jeffamine D‐400). Transmission electron microscopy and wide angle X‐ray diffraction were employed to reveal the morphology of epoxy/Al₂O₃ nanocomposites. Dynamic mechanical analysis results showed that the storage modulus and the glass transition temperature (T_g) of epoxy were improved. Tensile strength and Young's modulus also increased with increasing Al₂O₃ loading. Fracture toughness, as indicated by the stress intensity factor, K_Q, was determined using single edge notch bending method, and 40% increase in K_Q was observed with only 2 vol % Al₂O₃. Scanning electron microscopy study of fracture surface showed a rather smooth and flat morphology for neat epoxy. However, massive plastic deformation was observed for epoxy/Al₂O₃ nanocomposites, leading to the significant increase in fracture toughness. The influence of spherical Al₂O₃ nanoparticles on thermophysical properties of epoxy was discussed and compared with that of sheet‐like nanoclays. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1466–1473, 2006     

Styrene 4‐vinylbenzocyclobutene copolymer for microelectronic applications

Styrene and 4‐vinylbenzocyclobutene (vinyl‐BCB) random copolymers were prepared by free radical polymerization and studied for suitability as a dielectric material for microelectronic applications. The percentage of vinyl‐BCB in the copolymer was varied from 0 to 26 mol % to optimize the physical and mechanical properties of the cured copolymer as well as the cost. Copolymer in which 22 mol % of vinyl‐BCB was incorporated along with styrene produced a thermoset polymer which, after cure, did not show a T_g before decomposition at about 350 °C. The polymeric material has a very low dielectric constant, dissipation factor, and water uptake. The fracture toughness of the copolymer was improved with the addition of 20 wt % of a star‐shaped polystyrene‐block‐polybutadiene. Blends of the poly(styrene‐co‐vinyl‐BCB) with the thermoplastic elastomer provided material that maintained high T_g of the cured copolymer with only a slight decrease in thermal stability. The crosslinked styrenic polymer and toughened blends possess many properties that are desirable for high frequency‐high speed mobile communication applications. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2799–2806, 2008     

Toughening of a High-performance Bis-nadimide Thermoset by Blending with High-Glass Transition Temperature Linear Polyimides

A nadimide end-capped thermosetting oligomer was modified by blending with three homologous soluble linear polyimides containing bulky lateral fluorene groups with the intention of improving its fracture toughness. These linear polyimides were prepared by polycondensation between 4,4′-(9H-fluoren-9-yliden)-bisphenylamine (cardo structure) and three different bis-phthalic anhydride derivatives, containing between the bis-phthalic moities a secondary alcohol function, a carbonyl function or a hexafluoropropylidene group respectively. The thermoset produced upon heating a thermostable polynadimide network having a glass transition temperature (T_g) close to 300° and a critical stress intensity factor equal to 0.9 MPa.m^1/2. The T_gs of the studied linear polyimides were located above 340° in connection with the chain–chain molecular interactions. After dissolving, the precipitated blend powders with different compositions were thermally polymerized under pressure to give bulk specimens. The resulting morphologies were dependent on the chemical structure of the linear polyimide. As shown by the position of heat deflection temperatures, a well-defined two-phase blend was obtained by introducing the hexafluoropropylidene-containing polyimide, when a fully miscible system was formed with the secondary alcohol-containing polyimide. The parallel increase in fracture toughness seemed to be controlled by the degree of phase separation between the blend components. The greater improvement resulted from the partially fluorinated polyimide: the corresponding K_IC reaching 1.23 MPa.m^1/2 with 20 wt% of linear component. Finally, the toughening effect due to the latter polymer was examined in relation to its average molecular weight. Almost no change was observed if the corresponding inherent viscosity in N-methyl pyrrolidone solution was above 0.2 dl/g. In any case, owing to the high T_g of the linear component, the thermomechanical stability of the blend was maintained at the same level as that of the initial polynadimide network. © 1997 John Wiley & Sons, Ltd.     

Solvent crazing of “dry” polystyrene and “dry” crazing of plasticized polystyrene

The critical strain ε_c for crazing of polystyrene in each of a variety of organic liquids has been measured along with the degree of swelling of the polymer by the liquid and the attendant reduction in the glass transition temperature T_g of the polymer. The critical strain for the crazing in air and the T_g of each of a set of specimens molded from mixtures of o-dichlorobenzene and polystyrene have also been determined. Correlations of ε_c with T_g in the two cases are identical within experimental error for the first 40°C of T_g reduction; these results imply (1) that organic liquids do not exercise a significant surface energy role in solvent crazing and (2) that their only roles are associated with flow processes. Correlation of solvent crazing ε_c with solubility parameter of the crazing fluid is very poor for several reasons that are discussed.     

Synthesis,characterization, and properties of linear poly(ether sulfone)s with dendritic terminal groups

Hybrid linear‐dendritic ABA polymers, where A and B are dendritic and linear polymers, respectively, were synthesized in a single step via step‐growth polymerization of 4,4′‐difluorodiphenylsulfone and bisphenol A using arylether ketone dendrons of first and second generations (G1‐OH and G2‐OH) as monofunctional end‐cappers. These G1 and G2‐terminated poly(ether sulfone)s (G1‐PESs and G2‐PESs) were characterized by ¹H NMR, SEC, DSC, TGA, melt rheology, and tensile tests. The comparison of the glass transition temperatures (T_gs) of these polymers with those of t‐butylphenoxy‐terminated polysulfones reveal that the G1‐ and G2‐PESs have lower T_gs at all molecular weights investigated. However, a plot of T_g versus 1/M_n shows that the difference between the three series becomes negligible at infinite molecular weight and agrees to the chain end free volume theory. The melt viscosities of G1‐PES and G2‐PES with high molecular weights do not show a Newtonian region and, in the high frequency region, their viscosities are lower than that of the control while the stress–strain properties are comparable to those of the control, suggesting that it is possible to reduce the high shear melt viscosity of a PES without affecting the stress–strain properties by introducing bulky dendritic terminal groups. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 958–969, 2008     

Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004