Relating fracture energy to entanglements at partially miscible polymer interfaces

A new model has been developed to calculate the areal chain density of entanglements (Σ_eff) at partially miscible polymer–polymer interfaces. The model for Σ_eff is based on a stochastic approach that considers the miscibility of the system. The values agree between Σ_eff calculated from the model and literature values for the reinforced interfaces. Using Σ_eff calculated from the model, the interfacial width, and the average distance between entanglements, an equation for the fracture energy of nonreinforced polymer interfaces is proposed. This equation is used to model the transition from chain pullout to crazing. As a function of system miscibility, the model for Σ_eff also accurately predicts a maximum in mode I fracture energy (G_c) as a result of the transition from gradient‐driven to miscibility‐limited interdiffusion, which is observed experimentally. As Σ_eff increases, the fracture energy increases accordingly. Compared with a recent model developed by Brown, the new model correctly predicts a reduced G_c (attributed to chain pullout) when the interfacial width is less than the average distance between entanglements. Theoretical predictions of the change in fracture energy with respect to interfacial width agree with the experimental measurements. Finally, it is postulated that the use of a miscibility criterion for G_c may reveal the universal nature of the pullout to crazing transition. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2292–2302, 2002     

Segmental relaxation and partial crystallization of chain‐extended Poly(l‐lactic acid) reinforced with carboxylated carbon nanotube

Temperature‐modulated differential scanning calorimetry (TMDSC) and broadband dielectric spectroscopy (BDS) were employed to study the glass transition, size of the cooperative rearranging regions (CRRs), crystallization kinetics, and dielectric relaxation response of nanocomposites constituted by chain‐extended poly(L‐lactide) (PLLA) and carboxylated carbon nanotubes (f‐CNTs). The CRR size and the number of relaxing structural units decreased in the presence of crystals during isothermal crystallization. All samples displayed both a primary (α) and secondary (β) relaxation in BDS spectra. The relaxation dynamics of PLLA chains was barely affected by the presence of the f‐CNT. Constrained polymer chains and thickness of interphase (t _i) were measured using dielectric spectra in tan δ representation. t _i values were found to be 46 and 24 nm for sample containing 0.2 and 0.5% weight fraction of f‐CNT, respectively. All samples underwent partial crystallization (with roughly 30% of final crystalline fraction) some 15 or 20° above their glass‐transition temperature (T _g). Crystallization leads to a fragile‐to‐strong transition in the temperature dependence of the cooperative α relaxation and to the increased visibility of a Maxwell–Wagner–Sillars (MWS) interfacial relaxation, which appears to be present in all samples. The heterogeneity of the polymeric samples was quantified in terms of a new parameter, the heterogeneity index (H). © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 222–233     

Coil‐stretch transition in deformation flows

We present a novel Monte‐Carlo lattice model for the study of the coil‐stretch transition for polymer chains in deformation flows. Our results indicate that elongational flows are much more effective than shear flows in stretching polymer chains, in full agreement with experimental observation. Our model data also show that the ε˙_c∼M^−1.5 powerlaw observed experimentally for the dependence of critical flow rate on polymer molecular weight can be fully explained through a nonuniform stretching of the chain by the flow. A higher powerlaw exponent is predicted in more affine deformation cases. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2422–2428, 2000     

Interfacial structure and properties in polystyrene/epoxy bilayer films

The interfacial structure and properties of immiscible deuterated polystyrene (dPS)/epoxy bilayer films were investigated with neutron reflectivity as functions of the composition of the epoxy layer, the thickness of the dPS layer, and the annealing time. We have found that the interfacial width and its growth rate depend strongly on the compositions of the epoxy layer but only weakly on the thickness of the dPS layer. The effect of the resin/crosslinker composition on the interfacial width and its growth rate is likely due to the different near‐surface structures that result for different epoxy stoichiometries. For an ultra‐thin dPS film (thickness = 2R_g), the data suggest a slight suppression of the growth of the interfacial width that could be due to confinement effects for the long‐chain molecules such as have been previously reported for a thickness of less than approximately 4R_g, where R_g is the radius of gyration of polymer molecules. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2653–2660, 2002     

The effects of monoepoxide chain termination and their derived soluble fractions on the structure‐property relationships of controlled epoxy networks

A new series of monoepoxide terminated controlled epoxy networks (CENs) and a corresponding soluble fraction polymer (SFP) were prepared to further investigate the effects of chain termination on epoxy thermoset structure‐property relationships. CENs having an initial molecular weight between crosslinks (M_c,i) of ～3000 g/mol using phenylglycidyl ether (PGE) as the chain terminator have thermal and mechanical properties consistent with previously studied monophenol terminated CENs. Glass transition temperature (T_g) decreases monotonically with PGE concentration (ε), whereas fracture toughness decreases sharply at a critical PGE concentration (ε_c). A PGE terminated SFP was prepared corresponding to the soluble fraction expected for the CEN composition at ε_c. The SFP behaves as a weak antiplasticizer in these epoxy thermosets; T_g is reduced and follows the inverse rule of mixtures, and fracture toughness is slightly reduced. By difference it is inferred that most of the deterioration of epoxy thermoset properties resulting from incorporation of chain terminators above ε_c is a result of the presence of nonelastically active pendant chains and by the increase in M_c. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 72–79, 2009     

Effect of nanoclay on relaxation of poly(vinylidene fluoride) nanocomposites

The effect of Lucentite™ STN nanoclay on the relaxation behavior of poly(vinylidene fluoride) (PVDF) nanocomposites was investigated using dielectric relaxation spectroscopy (DRS) and wide- and small-angle X-ray scattering. Lucentite™ STN is a synthetic nanoclay based on hectorite structure containing an organic modifier between the hectorite layers. The addition of this nanoclay to PVDF results in preferential formation of the beta-crystallographic phase. When the STN content increased to 5% and 10%, only the beta-phase was observed. Bragg long period and lamellar thickness both decrease with STN addition. The relaxation rates for processes termed α_a (glass transition, related to polymer chain motions in the amorphous regions) and α_c (related to polymer chain motions in the crystalline regions and fold surfaces) can be described either with the Vogel-Fulcher-Tamman equation or with Arrhenius behavior, respectively. DRS shows that the α_a relaxation rate increases with the concentration of STN because of the reduction of intermolecular correlations between the polymer chains, caused by the presence of layered silicate nanoclay particles, which serve to segregate polymer chains in the amorphous regions. Comparing samples with beta-crystal phase dominant, the relaxation rate for the α_c relaxation also increases with concentration of STN in all nanocomposite samples. Dielectric properties at low frequencies are dominated by the dc conductivity, and as more STN is added, the conductivity increases rapidly. The addition of 10% STN makes the dc conductivity increase by almost four decades when compared with neat PVDF. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2520–2532, 2009     

Relationship between the positive temperature coefficient of resistivity and dynamic rheological behavior for carbon black‐filled high‐density polyethylene

Studies on the relationship between resistivity and dynamic rheological properties of carbon black‐filled high‐density polyethylene (CB/HDPE) composites were carried out. Change of resistivity ρ is associated with the dynamic modulus before the positive temperature coefficient/negative temperature coefficient (PTC/NTC) transition temperature. When the temperature approaches the melting point of HDPE, ρ increases rapidly with a decreasing modulus, corresponding to PTC transition. The resistivity‐dynamic viscoelasticity relationship in the PTC region can be divided into two parts in which the changes of ρ with storage modulus G′ and loss modulus G″ can be described by the scaling laws given by the critical storage modulus and loss modulus G′_c and G″_c; adjustable parameters ρ′_1c, ρ′_2c, ρ″_1c and ρ″_2c; and nonlinear exponents n and m, respectively. The accordance between the experimental data and the scaling functions of the dimensionless quantities (G′/G′_c ? 1) and (G″/G″_c ? 1) in the PTC transition region suggests that the ρ jump may be the result of a modulus‐induced percolation. G′_c and G″_c increase, but the four scaling resistivitis, ρ′_1c, ρ′_2c, ρ″_1c, and ρ″_2c, decrease with increasing CB concentration, implying that the microstructure change of the composites is the determinant factor for the PTC behavior and the resistivity‐dynamic modulus relationship. However, ρ′_2c and ρ″_2c exhibit no scaling dependence. It is suggested that a threshold concentration exists for the modulus of the composites on the basis of examining the plot of both G′_c and G″_c against CB concentration. The scaling laws G′ ～ Φ^x and G″ ～ Φ^y hold for the concentration dependence of the critical modulus when Φ > Φ_c and the estimated values of x and y are 1.10 ± 0.10 and 0.89 ± 0.29, respectively. The resistivity‐dynamic modulus can shift to form a master curve. The horizontal factors a_G′ and a_G″ and the vertical factors a′ and a″ are relevant to the concentration dependence of the dynamic modulus or PTC behavior. It is believed that the former would be involved in changing the mechanical microstructure formed by the complicated interaction of CB particle and polymer segments, and the latter would be involved in the overall changes of conducting a network during the PTC transition region. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 983–992, 2003     

Short‐time elasticity of polymer melts: Tobolsky conjecture and heterogeneous local stiffness

An extended molecular‐dynamics study of the short‐time “glassy” elasticity exhibited by a polymer melt of linear fully‐flexible chains above the glass transition is presented. The focus is on the infinite‐frequency shear modulus G_∞ manifested in the picosecond time scale and the relaxed plateau G_p reached at later times and terminated by the structural relaxation. The local stiffness of the interactions with the first neighbors of each monomer exhibits marked distribution with average value given by G_∞. In particular, the neighborhood of the end monomers of each chain are softer than the one of the inner monomers, so that G_∞ increases with the chain length. G_p is not affected by the chain length and is largely set by the nonbonding interactions, thus confirming for polymer melts the conjecture formulated by Tobolsky for glassy polymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1401–1407     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

Chain overlap and entanglements in dilute polymer solutions: Brownian dynamics simulation

We have analyzed chain conformations and the existence — or otherwise — of chain overlaps and entanglements in dilute polymer solutions (at concentrations c < C^*, c^* = critical concentration). The fundamental problem of existence of chain overlaps in dilute solutions is also related to the drag reduction phenomenon (DR). Some experimental results pertinent to DR are explained in terms of entanglements even for solutions at concentrations defined in ppm. We report results of Brownian dynamics simulations of polymer solutions in which the equations of motion of the chains are solved by using the Langevin equation. Chains move according to actions of a systematic frictional force and a randomly fluctuating force w(t), where t is time. In addition, a shear flow field can be introduced into the model. To evaluate the structure of polymer chains in solution we have devised a measure of interchain contacts and two different measures of entanglements. The results for c = 0.3 c^* demonstrate that both chain entanglements and overlaps take place even in dilute solution. They also confirm predictions from an earlier combinatorial model.     

The dynamics of polymer melts as seen by neutron spin echo spectroscopy

Using the neutron spin echo spectroscopy, the internal segmental diffusion of chain molecules in polymer melts and concentrated solutions was studied. These investigations show that beyond a characteristic length d_t and after a cross over time τ_e(d_t) the segmental diffusion of the single chains is strongly impeded and deviates from the Rouse dynamics. d_t is polymer specific and depends on the temperature as well as on the polymer concentration. Within the framework of the reptation concept, where d_t is identified with the mean distance between intermolecular entanglements or with the tube diameter, the microscopically determined d_t-values agree quite well with those derived from related macroscopic measurements of the plateau modulus. A similar good agreement is also found with respect to the segmental friction coefficients obtained either from the Rouse regime of the NSE spectra or from Theological data of corresponding short chain systems, where entanglements are not yet effective.     

1H NMR study of phase transition of uncharged and negatively charged poly(N-isopropylmethacrylamide) in D2O solutions

¹H NMR spectroscopy has been applied to the analysis of dynamic-structural changes during temperature-induced phase transition of non-ionized poly(N-isopropylmethacrylamide) (PIPMAm) and ionized copolymers of N-isopropylmethacrylamide with sodium methacrylate, all in D₂O solutions with various polymer concentrations (c = 0.1-10 wt.-%) and ionic comonomer mole fractions (i = 0-10 mole %). It was found that the formation of compact globular-like structures during the phase transition is independent of polymer concentration for non-ionized samples; the presence of negative charges on the polymer chains leads to a dependence of the phase transition temperature on c and i. Virtually all PIPMAm segments are in globular-like structures for low polymer concentrations; for c ⩾ 1 wt.-%, this holds only for low content i of the ionic comonomer. An increase in c and i leads to a decrease in the fraction of polymer segments in globular-like structures; for samples with highest values of c and i, the phase transition was not observed.     

Glass transition broadening via nanofiller-contiguous polymer network in aromatic thermosetting copolyester nanocomposites

The glass transition is a genuine imprint of temperature-dependent structural relaxation dynamics of backbone chains in amorphous polymers, which can also reflect features of chemical transformations induced in macromolecular architectures. Optimization of thermophysical properties of polymer nanocomposites beyond the state of the art is contingent on strong interfacial bonding between nanofiller particles and host polymer matrix chains that accordingly modifies glass transition characteristics. Contemporary polymer nanocomposite configurations have demonstrated only marginal glass transition temperature shifts utilizing conventional polymer matrix and functionalized nanofiller combinations. We present nanofiller-contiguous polymer network with aromatic thermosetting copolyester nanocomposites in which carbon nanofillers covalently conjugate with cure advancing crosslinked backbone chains through functional end-groups of constituent precursor oligomers upon an in situ polymerization reaction. Via thoroughly transformed backbone chain configuration, the polymer nanocomposites demonstrate unprecedented glass transition peak broadening by about 100 °C along with significant temperature upshift of around 80 °C. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1595–1603     

Interfacial tension coefficient from the retraction of ellipsoidal drops

A new method for the determination of the interfacial tension coefficient between two immiscible fluids is proposed. The method is particularly useful for the binary polymer blends. The deformed drop retraction method, DDRM, makes it possible to determine the dynamic interfacial tension coefficient, ν, from the time evolution of a distorted fluid drop toward its equilibrium form. Analysis of this interfacial tension-driven process led to a theoretical relation between the shape retraction rate and the system's geometrical and rheological characteristics. Measurements of either low viscosity model systems or high viscosity industrial polymer mixtures led to a good agreement with values obtained from the widely used breaking thread method. DDRM enables to measure ν in polymeric blends of commercial interest—the high viscosity systems that would be very difficult to characterize by other techniques. Furthermore, for the first time it is possible to follow the time dependence of the interfacial tension coefficient, thus unambiguously determine the dynamic and equilibrium values of ν₁₂. For example, in low density polyethylene blends with polystyrene, LDPE/PS, ν decreased with the polymer-polymer contact time, t_c, from ν = 6.9 mN/m at t_c = 12 min, to ν = 5.2 mN/m at t_c ≥ 75 min—the latter may represent the true thermodynamic equilibrium value, ν₁₂. However, it is not clear whether such a reduction is exclusively due to the thermodynamically driven migration of chain-ends, low molecular weight fractions and additives, or by the thermal degradation as well. The contact time dependence of ν explained some of the differences reported for the data obtained using different measurement techniques, viz. pendant drop, capillary breakup, or ellipsoid retraction techniques. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1393–1403, 1997     

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     

Free radical dispersion polymerization of styrene in a mixture of 2-propanol and tetrahydrofuran

Free radical dispersion polymerization of styrene in a mixture of 2-propanol and tetrahydrofuran was carried out at 70°C up to high conversions. The influence of the change of the critical chain length on the evolution of the insoluble polymer component was examined. Monomer conversion and the formation of the insoluble polymer component were measured in order to test a mathematical model presented in our previous article. The critical polymer chain length i₀, the initiation rate constant k_d, and the ratio k_p/k, where k_p and k_t are propagation and termination rate constants, respectively, have been obtained and compared with those reported in the literature. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2757–2761, 1998     

Selective adsorption behavior of polymer at the polymer–nanoparticle interface

Coarse‐grained molecular dynamics simulations are used to investigate the adsorption behavior of monodisperse and bidisperse polymer chains on the nanoparticle (NP) surface at various polymer–NP interactions, chain lengths, and stiffness. At a strong polymer–NP interaction, long chains preferentially occupy interfacial region and squeeze short chains out of the interfacial region. Semiflexible chains with proper stiffness wrap NPs dominantly in a helical fashion, whereas fully flexible chains constitute the surrounding matrix. As chain stiffness increases, the results of the preferential adsorption are the opposite. The chain‐length or chain‐stiffness‐induced selective adsorption behavior of polymer chains in the polymer–NP interfacial region relies on a delicate competition between entropic and enthalpic contributions to the total free energy. These results could provide insights into polymer–NP interfacial adsorption behavior and guide the design of high‐performance nanocomposites. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1829–1837     

Synthesis and characterization of silica‐graft‐polystyrene hybrid nanoparticles: Effect of constraint on the glass‐transition temperature of spherical polymer brushes

The effect of the chain constraint on the glass‐transition temperature of polystyrene (pS) was studied in the context of polymer tethering to curved surfaces. The synthesis and characterization of silica‐graft‐polystyrene (SiO₂‐g‐pS) hybrid nanoparticles is reported. Silica nanoparticles possessing covalently bound pS chains were prepared by the atom transfer radical polymerization of styrene from functionalized colloidal surfaces. These hybrid nanoparticles serve as interesting examples of spherical polymer brushes, as a high density of grafted pS was achieved on the inorganic colloid. The confirmation of a brushlike extension of immobilized chains in a good solvent was obtained with dynamic light scattering in toluene of SiO₂‐g‐pS colloids possessing various molar masses of tethered pS. The solid‐state morphology of SiO₂‐g‐pS ultrathin films was assessed with transmission electron microscopy, and this confirmed that the silica colloids were well‐dispersed in a matrix of the tethered polymer. Differential scanning calorimetry was used to study the effects of tethering and chain immobilization on the glass‐transition temperature of pS. The measured glass‐transition temperature of annealed bulk films of the hybrid nanoparticles was elevated with respect to the value for pure bulk pS. The enhancements ranged from 13 to 2 K for SiO₂‐g‐pS brushes possessing tethered pS with number‐average molecular weights of 5230 and 32,670 g/mol, respectively. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2667–2676, 2002     

Interfacial adhesion mechanisms in incompatible semicrystalline polymer systems

The mechanism of adhesion at semicrystalline polymer interfaces between isotactic polypropylene (iPP) and linear low‐density polyethylene (PE) was studied with transmission electron microscopy (TEM) and an asymmetric‐double‐cantilever‐beam test. From the TEM images, both the interfacial width and the lamellar thickness of the polymers were extracted. During annealing, the interfacial width increased with the annealing temperature, and this indicated the accumulation of amorphous polymers at the interface. The interfacial strength, determined from the critical fracture energy (G_c), also increased with the annealing temperature and reached a maximum above the melting temperatures of iPP and PE, whereas the smallest G_c value was obtained below the melting temperatures of the two materials. A mechanism of interfacial strengthening was proposed accounting for the competition between the interdiffusion of PE and crystallization of iPP. As the annealing temperature increased, the rates of PE diffusion and iPP crystallization increased. Although the crystallization of iPP hindered the interdiffusion of PE, both the interfacial width and the fracture energy increased with the temperature, and this indicated that PE interdiffusion dominated iPP crystallization. Below the critical temperature, the fracture surfaces of both iPP and PE were smooth, and chain pullout dominated the fracture mechanism. Above the critical temperature, iPP crystallization still hindered the interdiffusion, and crazes could be seen on the iPP side. Above the melting temperatures of the two materials, ruptured surfaces could also be seen on the PE side, and crazing was the fracture mechanism. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2667–2679, 2004     

Micellization to gelation of a triblock copolymer in water: Thermoreversibility and scaling

Aqueous solutions of a poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) triblock copolymer, Pluronic F108 (PEO₁₃₃PPO₅₀PEO₁₃₃), ranging from 1 to 35 wt %, were studied with differential scanning microcalorimetry and rheology. The thermoreversible micellization and gelation were examined through a heating process and a subsequent cooling process at a fixed rate of 1 °C/min. The critical micellization temperature (CMT), determined by the onset temperature of the endothermic peak in the heating process, was a decreasing function of the F108 concentration. A small secondary endothermic peak appeared only when the polymer concentration was 22.5 wt % or higher, indicating that there was a sol–gel transition but that the gelation was a nearly athermic process. Upon heating, an abrupt increase was observed in both the dynamic storage modulus (G′) and dynamic loss modulus (G″) within a narrow temperature range. T_G′, the temperature for the transition in G′, was a linear decreasing function of the polymer concentration and different from CMT. T_G′ tended to approach CMT with an increasing F108 concentration. Beyond this transition, G′ reached a plateau, and the plateau increased in height and broadened with the polymer concentration. The value of G′ at 70 °C (G′₇₀) could be approximately scaled with concentration c by G′₇₀ ∝ c^7.3. In addition, the definition for a gel to obey G′ > G″ was valid only when c was greater than 22.5 wt %, and this was in agreement with the secondary endothermic peak found with differential scanning calorimetry. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2014–2025, 2004