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     

Effects of composition drift on the effectiveness of random copolymer reinforcement at polymer–polymer interfaces

Random copolymer layers are surprisingly effective at reinforcing polymer–polymer interfaces. One hypothesis is that composition drift during synthesis can account for the higher than expected toughening. To test this hypothesis, we polymerized a series of poly(d‐styrene‐r‐2‐vinylpyridine) (dPS_f‐r‐PVP_1?f) copolymers with various fractions (f) of deuterated styrene to only 10% completion to avoid composition drift. The fracture energies (G_c) of polystyrene/dPS‐r‐PVP/poly(2‐vinylpyridine) interfaces with relatively thick layers of dPS‐r‐PVP were measured. G_c decreased relative to interfaces reinforced with composition‐drifted dPS‐r‐PVP. Conversely, G_c increased when two or more copolymers were blended together. In such samples, the copolymers form distinct layers with multiple interfaces characterized by the difference in f (Δf) between adjacent layers. We find that G_c is governed by Δf_max, the largest difference in adjacent compositions, and, therefore, by the width of the narrowest interface (w_min). G_c increases strongly as w_min increases from 3 to 5 nm. Remarkably, these w_min values are about half the entanglement spacing in bulk polystyrene. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2363–2377, 2001     

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     

Thermodynamic characterization of polymer‐polymer interfaces

The properties of multiphase polymer blends are determined in part by the nature of the polymer‐polymer interface. The interfacial tension, γ, influences morphology development during melt mixing while interfacial thickness, λ, is related to the adhesion between the phases in the solid blend. A quantitative relation between the thermodynamic interaction energy and these interfacial properties was first proposed in the theory of Helfand and Tagami and has since been correlated with experimental measurements with varying degrees of success. This paper demonstrates that the theory and experiment can be unified for polymer pairs of some technological importance: copolymers of styrene and acrylonitrile (SAN) with poly (2, 6‐dimethyl‐1, 4‐phenylene oxide) (PPO) and with bisphenol‐A polycarbonate (PC). For each pair, the overall interaction energy was calculated using a mean‐field binary interaction model expressed in terms of the interactions between repeat unit pairs extracted from blend phase behavior. Predictions of γ and λ as a function of copolymer composition made by combining the binary interaction model with the Helfand‐Tagami theory compare favorably with experimental measurements.     

Temperature‐dependent polymer–polymer interactions in polystyrene–polyethylene blends

The effect of the temperature on the interaction between the components of an immiscible polystyrene–polyethylene blend has been analyzed with different techniques. Lap‐shear‐strength data and morphological observations indicate an enhanced interaction between the polymeric phases at elevated temperatures, at which dispersive forces are known to predominate. This raises the degree of compatibility of the polymeric components. Rheological measurements also justify the concept of increased adhesion between the components of the blend when it is processed at very high temperatures. Differential scanning calorimetry analysis lends support to an improved homogeneity of the blend at an elevated temperature; this is again consistent with an improved interaction between the blend phases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2545–2557, 2004     

Properties of fracture surfaces of glassy polymers: Chain scission versus chain pullout

Fresh fracture surfaces formed by tensile failure of craze in molded polystyrene (PS) bars have been compared with the molded surfaces of the same bars, using an atomic force microscope with a thermal probe and operated in local thermal analysis. The results indicate that molecular weight is much higher in the interior of the sample than at the surface. No evidence was found for degradation of the PS chains via chain scission during crazing. Alternative explanations for the low‐molecular weights at the molded surface are discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Free energy of an inhomogeneous polymer–polymer–solvent system. II

A complete expression for the enthalpy of mixing of inhomogeneous polymer–polymer–solvent systems applicable for small as well as large concentration fluctuations has been developed. This is used to express the free energy of inhomogeneous polymer–polymer–solvent systems in an extended form of the Landau-Ginzburg functional. The gradient energy parameters obtained here are consistent with the published results. The free energy functional has been applied to develop a generalized continuity equation for spinodal decomposition in polymer–polymer systems. A linearized version of this continuity equation has been used to study the effect of the gradient terms on the dominant wavelength during spinodal decomposition.     

Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004     

A TSC investigation of polymer–polymer contact charging

The transfer of charge across the interface between two materials brought into contact was studied by measuring the small currents produced when layered films composed of two dissimilar films were first heated and then held under isothermal conditions. It was found that, given a fixed electrode orientation, the polarity of the current generally reversed when the relative position of the films were reversed. The sense of the current was in agreement with that expected from the polymer work functions. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2901–2912, 1997     

A quantitative model for the specific volume of polymer–diluent mixtures in the glassy state

A mathematical model to describe the specific volume of glassy mixtures of a polymer and a low molecular weight diluent or additive is presented. The model is based on understandable physical assumptions and relies on parameters that can be determined experimentally or estimated from methods available in the literature. The predictions of the model show good agreement with the experimental data for mixtures of four polymers with diluents that in the pure state are liquid, glassy, or crystalline. The observed negative departure from volume additivity, as defined by simple additivity of the specific volume of the pure glassy polymer and the pure amorphous diluent, is the result of the relaxation of the excess volume of the glassy mixture relative to the equilibrium state caused by mixing two components with different glass transition temperatures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1037–1050, 1998     

Models for adhesion at weak polymer interfaces

The weak interfaces between immiscible polymer pairs typically fail through chain scission. The critical facture toughness for such interfaces is closely related to the density of intermolecular entanglements at the interface. From scaling analysis, a simple correlation between facture toughness and chain entanglement was developed. It predicts well the interfacial adhesion for many immiscible polymer pairs found in the literature. For an interface with block copolymer reinforcement, its critical fracture toughness comes from both intermolecular entanglements of homopolymers and copolymer bridges. In the chain scission regime (low copolymer coverage), the block copolymer contribution is found proportional to copolymer interfacial coverage, with the coefficient being the energy to stretch and break a copolymer chain. The chain‐breaking energy for different copolymers was evaluated and compared to literature data. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2313–2319, 2009     

Microstructure and fracture behavior of semicrystalline polymer–clay nanocomposites

The relationships between the microstructure and the fracture behavior of three polymer/clay nanocomposites were studied. Two different polymer matrices were chosen, namely polyamide‐6 and polyethylene (compatibilized with PE‐g‐MA or PE‐g‐PEo), to reach very different clay dispersion states. The microstructure was characterized in terms of polymer crystallinity, orientation of the polymer crystalline lamellae, clay dispersion state, and orientation of the clay tactoids. The mechanical behavior was characterized by tensile tests. The essential work of fracture (EWF) concept was used to determine the fracture behavior of the nanocomposites. Both tensile and EWF tests were performed in two perpendicular directions, namely longitudinal and transversal. It is shown that the fracture behaviors of the matrices mainly depend on the polymer crystalline lamellae orientation. For the nanocomposites, the relationships between the matrix orientation, the clay dispersion states, the values of the EWF parameters (w_e and βw_p), and their anisotropy are discussed. The results show that the lower the average clay tactoid thickness, the lower is the decrease of fracture performance for the nanocomposite and the more consumed energy as longer the path of the crack. Besides, a linear dependence of the anisotropy of the EWF parameters of the nanocomposites on the average clay aspect ratio is found. The more exfoliated the structure is, the less pronounced the anisotropy of the EWF parameters. Interestingly, it is thought that the average clay aspect ratio is the parameter representing the clay dispersion state that governs the fracture anisotropy of the nanocomposites (as the elastic properties determined by tensile tests). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1820–1836, 2008     

Growth and decay of concentration fluctuations in polymer–polymer mixtures

A computer simulation based on the Cahn–Hilliard nonlinear diffusion equation, developed in the field of metallurgy, is applied to the demixing behavior of a polymer–polymer mixture. The simulation is a one-dimensional version. Spatially periodic concentration fluctuations appear at a very early stage and evolve with the wave number almost constant. Later some waves are absorbed into neighboring ones, resulting in a decrease in the average wave number of the concentration fluctuation. Thus, characteristic phenomena in the demixing are successfully described by the computer simulation. Furthermore, the simulated time variation of wave number agrees with experimental results in the literature. The analysis is extended to two-step quenching: after a homogeneous mixture undergoes the first temperature-jump from the single-phase region to the two-phase region of the phase diagram, the system is allowed to demix isothermally for a time, and then the demixed system undergoes the second jump to deeper or shallower quench. When the quench depth of the second jump (ΔT₂) is smaller than half the first depth (ΔT₁), the concentration fluctuation as developed under ΔT₁ decays with time after the second jump. When ΔT₂ is between ΔT₁ and (ΔT₁/2), the fluctuation decays slightly after the second jump and then increases. When the second jump is to a deeper quench (ΔT₂ > ΔT₁), a new fluctuation of short wavelength is superimposed on the previously developed one.     

Effect of chain interpenetration on polymer–polymer interaction in solution

Two series of monodisperse polystyrenes have been prepared with a molecular weight range of 3,000 to 300,000. One series was lightly substituted with dimethylbenzylamine groups, the other with 2,6 dinitro-4-benzoyloxyphenol groups. Members of each series were dissolved together in benzene solution in the range of 0.1–30%, and the equilibrium constant for the formation of the ammonium phenolate ion pair measured. Also measured was the corresponding equilibrium constant between comparable small molecular weight analogs, and between these analogs and the substituted polymers. The degree of association found between the models and between the models and the polymers was independent of molecular weight, but deviations were found in the polymer–polymer interaction. Normal equilibrium constants were found at high polymer concentrations indicating that chain interpenetration occurred freely. At low concentrations of polymer, if several links per chain were possible it was found an excess of linkages were formed. If only one link per chain was possible, low degrees of association were found for high molecular weight polymers, but the effect was not as large as a consideration of excluded volumes on a spherical model would predict.     

Model for anomalous moisture diffusion through a polymer–clay nanocomposite

Experimental data are reported on moisture diffusion and the elastoplastic response of an intercalated nanocomposite with vinyl ester resin matrix and montmorillonite clay filler at room temperature. Observations in diffusion tests showed that water transport in the neat resin is Fickian, whereas it becomes anomalous (non‐Fickian) with the growth of the clay content. This transition is attributed to immobilization of penetrant molecules on the surfaces of hydrophilic clay layers. Observations in uniaxial tensile tests demonstrate that the response of vinyl ester resin is strongly elastoplastic, whereas an increase in the clay content results in a severe decrease of plastic strains observed as a noticeable reduction in the curvatures of the stress‐strain diagrams. This is explained by slowing down the molecular mobility in the host matrix driven by confinement of chains in galleries between platelets. Constitutive equations are developed for moisture diffusion through and the elastoplastic behavior of a nanocomposite. Adjustable parameters in these relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. A striking similarity is revealed among changes in diffusivity, ultimate water uptake, and the rate of plastic flow with an increased clay content. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 476–492, 2003     

Study of the carbon fiber–poly(ether–ether–ketone) (PEEK) interfaces, 2: relationship between interfacial shear strength and adhesion energy

In the second part of this general study, the carbon fiber–PEEK interfacial shear strength is measured by means of a fragmentation test on single-fiber composites. Different thermal treatments (continuous cooling from the melt, isothermal treatments and long melting temperature time) are applied to these model composites prior to testing. The results are systematically compared with the previously determined reversible work of adhesion between carbon fiber and PEEK. It is shown that physical interactions at the interface determine, to a large extent, the magnitude of the interfacial shear strength between both materials. However, it appears that the magnitude of the stress transfer from the matrix to the fiber is affected either by the existence of an interfacial layer or by a preferential orientation of the polymer chains near the fiber surface. The results obtained on systems that have been subjected to isothermal treatments (isothermal crystallization of PEEK) seem to confirm the existence of a transcrystalline interphase, the properties of which are dependent upon the crystallization rate of the matrix and the interfacial adhesion energy.     

Molecular mobility of nitroxide spin probes in glassy polymers. Quasi‐libration model

ESR spectra of three spin probes with different molecular volumes: 2,2,6,6‐tetramethyl‐4‐oxopiperidine‐1‐oxyl, di‐p‐anisylnitroxide, and nitroxide derivative of fullerene in glassy polystyrene, polyvinyl trimethylsilane, and Teflon AF‐2400 were calculated numerically within the model of quasi‐libration motions. Temperature ranges, where the model is capable to reproduce spectra within experimental errors, were defined. It was found that simulation of X‐band ESR spectra allows to determine quasi‐libration amplitudes around molecular axes X and Y with accuracy ～ 3° and around Z axis with accuracy ～ 15–20°. A shape of distribution of quasi‐libration amplitudes was also determined qualitatively by ESR spectra simulations. It was established that the average amplitude of quasi‐libration motion depends on the free volume of each polymer and geometrical molecular volume of a spin probe. Quasi‐libration amplitudes increase as the temperature increases, and reach the value of 40 degrees. We found that upon further temperature increase, quasi‐libration model becomes inapplicable for quantitative numerical spectra simulation. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 107–120, 2009     

Griffith fracture of a phenol–formaldehyde polymer

Cast samples of a phenol–formaldehyde polymer with a crack of length defined by a metallic foil inclusion were fractured in tension. The stress at fracture was inversely proportional to the square root of the crack length, in agreement with the Griffith equation for brittle fracture. The behavior did not conform to the Griffith equation with respect to the experimental value of surface free energy, which was several orders of magnitude higher than a theoretically calculated value. However, as the temperature of tensile testing was raised, the experimental value did approach the calculated value. Consistently the appearance of the fracture surface was observed to change from one showing evidence of plastic deformation at room temperature to a featureless appearance, characteristic of brittle fracture, at higher temperatures.