Variation of periodic crazing based on polymer blends of an ultra‐high and a low molecular weight poly(methyl methacrylate)

Periodic crazes are caused in a polymer film by the unique mechanical method using bending. Generation of a craze depends on entanglements of the molecular chains of a polymer. Therefore, control of composite morphology of periodic crazes was attempted by varying the entanglements of molecular chains. An effective entanglement network became sparse by polymer blends of an ultra‐high molecular weight polymethylmethacrylate (PMMA) and a low molecular weight PMMA. Consequently, the composite morphology of periodic crazes caused in the blend film varied. In other words, the periodic craze can be used for the evaluation of the effective entanglements. In addition, it was figured out that PMMA of which the number‐average molecular weight (M_n) is less than twice of the effective entanglement molecular weight (M_e^*) works as a plasticizer in the blend film. And also, it was revealed that the mechanical properties of the blend film decreased dramatically at M_n ≒ 6M_e^*. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44332.     

Role of chain entanglements on fiber formation during electrospinning of polymer solutions: good solvent, non-specific polymer-polymer interaction limit

Chain entanglements are one of many parameters that can significantly influence fiber formation during polymer electrospinning. While the importance of chain entanglements has been acknowledged, there is no clear understanding of how many entanglements are required to affect/stabilize fiber formation. In this paper, polymer solution rheology arguments have been extrapolated to formulate a semi-empirical analysis to explain the transition from electrospraying to electrospinning in the good solvent, non-specific polymer-polymer interaction limit. Utilizing entanglement and weight average molecular weights (M_e, M_w), the requisite polymer concentration for fiber formation may be determined a priori, eliminating the laborious trial-and-error methodology typically employed to produce electrospun fibers. Incipient, incomplete fiber formation is correctly predicted for a variety of polymer/solvent systems at one entanglement per chain. Complete, stable fiber formation occurs at ≥2.5 entanglements per chain.     

A model for the zero shear viscosity

An empirical equation for the number of entanglements per molecule has been proposed, which applies over all the molecular weight range. On this ground a simple equation for the zero shear viscosity of monodisperse polymer melts, η₀, has been worked out that appears able to properly take into account the sharp transition of viscosity between the monomeric and the entanglement regimes. The molecular parameters appearing in the new viscosity equation are: the monomeric molecular weight m₀, the monomeric friction factor ζ₀, the molecular weight M, the average molecular weight between entanglements M_e, and the entanglement friction factor ζ_e^3.4. This last parameter was evaluated for a number of monodisperse polymers.     

Entanglement network of chitin and chitosan in ionic liquid solutions

Concentrated solutions of a chitin from squid pens and of two commercial samples of chitosan were successfully prepared by using an ionic liquid 1‐butyl‐3‐methylimidazolium acetate as a solvent. The dynamic viscoelasticity data for the solutions exhibited rubbery plateaus, indicating the existence of entanglement network of chitin and chitosan in the solutions. To characterize the network, the values of the molecular weight between entanglements (M_e) for chitin and chitosan in the solutions were determined from the plateau moduli. Then the values of M_e in the molten state (M_e,melt), a material constant reflecting the inherent nature of polymer species, for chitin and chitosan were estimated to be 1.7 × 10³ and 3.0 × 10³, respectively. It was found that there was a significant difference in M_e,melt between chitin and chitosan. Compared with other polysaccharides such as cellulose and agarose in terms of the number of monosaccharide units between entanglements (N_unit), chitin had significantly smaller N_unit of 8, while chitosan had equivalent N_unit of 19. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2439–2443, 2013     

Rheological properties of concentrated solutions of agarose in ionic liquid

The rheological properties of agarose solutions were examined under the effect of entanglement coupling between agarose chains. Agarose solutions were prepared by using an ionic liquid 1‐butyl‐3‐methylimidazolium chloride as a solvent. The concentration of agarose was varied from 1.1 × 10¹–2.1 × 10² kg m^?3. The master curves of the angular frequency (ω) dependence of the storage modulus (G′) and the loss modulus (G″) showed a rubbery region in the middle ω region and a flow region at low ω region, respectively. The molecular weight between entanglements (M_e) for agarose was calculated from the plateau modulus. Moreover, M_e for agarose melt was determined to be 2.3 × 10³ from the concentration dependence curve of M_e. By using well‐known empirical relations in polymer rheology, information on molecular characteristics of sample agarose was derived. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Polymer Network Mobility and Environmental Stress Cracking Resistance of High Density Polyethylene

Zero shear viscosity and molecular weight between entanglements (M _e ) are determined from dynamic oscillatory shear experiments. Lower M _e value means higher number of entanglements in the system and is associated with increasing strain hardening stiffness. With the understanding that strain hardening is related to environmental stress cracking resistance (ESCR) of high density polyethylene (HDPE), M _e is then related to the ESCR of several resins in this study. The inversely proportional relationship between M _e and ESCR indicates that low network mobility due to an increasing number of chain entanglements increases the ESCR of HDPE.     

Predicting chain conformation and entanglement of polymers from chemical structure

The characteristic ratio C_∞ and the entanglement molecular weight M_e are two key molecular parameters that control melt viscoelasticity, solid mechanical (brittle/ductile) behavior, and adhesion of polymers. We show that the characteristic ratio C_∞ and the entanglement molecular weight M_e can be predicted from chemical structure by group additivity with uncertainties usually less than ～ 7% for C_∞ and ～ 15% for M_e, comparable with the accuracies of experimental values.     

The Effect of the Density and Nature of Spatial Network in Elastomers on Their Viscoelastic Characteristics

Abstract

We have studied the effect of the density of the networks formed by fluctuating entanglements and chemical crosslinking on the relationships between the circular frequency ω and the storage and loss moduli, G' and G”, for polybutadienes of narrow and wide molecular weight distributions (the ratio M_w/M_n varied from 1.1 to 3.35) and different microstructure. Polybutadienes were crosslinked by thermal, radiation, and sulphur vulcanization. With increasing density v of a network of chemical crosslinks, which is characterized by the average molecular weight of a chain length (M_e ), pseudo-equilibrium plateau extends to the side of low frequencies with a certain small increase of its level. This increase becomes noticeable when M_e is approximately equal to the average molecular weight M_e of the chain length between the fluctuating entanglements of an uncrosslinked elastomer. At the same time the maxima on the curves of G”(ω) are smoothed out and the losses reduce to negligibly small values with decreasing frequency.     

Preparation of long‐chain branched poly(ethylene terephthalate): Molecular entanglement structure and toughening mechanism

Poly(ethylene terephthalate) (PET) was long‐chain branched (LCB) by ring‐opening reaction with both pyromellitic dianhydride and tetrahydrophthalic acid diglycidyl ester as chain extenders through reactive melt processing. It was found that with the increase of chain extenders dosage, the intrinsic viscosity of PET increased and melt index decreased greatly, while both the tensile strength and impact strength of PET were remarkably improved. The elastic modulus (G′) and viscous modulus (G″) were enhanced by chain branching. Compared with PET, the complex viscosities of LCB‐PET were much higher at full frequency range, and obvious shear thinning was presented. The Cole–Cole curve deviated from the semicircular shape and the curve end was inclined to upward in high viscosity region, indicating the formation of the multiple hierarchical structures. The molecular weight of the branch (M_B) was much greater than critical entanglement molecular weight (M _e), which essentially confirmed the existence of LCB structure and fairly strong molecular entanglement in the LCB‐PET molecular chain. When subjected to external force, the entanglement point, acting as physical crosslinking point between the molecules, was in favor of increasing the molecular interaction, reducing the molecular slippage, and bearing a large deformation. POLYM. ENG. SCI., 59:1190–1198 2019. © 2019 Society of Plastics Engineers     

Effect of soft segment molecular weight on tensile properties of poly(propylene oxide) based polyurethaneureas

Influence of soft segment molecular weight and hard segment content on the morphology, thermomechanical and tensile properties of homologous polyurethaneurea copolymers based on narrow molecular weight poly(propylene oxide)glycol (PPG) oligomers were investigated. A series of polyurethaneureas with hard segment contents of 12–45% by weight and PPG number average molecular weights <M_n> of 2000 to 11,800 g/mol were synthesized and characterized structurally by SAXS and mechanically by DMA and stress strain analysis. Bis(4-isocyanatocyclohexyl)methane and 2-methyl-1,5-diaminopentane were used as the diisocyanate and the chain extender respectively. All copolymers displayed microphase separation by SAXS and DMA. The critical entanglement molecular weight (M_e) of PPG is reported to be around 7700 g/mol. Our mechanical results suggest that when copolymers possess similar hard segment contents and are compared to those based on soft segments with number average molecular weights (M_n) greater than M_e, they generally displayed higher tensile strengths and particularly lower hysteresis and creep than those having soft segment molecular weights below M_e. These results imply that soft segment entanglements in thermoplastic polyurethaneureas may provide a critical contribution to the tensile properties of these copolymers – particularly in the range where the soft segment content is dominant.     

Influence of polymer microstructure on the performance of post‐treated latex‐based pressure sensitive adhesives

Latex‐based butyl acrylate (BA)/acrylic acid (AA)/2‐hydroxyethyl methacrylate (HEMA) pressure sensitive adhesive (PSA) films with various microstructures were heated to improve their performance. The treated PSA films showed significantly better performance than original latex‐based PSA films with similar polymer microstructures. The effect of the heat treatment depended on the polymer microstructure of the untreated PSA films (or corresponding latices). Decreasing the amount of very small sol polymers (i.e., M_x < 2M_e) in gel‐free untreated PSA films, or both very small (i.e., M_x < 2M_e) and very large sol polymers (i.e., M_x > 20M_e) in gel‐containing untreated PSA films led to treated PSA films with significantly better performance. (Note: M_e is the molecular weight between two adjacent entanglement points in a polymer material.) In addition, simultaneously increasing the sol polymer molecular weight (M_w) as well as the size of the chain segments between two adjacent cross‐linking points (M_c) of the gel polymer in the original PSAs resulted in treated PSA films with better performance. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Influence of molecular weight on the fracture of poly(methyl methacrylate) (PMMA)

A model is proposed to explain the dependence of fracture parameters on the molecular weight of glassy polymers. The model assumes that the fracture event occurs in two stages; the first involves the orientation of polymer chain segments between entanglement points and the second, the fracture itself. A value has been calculated, (～0.6J m^?2), for the fracture surface energy corresponding to the lower critical molecular weight between entanglements, M=M_e. Allowing for the simplifying assumptions made in its derivation, this value is in good agreement with that found experimentally. It is proposed that, after the chain segments between entanglements crossing a plane have been fully extended, two possible mechanisms are involved; chain ‘pull-out’ up to a maximum governed by the time scale of the local fracture event, or chain scission. Using the concept of a reptating chain it is proposed that above M ～2 M_e there is a relationship between the fracture energy (γ) and the molecular weight of the form γ∝ ∝M² up to a critical value of M, above which γ is constant. It has been shown that there is some agreement with experimental relationships determined independently.     

Craze microstructure and molecular entanglements in polystyrene-poly(phenylene oxide) blends

Polystyrene and poly(phenylene oxide) are miscible over the entire range of compositions. Thin films of five blends of high molecular weight polystyrene (PS) with high molecular weight poly(phenylene oxide) (PPO), and four blends of low molecular weight PS (whose molecular weight lies below its entanglement molecular weight M_e) with the same PPO have been prepared. Following bonding of these films to copper grids, crazes were grown by uniaxial straining in air. Suitable crazes were then observed by transmission electron microscopy. From microdensitometry of the image plates it is possible to measure the extension ratio λ_craze within crazes in the nine blends. These measured values are compared with predicted values of λ_max, computed from λ_max = I_ed, where I_e is the chain contour length between entanglements and d is the root mean square end-to-end distance for a chain of molecular weight M_e. For the high molecular weight PS blends λ_max depends on the entanglement properties of both PS and PPO chains. For the low molecular weight PS blends, the PS chains cannot form part of the entanglement network and the correct value of λ_max is obtained from appropriate scaling of the pure PPO value. Comparison of λ_craze and λ_max for both types of blends shows excellent agreement, demonstrating the importance of the entanglement network in determining craze parameters and hence the toughness of a given polymer.     

Rheological quantification of molecular parameters: Application to a hydrogen bond forming blend

The component dynamics and molecular parameters were investigated for miscible poly(4‐vinyl phenol)/poly(ethylene oxide) (PVPh/PEO) blends. Global values of molecular weight between entanglements (M_e) were first estimated for the blends and were compared with existing athermal model predictions. Global interchain friction coefficients (ξ) of the blends were deduced from the zero‐shear viscosity. A maximum was observed at a composition of 20–30 wt % of PEO. Chain dimensions of this phase are estimated by using a relationship between the plateau modulus and a packing length (i.e., number of individual chains present in a given small volume of the melt). A slight increase in M_e is observed at low PEO weight fraction (before 0.20), followed by a sharp decrease in M_e values after this concentration. Values of ξ in PVPh/PEO blends show a maximum value at 20–30 wt % of PEO. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1623–1630, 2004     

Dependence of zero-shear viscosity and steady-state compliance on molecular weight between entanglements for ethylene-cycloolefin copolymers

Dynamic viscoelastic properties of a series of cyclic olefin copolymers have been investigated. The specimens differ in total molecular weight as well as molecular weight between entanglements. The angular frequency (ω) dependence curves of dynamic storage and loss moduli (G′ and G″, respectively) of the specimens have shown that G′ ∝ ω² and G″ ∝ ω in the terminal region, and a plateau region at high ω. On the basis of the experimental results, the dependence of total molecular weight as well as molecular weight between entanglements has been examined for zero-shear viscosity (η₀) and steady-state compliance (J_e). It is shown that for the melts of the copolymers in the entangled regime, M_w being the weight-average molecular weight and M_e the molecular weight between entanglements. The steady-state compliance J_e for the melts scales with M_e and M_w as .     

Impact modification of engineering thermoplastics

Impact modification was studied for a variety of engineering thermoplastics to determine if notched Izod data obtained at various temperatures and modifier concentrations could be correlated with particle size or surface-to-surface interparticle distance of the modifier. Elastomers evaluated were characteristic of those used in commercial blend systems for those polymers, and both functionalized and nonfunctionalized materials were studied. For the single matrix polymer/elastomer-modified blend systems studied [poly(phenylene sulfide) (PPS), polyoxymethylene (POM), poly(butylene terephthalate) (PBT)], elastomer interparticle distance provides a better correlation to brittle–tough transition temperature than does particle size, as predicted by the Wu model. In POM, the dispersion morphology of the samples used was not adequate to achieve the critical interparticle distance required for supertoughening at room temperature. In this study, the critical interparticle distance has been shown to depend on the degree of crystallinity (PPS) and the modulus of the impact modifier relative to the matrix (PBT). Actual adhesion of the polymer to the matrix (variation of functionality levels) was not found to have a strong influence (PBT). In POM, the increase in impact at the brittle–tough transition was dependent on the molecular weight of the base resin. This is examined with respect to the ratio of the molecular weight (M_n) to the entanglement molecular weight (M_e), which determines the critical molecular weight necessary to achieve useful physical properties. In polyester (PET)/polycarbonate (PC)/elastomer blends, the molecular weight of the primary matrix resin (PET) determined impact properties within the molecular weight range of the resin studied. This was again related to the M_n/M_e ratio for PET and PC. © 1994 John Wiley & Sons, Inc.     

Blends containing amphiphilic polymers. V. Compatibilization of N‐alkylitaconamic acid‐co‐styrene copolymers with interacting polymers

The phase behavior of blends containing N‐alkylitaconamic acid‐co‐styrene copolymers (NAIA‐co‐S) with poly(N‐vinyl‐2‐pyrrolidone) (PVP) of two different weight average molecular weights (M _w ), poly(2‐vinylpyridine) (P2VPy) and poly(4‐vinylpyridine) (P4VPy), was analyzed by differential scanning calorimetry and Fourier transform infrared spectroscopy. Copolymers containing 80% S are miscible with PVP₁₀, PVP₂₄, and P4VPy over the whole range of composition. In the case of blends with P2VPy, miscibility is observed only for the first three members of the series, i.e., NEIA‐co‐S, NPIA‐co‐S, and NBIA‐co‐S. For copolymers containing hexyl to dodecyl moieties, phase separation is observed in blends with P2VPy. Copolymers containing 50% S are miscible over the whole range of composition irrespective of the homopolymer and the length of the side chain of the itaconamic moiety of the copolymer. This behavior is interpreted in terms of steric hindrance, in the sense that the copolymers with long side chains are not able to interact with the nitrogen of P2VPy because of the position in the aromatic ring. The interactions between copolymers and homopolymers are discussed in terms of specific interactions like hydrogen bonds between the itaconamic moiety and the different functional groups of the homopolymers, together with the hydrophobic interaction, which cannot be disregarded. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 2512–2519, 2006     

Elastic behavior of concentrated solutions of acrylonitrile copolymers

The elastic behavior of concentrated solution of acrylonitrile copolymer was investigated by the capillary end correction method. The results were as follows. (1) The shear stress is proportional to recoverable shear strain in accordance with Hooke's law below critical concentration; above a critical concentration, however, the shear modulus depends on shear stress. (2) The log–log plots of zero shear modulus against polymer concentration and molecular weight fall on two straight lines with different slopes. The intersection of lines is considered to be the onset of elastically deformable entanglement network. We denote this inflection point as (C_c)_e or (M_c)_e. (3) The log–log plot of viscosity against polymer concentration does not show a change of slope at the critical concentration (C_c)_e. (4) By the application of the kinetic theory of rubberlike elasticity to the pseudo-network structure of concentrated polymer solution, in the range of C_c < C < (C_c)_e or M_c < M < (M_c)_e, the number of chain entanglement per molecule is kept one; moreover, in the range of C > (C_c)_e, or M > (M_c)_e, the number of chain entanglement increases to three.     

Effect of network morphology on adhesive performance in emulsion blends of acrylic pressure sensitive adhesives

High-gel containing latices and gel-free latex were blended at various weight ratios. The high-gel containing latices was made of poly(2-ethyl hexylacrylate-stat-acrylic acid) and the gel-free latex was made of poly(2-ethyl hexylacrylate-stat-acrylic acid-stat-isobutoxymethyl acrylamide) using semicontinuous emulsion polymerization. Films were cast at room temperature and dried at 121°C for 10 min. Adhesive performance was evaluated in terms of loop tack, peel, and shear holding power. It was found that interlinking the microgels by the linear polymer due to the isobutoxymethyl acrylamide-acrylic acid reaction in the film when heated gave synergistic effects in increasing shear. This interlinking could take place only if the molecular weight between crosslinks (M_c) of the microgels was greater than the entanglement molecular weight of the linear polymer (M_e), and if the weight average molecular weight of the linear polymer (M_w) was greater than 2 × M_e. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2109–2117, 2001     

Investigation on the role of the molecular weight of polyvinyl pyrrolidone in the shape control of high-yield silver nanospheres and nanowires

Serving as shape control agent, polyvinyl pyrrolidone (PVP) has been widely used in chemical synthesis of metal nanoparticles. However, the role of molecular weight (MW) of PVP has been rarely concerned. In this study, we show a facile method to control the shapes of silver nanocrystals using PVP with different MWs. PVP_MW=8,000, PVP_MW=29,000, PVP_MW=40,000, and PVP_MW=1,300,000 are compared in the present study. Surprisingly, high-yield silver rodlike nanostructures, nanospheres, and nanowires can be obtained under the same growth environment and reactant concentrations by simply changing the MW of PVP. The mechanism studies of the role of PVP with different MWs in the growth process were carried out systemically using the morphology and spectroscopic measurement, FT-IR spectrum analysis, and seed crystallization monitoring. The results indicate that the MW of PVP plays a determinant role in the morphology and optical property control of the silver nanocrystals. Meantime, the concentration of PVP was found to be an assistant factor to further improve the shape and the yield of the synthesized nanocrystals.