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.     

The dispersion of magnetic nanorods in poly(2‐vinylpyridine)

The dispersion of magnetic nanorods in poly(2‐vinylpyridine) (PVP) as a function of rod length, particle loading and molecular weight of PVP was investigated. The nanorods were organized into small spherical clusters at low particle loading. Further increasing the particle concentration caused an increase in the size of the aggregates. Additionally, the internal structure of the nanorods developed into a raft‐like structure, forming rectangular clusters. The incorporation of longer nanorods in the PVP amplified the magnetic interaction energy, which created conditions to induce extensive aggregation. The entanglement of the polymer also played an important role in the arrangement of the nanorods. This behavior could be categorized into two regimes, M_PVP > M_e and M_PVP < M_e, where M_PVP and M_e are the number‐average molecular weight and entanglement molecular weight of PVP, respectively: for M_PVP > M_e, PVP formed entanglements that prevented nanorods from extensive aggregation; for M_PVP < M_e, PVP could not form entanglements, and nanorods could move freely in the PVP, and thus significant rod aggregation occurred. Simple calculations to assess the contribution of the magnetic interaction, the van der Waals interaction and the free energy of mixing of the system to the arrangement of magnetic nanorods in the homopolymer are discussed. © 2013 Society of Chemical Industry     

Diffuse shear banded zones of blends of polystyrene and poly(2,6-dimethyl-1,4-phenylene oxide)

The formation, mechanical properties, thermal characteristics, and density of diffuse shear banded zones of polystyrene, poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), and their miscible blends were studied. A significant increase in density of 0.2 to 0.3 percent was found for the diffuse shear banded zones. Differential scanning calorimetry results revealed a volume recovery process that occurs below T_g for the diffuse shear banded zones. The post-yield-stress drop, anelastic shear strain within the zone, and anelastic tensile strain were all found to decrease with increasing PPO content in an identical manner. The sharp shear band to diffuse shear banded zone transition was related to chain mobility, molecular packing, and free energy as manifested in the post-yield-stress drop. The decrease in anelastic shear strain with increasing PPO content for the blends is possibly related to the beta transition and length between entanglements.     

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     

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     

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.     

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.     

Enhanced strain hardening in elongational viscosity for HDPE/crosslinked HDPE blend. II. Processability of thermoforming

Rheological properties and processability of thermoforming were studied for high‐density polyethylene (HDPE) and a blend of HDPE with crosslinked HDPE (xHDPE). Blending the xHDPE, which enhances melt strength and strain hardening in elongational viscosity of HDPE, helps the sheet avoid sagging in thermoforming. Moreover, the product of the blend obtained by vacuum forming has uniform wall thickness. Melt strength and strain hardening of the blend were, however, depressed by a processing history in a single‐screw extruder, whereas reprocessing by a two‐roll mill enhanced the melt strength again. It is considered that the processing history by a single‐screw extruder, in which shear‐dominant flow takes place, depresses the trapped entanglements between network chain of xHDPE and linear HDPE molecules, and results in low level of melt strength. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 79–83, 2002     

Investigations of environmental stress cracking resistance of HDPE/EVA and LDPE/EVA blends

HDPE/poly(ethylene‐co‐vinylacetate) (EVA) and low‐density polyethylene (LDPE)/EVA blends were tested and compared with respect to their environmental stress cracking resistance (ESCR) using the Bell‐telephone test. The time to failure in the ESCR test improves with increasing EVA content, and considerable improvements were produced for LDPE/EVA blends while small improvements were observed for HDPE/EVA blends. Thermal, rheological, mechanical, and morphological studies were conducted which established a quantitative relationship between morphological features and composition. Furthermore, the failed specimens were further characterized by scanning electron microscopy and fractographic methodology to investigate the failure mechanism for ESCR samples. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39880.     

Experimental study on the effect of molecular weight and chemical composition distribution on the mechanical response of high-density polyethylene

This article aims to appraise the effect of microstructure comprising molecular weight distribution and chemical composition distribution on the mechanical properties of high-density polyethylene (HDPE). HDPE resins were synthesized using several titanium–magnesium-supported Ziegler–Natta catalysts in the industrial gas phase reactor under the same polymerization condition. Gel permeation chromatography and crystallization elution fractionation (CEF) were conducted on the resins to characterize the molecular weight and comonomer distribution. Crystallization, thermal and rheological behavior were evaluated following differential scanning calorimetry, polarization light microscopy, and rheometric mechanical spectrometry. The resins with higher soluble fraction in trichlorobenzene below 80°C (highly branched low molecular weight chains) exhibited longer crystallization time based on the crystallization kinetic obtained from the Avrami model. Rheological determination of the molecular weight between entanglements (M_e) and the average lamella thickness based on the Gibbs–Thomson equation revealed that the entanglement density and impact strength decreased, and the average lamella thickness increased with an increase in the ratio of CEF eluted fraction below 80°C to the crystallizable fraction in the range of 80–90°C.     

Deformation behavior of poly(dimethyl siloxane) networks. I. Applicability of various theories to modulus prediction

The shear moduli of end-linked poly(dimethyl siloxane) networks were measured as a function of mol wt between chemical crosslinks (M_c) and the dilution-at-cure (C_x). The results were interpreted in terms of theories that take into account contributions from trapped entanglements. It was found that the network deformation follows the predictions of the theory of “phantom” networks, with an added contribution from trapped entanglements. At high mol wts of the precursor polymer, network imperfections play a role, as seen in the frequency dependence of the shear modulus. This results in deviation from predicted behavior. © 1993 John Wiley & Sons, Inc.     

On the origin of strain hardening in glassy polymers

The influence of network density on the strain hardening behaviour of amorphous polymers is studied. The network density of polystyrene is altered by blending with poly(2,6-dimethyl-1,4-phenylene-oxide) and by cross-linking during polymerisation. The network density is derived from the rubber-plateau modulus determined by dynamic mechanical thermal analysis. Subsequently uniaxial compression tests are performed to obtain the intrinsic deformation behaviour and, in particular, the strain hardening modulus. At room temperature, the strain hardening modulus proves to be proportional to the network density, irrespective of the nature of the network, i.e. physical entanglements or chemical cross-links. With increasing temperature, the strain hardening modulus is observed to decrease. This decrease appears to be related to the influence of thermal mobility of the chains, determined by the distance to the glass-transition temperature (T−T_g).     

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     

Effect of sparse long‐chain branching on the step‐strain behavior of a series of well‐defined polyethylenes

The effect of sparse long chain branching, LCB, on the shear step‐strain relaxation modulus is analyzed using a series of eight high‐density polyethylene (HDPE) resins. Strains of 1 to 1250% are imposed on materials with LCB content ranging from zero to 3.33 LCB per 10,000 carbon atoms. All materials are observed to obey time–strain separation beyond some characteristic time, τ_k. The presence of LCB is observed to increase the value of τ_k relative to the linear resin. The behavior of the relaxation modulus at times shorter than τ_k is investigated by an analysis of the enhancement seen in the linear relaxation modulus, G⁰(t), as a function of strain and LCB content. This enhancement is seen to (1) increase with increasing strain in all resins, (2) be significantly larger in the sparsely branched HDPE resins relative to the linear HDPE resin, and (3) increase in magnitude with increasing LCB content. The shape and smoothness of the damping function is also investigated. The finite rise time to impose the desired strain is compared to the Rouse relaxation time of linear HDPE resins studied. Sparse LCB is found to increase the magnitude of the relaxation modulus at short times relative to the linear resin. POLYM. ENG. SCI., 2010. © 2010 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 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.     

Effects of molecular weight and molecular weight distribution on creep properties of polypropylene homopolymer

The molecular weights of the industrial-grade isotactic polypropylene (i-PP) homopolymers samples were determined by the melt-state rheological method and effects of molecular weight and molecular weight distribution on solid and melt state creep properties were investigated in detail. The melt-state creep test results showed that the creep resistance of the samples increased by M_w due to the increased chain entanglements, while variations in the polydispersity index (PDI) values did not cause a considerable change in the creep strain values. Moreover, the solid-state creep test results showed that creep strain values increased by M_w and PDI due to the decreasing amount of crystalline structure in the polymer. The results also showed that the amount of crystalline segment was more effective than chain entanglements that were caused by long polymer chains on the creep resistance of the polymers. Modeling the solid-state viscoelastic structure of the samples by the Burger model revealed that the weight of the viscous strain in the total creep strain increased with M_w and PDI, which meant that the differences in the creep strain values of the samples would be more pronounced at extended periods of time.     

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     

Experimental investigation of flow induced molecular weight fractionation during extrusion of HDPE polymer melts

In this work, two different HDPEs with virtually identical number, M_n, and weight, M_w, average molecular weights were investigated from rheological as well as die drool phenomenon point of view. It has been revealed that long-chain branching, low polymer melt elasticity and shear viscosity significantly reduce die drool phenomenon at the die exit region. It has been concluded that die drool phenomenon of HDPE polymer melts can be explained by the flow induced molecular weight fractionation.