Van Gurp Palmen Plot Research Articles

Degradation behavior of polycarbonate during melt processing with an aqueous solution of sodium hydroxide

In this study, we aimed to enhance the reactivity of polycarbonate (PC) with the epoxy group of styrene-co-glycidyl methacrylate copolymer (SGMA) by introducing aqueous solutions of sodium hydroxide during the melt processing of PC. This approach led to the generation of hydroxyl groups at the ends of PC molecules, facilitating the formation of PC-SGMA copolymer. The effectiveness of this method in improving the compatibility of PC and styrene-acrylonitrile (SAN) blends was successfully confirmed through blending experiments with SAN and SGMA. Additionally, we investigated the impact of alkali-promoted hydrolysis on the rheological properties of PC, apart from the functionalization of PC end groups. Our findings revealed that an increase in the concentration of sodium hydroxide resulted in a decrease in the complex viscosity of PC. However, beyond a certain concentration level, the viscosity exhibited an upward trend. Furthermore, when constructing van Gurp-Palmen plots for the modified PC, we observed a significant deviation in curve shape compared to pure PC or water-modified PC. This observation suggests that changes in the microstructure occur during the degradation process due to the interaction between PC molecules and sodium ions.

Temperature and Frequency Dependence of the Dynamic Viscoelastic Properties of Silicone Rubber.

Temperature-frequency sweep tests were performed on silicone rubber to investigate the dynamic viscoelastic properties. The test results show that the viscoelasticity of silicone rubber presents significant temperature dependence and frequency dependence. The dynamic viscoelastic test curves at different temperatures can be shifted along the logarithmic frequency coordinate axis to construct smooth master curves at the reference temperature of 20 °C, covering a frequency range of 10 decades, which indicates thermorheological simplicity on a macro level and frequency temperature equivalence of the silicone rubber material in the experimental temperature range. The van Gurp-Palmen plot and Cole-Cole plot for the test data at various temperatures merge into a common curve, which further validates thermorheological simplicity. The temperature dependent shift factors of silicone rubber material were well characterized by the Williams-Landel-Ferry equation. Moreover, the fractional-order differential Kelvin (FDK) model, the fractional-order differential Zener (FDZ) model, and the improved fractional-order differential Zener (iFDZ) model were used to model the asymmetric loss factor master curve. The result shows that the iFDZ model is in good agreement with the test results, indicating that this model is suitable for describing the asymmetry of dynamic viscoelastic properties of silicone rubber.

Dynamic Response and Molecular Chain Modifications Associated with Degradation during Mixing of Silica-Reinforced Natural Rubber Compounds

Mixing silica-reinforced rubber for tire tread compounds involves high shear forces and temperatures to obtain a sufficient degree of silanization. Natural Rubber (NR) is sensitive to mastication and chemical reactions, and thus, silica-NR mixing encounters both mechanical and thermal degradation. The present work investigates the degradation phenomena during the mixing of silica-reinforced NR compounds in-depth. The Mooney stress relaxation rates, the dynamic properties with frequency sweep, a novel characterization of branch formation on NR using Δδ values acc. Booij and van Gurp-Palmen plots, together, indicate two major competitive reactions taking place: chain scission or degradation and preliminary cross-linking or branch formation. For masticated pure NR and gum compounds, the viscous responses increase, and the changes in all parameters indicate the dominance of chain scission with increasing dump temperature. It causes molecular weight decrease, broader molecular weight distribution, and branched structures. Different behavior is observed for silica-filled NR compounds in which both physical and chemical cross-links are promoted by silanization and coupling reactions. At high dump temperatures above 150 °C, the results indicate a significant increase in branching due to preliminary cross-linking. These molecular chain modifications that cause network heterogeneity deteriorate the mechanical properties of resulting vulcanizates.

Characterizations of Polypropylene/Single-Walled Carbon Nanotube Nanocomposites Prepared by the Novel Melt Processing Technique with a Controlled Residence Time

Melt processing is considered one of the favored techniques to produce polymer nanocomposites with various inorganic fillers such as graphene and carbon nanotubes (CNTs). Due to their superior conductivity and tensile properties, among others, CNTs have been applied in broad applications. When a low filler fraction is desired, a high degree of dispersion is required in order to benefit from the intrinsic properties of CNTs. However, due to their high cohesive energy, dispersing CNTs in polymer melts is a difficult task. This study employed the melt mixing technique with a controlled residence time of 20 min to disperse single-walled carbon nanotubes (SWNTs) into a polypropylene matrix. The composites were prepared by using a corotating twin-screw extruder equipped with a back-conveying element with varying amounts of SWNTs from 0.29 to 6.56 wt.%. Mechanical, electrical, morphological, and rheological properties were evaluated. Due to the filler effect, storage, loss modulus, and complex viscosity increased with the SWNT content. Based on the van Gurp–Palmen plot, 0.29 wt.% SWNTs was the rheological percolation threshold, and the electrical property measurement revealed a 1.4 wt.% SWNT electrical percolation threshold based on the statistical percolation theory. Relatively large agglomerates were found when the SWNT content increased more than 1.28 wt.%.

Rheological properties of high-density polyethylene/linear low-density polyethylene and high-density polyethylene/low-density polyethylene blends

In this work, the effect of the linear low-density polyethylene (LLDPE) containing 1-butene or 1-hexene α-olefin short-chain branching (SCB) and low-density polyethylene (LDPE) containing long-chain branching (LCB) on the rheological properties of high-density polyethylene (HDPE)/LLDPE and HDPE/LDPE blends was investigated. The neat polymers and the blends were characterized by torque rheometry and rheological measurements under dynamic oscillatory shear flow. From torque rheometry analysis, an increase in the viscosity of HDPE/LLDPE blends with the increase in LLDPE content was observed. The inverse was observed for HDPE/LDPE blend, where the viscosity decreased with the increase in the LDPE content. Rheological measurements showed an increase in the complex viscosity of the HDPE/LLDPE and HDPE/LDPE blends with the increase in the LLDPE or LDPE content. HDPE/LDPE blends showed a strong shear-thinning behavior due to the presence of LCB in LDPE. Similar rheological behavior was observed for HDPE/LLDPE blends containing 1-butene and 1-hexene SCB. Cole–Cole, Han plots, and van Gurp–Palmen plots indicated miscibility between HDPE and LLDPE and immiscibility between HDPE and LDPE.

The role of rheological premonitory of hydrogels based on cellulose nanofibers and polymethylsilsesquioxane on the physical properties of corresponding aerogels

AbstractCellulose nanofibers (CNFs) and polymethylsilsesquioxane (PMSQ)‐based aerogels (CNF/PMSQ aerogels) have been prepared by the sol–gel method. The extraction of CNFs from pine wood and formation of composite aerogel with PMSQ were confirmed by Fourier transform infrared spectroscopic and field emission scanning electron microscopic analyses. The rheological premonitory of hydrogel has been performed to predict the physical properties (i.e., density, mechanical properties) of aerogels. The variation in the precursor (methyltrimethoxysilane [MTMS]) and urea content has shown a considerable effect on the storage modulus and phase angle of the hydrogel. The variation in urea content showed a 4–8% increment in the density with a pronounced difference in aerogel's morphology. The increment in the MTMS concentration demonstrated a 10–20% enhancement in density with a minor change in morphology. The van Gurp–Palmen plot of hydrogel has represented a relationship between complex modulus and phase angle. This study establishes that hydrogel's premonitory analysis could compare aerogel's physical properties without going through drying and further analysis.

Temperature, time, pressure, and CO2concentration dependence of rheological properties for poly(methyl methacrylate)/expanded graphite composites

The effects of temperature, pressure, and supercritical carbon dioxide (scCO2) concentration are investigated on the rheological behavior of poly(methyl methacrylate)/expanded graphite (PMMA/EG) composites with 1, 4, and 7 wt. % EG. The validity of the time-temperature superposition and time-pressure-scCO2 concentration superposition principles for the PMMA/EG composites is explored. At atmospheric pressure, the time–temperature superposition principle holds for the composites with 1 and 4 wt. % EG but fails for that with 7 wt. % EG. This is demonstrated by the rheological master curves and the van Gurp–Palmen plots. The scanning electron microscopy micrographs, the Cole–Cole plots, and weighted relaxation spectra reveal that the composite with a higher content (7 wt. %) of EG exhibits a stronger interfacial interaction between the PMMA chains and EG layers and delayed chains’ relaxation. The viscosity evolution with testing time for the PMMA/EG composite samples during time sweep testing demonstrates that the EG layers hinder the dissolution of scCO2 into the PMMA matrix to some extent. Different from the time–temperature superposition principle, the time–pressure–scCO2 concentration superposition principle is valid for all the prepared PMMA/EG composite samples. This is because the dissolved scCO2 at the PMMA matrix-EG layer interfaces reduces the interfacial interaction between the PMMA chains and EG layers and weakens the effect of the EG layers on the chains’ relaxation.

Characterizing long-chain branching in commercial HDPE samples via linear viscoelasticity and extensional rheology

It is well established that polymer chain architecture and the distribution of molecular weight play a key role in the flow behavior (processing) and performance of a given polymer material. Long-chain branching (LCB) in particular is known to strongly affect the processability and the material performance of polymers. Often branching is a result of the polymerization process and therefore must be quantified in every sample. We study four commercial high-density polyethylene (HDPE) samples with unknown degrees of polydispersity and LCB. We first use size-exclusion chromatography and linear shear rheology to identify differences in molecular weight, polydispersity, and LCB. Each material is then tested in constant rate and constant stress uniaxial extension using a filament stretching rheometer to quantify extensional viscosity and strain hardening. Correlations between nonlinear extensional rheology, LCB and polydispersity are discussed. We show that the combination of the van Gurp-Palmen plot and extensional rheology allows for a full characterization of the LCB fraction and their effect on extensional rheology.

Comparative gelation of acrylic acid and acrylamide in diacrylate and dimethacrylate crosslinked matrices

The radiation-induced gelation of two monomers, acrylic acid and acrylamide, crosslinked using four model compounds was investigated using Fourier transform mechanical spectroscopy. The gel point characteristics of the resulting hydrogels were compared. The gelation characteristics of the two monomers were very similar. The fractal dimensions of the critical gels ranged between 1.77 and 1.82 when the reactions were controlled. The patterns of viscoelastic events of the products at the gel point were also similar, with the matching reactivity of the monomers and the comparable molecular weight of the crosslinkable species, providing a foundation for such events. All of the reactions exhibited low mutation numbers, indicating that the samples tested were quasi-stable during the measurements. The extent of the UV irradiance during crosslinking reactions is an important parameter in the gelation process, with an increase in UV irradiance decreasing the gel times, decreasing the network relaxation exponents (increased fractal dimensions), leading to stiffer critical gels. The evolution of δ with G*, undertaken as van Gurp–Palmen plots, shows that in the fully formed gels, however, the monomer choice and the crosslinker variation can dictate the viscoelasticity of the materials. In particular, the potential for greater steric effects/greater stabilities of the radical active centres of the dimethacrylate species, in comparison with the diacrylate species, resulting in lesser viscoelasticities in the fully formed gels.

Molecular structure influence on bending behavior of polyester filaments examined using a modified cantilever bending test

ABSTRACTAn experimental setup used to measure the bending stiffness of polymer filaments based on existing cantilever approaches is presented. Additionally, it is utilized to evaluate the influence of molar mass and long‐chain branching on filaments of poly(butylene terephthalate), modified with a multifunctional chain extender. Using shear rheological analysis process limits for extrusion of the modified material were revealed, indicated by a change of the curve shape of van Gurp–Palmen plots. For the processable modified materials, it was found that increasing molar mass and degree of long‐chain branching, caused by the modification, raise the bending stiffness of filaments. Also the Young's modulus was found to increase with the amount of chain extender used, while no difference could be generated by using different linear molar grades of the polymer. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47952.

Evaluation of electron beam‐induced crosslinking of poly(ε‐caprolactone)—Effect of elevated temperatures

ABSTRACTThe effect of elevated temperatures (40, 80, and 170 °C) on the electron beam (EB)‐induced crosslinking and degradation of poly(ε‐caprolactone) (PCL) in nitrogen atmosphere without adding crosslinking agents has been investigated. The increased mass average molecular mass of EB modified masticated PCL (mPCL) samples were measured by size exclusion chromatography. The sol–gel investigation showed that mPCL tended to dominating crosslinking at a temperature of 170 °C. At this temperature, the maximum gel content of 56% was observed for an EB treatment with a dose of 100 kGy. In addition, the ratio of chain scission density to density of crosslinked units amounted to 0.25. The dynamic rheological test demonstrated that EB treatment at 170 °C led to the most remarkable elasticity enhancement behavior with enhanced viscosity, modulus, and decreased loss factor (tan δ). The occurrence of branching structure was evidently detected by van Gurp–Palmen plot in combination with the Cole–Cole plot for dose values ≤50 kGy. Less δ and a broadened relaxation process can be observed due to the introduction of some branched structures into mPCL. The results of enhanced molar mass and gel content analysis were confirmed by the dynamic rheological measurements. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47866.

Linear Rheology of a Series of Second-Generation Dendronized Wedge Polymers

A series of second-generation dendronized wedge polymers were synthesized by ring-opening metathesis polymerization, and the linear viscoelastic response over a wide range of temperatures was investigated. From 0 to 90 °C the dynamic moduli (G′(ω) and G″(ω)) were determined, and frequency–temperature superposition was used to create master curves that showed behavior from the terminal zone to the glassy regime. An apparent extremely low rubbery plateau of ∼10 kPa was observed in both the dynamic response and in the corresponding van Gurp–Palmen plot. However, further investigation shows that the apparent rubbery plateau is related to the steady-state recoverable compliance, not the onset of entanglements. In addition, these wedge polymers exhibit an extremely low glassy modulus of ∼100 MPa at 0 °C, which is shown to increase at 1 Hz to ∼700 MPa at −80 °C for the wedge polymer 2G-EHW-311. In addition, both small- and wide-angle X-ray scattering patterns were obtained for all of the polymers investigated, and these showed that the polymer molecules adopt an extended cylinder conformation. Furthermore, based on calorimetric measurements, the polymers were found to exhibit two glass transition temperatures, with a 100 K difference between the higher (T_(g,hi) = 26.8 ± 0.7 °C) and lower glass transition temperatures (T_(g,lo) = −76.1 ± 1.1 °C) for the 2G-EHW-311 material. Hence, an intermediate regime extends to well below the T_(g,hi) to T_(g,lo), providing an explanation for the low glassy modulus of ∼100 MPa at 0 °C and its increase to ∼700 MPa when measured at T_(g,hi) – 100 °C and approaching the T_(g,lo).

Application of RAFT-synthesized reactive tri-block copolymers for the recycling of post-consumer R-PET by melt processing

The use of reactive tri-block copolymers of styrene (S), glycidyl methacrylate (GMA), and butyl acrylate (BA) synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization as chain extenders of recycled poly (ethylene terephthalate) (R-PET) by melt processing is reported. Emphasis is placed on the influence of controlled copolymer structures and glycidyl methacrylate content on physical properties, thermal properties and rheological behavior of recycled PET. RAFT-synthesized reactive copolymers turned out to be very effective chain extenders leading to an increase in the molar mass intrinsic viscosity and diminished melt flow, indicating better melt elasticity and processability of R-PET. Tensile and impact analysis showed that functional GMA blocks reacted with PET end groups, causing a dramatic increase in the elongation-at-break and significant improvement of impact and tensile strength. Complex viscosity and rheological moduli of R-PET also increase greatly, indicating that flexibility of modified R-PET is improved. The van Gurp–Palmen plot of chain-extended R-PET confirms the increase in melt elasticity.

Preparation and Rheology of Isocyanate Functionalized Graphene Oxide/Thermoplastic Polyurethane Elastomer Nanocomposites

Using monomer-functionalized nanofiller to prepare polymeric nanocomposites is a promising strategy toward achieving enhanced performance. In this study toluene-2,4-diisocyanate (TDI), one of the monomers used for synthesizing polyurethane, was covalently functionalized on graphene oxide (GO) and then the functionalized GO (TDI-GO) was polymerized with polycaprolactone diol (PCL) via in-situ polymerization, leading to chemically linked polyurethane nanocomposites through the covalent bonds between the isocyanate groups on GO and the hydroxyl-terminated PCL. Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD) and dispersion experiments of the nanofillers demonstrated that the TDI was successfully grafted onto the GO. The rheological properties were investigated to establish the structure-property relationships of the nanocomposites. The storage moduli (G’), loss moduli (G”) and complex viscosity (η*) of the samples increased monotonically with TDI-GO content, which is attributed to the strong polymer-filler interactions and the effective dispersion of the nanofillers. Additionally, the tan δ variation with frequency, the intersection of G’ and G”, Han plots, van Gurp-Palmen plots and Cole-Cole plots all showed that the incorporation of TDI-GO decreased the degree of microphase separation and improved the elastic properties of the nanocomposites. We suggest this is related to the enhanced interactions between the polymer and nanofillers, which strongly restricted the mobility and relaxation of the polymer chains.

Expanding the application of the van Gurp-Palmen plot: New insights into polymer melt rheology

We report on an extension of the van Gurp-Palmen (vGP) plot [van Gurp, M. and Palmen, J., Rheology Bulletin, 1998, 67(1), 5–8.] developed through a compilation of literature data for polymer melts with different topological structures: linear (pure and blend), ring, comb, and bottlebrush. We introduce a new parameter: the reciprocal of complex modulus at the first minimum moving from the terminal regime (1/Gδmin,1∗) and compare it with the steady-state recoverable compliance Js. Results show that 1/Gδmin,1∗ and Js while related to each other in that they follow similar dependences on the molecular weight (linear and bottlebrush polymers), weight fraction of high molecular weight content (linear blends), and backbone concentration (comb polymer), there are also differences. For example, in the unentangled regime both Js and 1/Gδmin,1∗ increase with increasing molecular weight but reach different plateau values as entanglement coupling sets in. In the case of ring polymers, the molecular weight dependences of 1/Gδmin,1∗(∼Mw1) and Js(∼Mw2) show very different scaling with molecular weight and do not reach a plateau value even for molecular weights as high as approximately 15 times the entanglement molecular weight of the linear counterpart. Furthermore, examination of the impact of linear additives on the vGP plots of the rings potentially provides a new way to assess their freedom from linear contamination. Also, because 1/Gδmin,1∗ occurs in the frequency regime above that of the terminal regime and Js requires either very good estimates of terminal behavior in dynamic measurements or direct determination from creep and recovery measurements, 1/Gδmin,1∗ is easier to obtain. The work shows that detailed analysis of the van Gurp-Palmen plot has the potential to provide new insights into the rheological response of polymer melts over what is obtained conventionally from viscoelastic characterization methods.

Phase transition and anomalous rheological properties of graphene oxide-carbon nanotube acrylonitrile butadiene styrene hybrid composites

Acrylonitrile butadiene styrene (ABS) nanocomposites with multiwalled carbon nanotubes (MWCNTs), reduced graphene oxide (RGO) and graphene oxide-carbon nanotubes (GCNTs) reinforced acrylonitrile butadiene styrene (ABS) composites were prepared using twin screw extruder. The effect of these reinforcements on dynamic rheological properties of composites was studied. Different carbon nanofillers significantly enhanced the viscoelastic properties of nanocomposites. The rheological studies showed that the material undergoes viscous to elastic transition for 5 wt % MWCNTs, 10% RGO and 7% GCNTs reinforced in ABS matrix. GCNTs hybrid composites show a higher dispersion as well as effectiveness for increased filler amount as compared to RGO and MWCNTs based ABS composites. The dynamic intersection frequency of GCNTs-ABS composites indicates its superiority over MWCNTs and RGO based ABS composites by solving the problem of restacking of graphene and agglomeration of MWCNTs. Modified Carreau-Yasuda model and Hershcel-Bulkey model have been used to determine the yield stress of the composites and van Gurp-Palmen plot to determine the viscoelastic properties. These models were used to compare the theoretical results with experiment data. Dynamic rheological measurements revealed the viscous-like (G">G') behavior at the lower loading of filler and elastic like (G'>G") behavior at higher loading of carbon nanofiller.

Investigation on Molecular Structures of Electron-Beam-Irradiated Low-Density Polyethylene by Rheology Measurements

While the effect of high-energy irradiation on low-density polyethylene (LDPE) has been extensively investigated, the molecular structure changes under different irradiation conditions are less well understood. In this work, we have made systematic investigations on the molecular structure of electron beam irradiated LDPE under various irradiation conditions. The microstructures have been mainly characterized by rheological measurements using small amplitude oscillatory shear (SAOS) and analyzed by a weighted relaxation spectrum and a van Gurp–Palmen plot. It was found that the linear viscoelasticity of LDPE exhibited a strong dependence on the radiation atmosphere due to oxidative degradation in the presence of oxygen. An improved/destroyed network structure could be acquired when LDPE was irradiated in a nitrogen/oxygen environment, as compared with that in air. Differences became more significant when LDPE was irradiated at higher temperature (80 °C) due to the facilitated diffusion of free radicals wi...

Phase transition and anomalous rheological behaviour of polylactide/graphene nanocomposites

Polylactide (PLA) nanocomposites with graphene nanoplatelet (GNP) contents of 0–15 wt% were prepared and characterised in terms of rheology and electrical conductivity. As expected for rigid nanofillers, GNP incorporation significantly enhanced the viscoelastic properties of the nanocomposites. Furthermore, above a certain GNP concentration the liquid-like melt flow behaviour changed into a solid-like behaviour. However, this rheological percolation threshold was found to decrease from near 9 wt% at 180 °C to below 6 wt% at 220 °C, detected and measured by Van Gurp-Palmen plots and Winter-Chambon method, respectively. It was also found that the viscoelastic properties of some of the nanocomposites increased with increasing temperature, which is in contrast to the rheology of ideal polymeric melts. The Electrical percolation threshold of the PLA/GNP system, which is determined by a sudden increase in DC conductivity and is indicative of establishment of interconnected conductive structures of GNPs within the matrix, was observed to be between 6 and 9 wt% GNPs. Morphological studies also showed physical contact between the platelets at 9 wt% while at 6 wt% they were still separated by the PLA matrix. These observations challenge the attribution of rheological percolation threshold to the formation of a percolating network of only filler particles within the matrix. A percolating network consisting of both polymer chains and filler particles might be the reason for the temperature dependency of rheological percolation threshold in the PLA/GNP system.

Linear and Extensional Rheology of Model Branched Polystyrenes: From Loosely Grafted Combs to Bottlebrushes

Monodisperse comb polystyrenes (comb-PS) with loosely to densely grafted architectures up to loosely grafted bottlebrush structures were synthesized via anionic polymerization. This comb-PS series, named PS290-Nbr-44, had the same entangled backbone, Mw,bb = 290 kg/mol, corresponding to a number of entanglements along the backbone Zbb ≅ 20, and similar branch length, Mw,br ≅ 44 kg/mol or Zbr ≅ 3, but varied in the number of branches per molecule, Nbr, from 3 to 190 branches. Consequently, the average number of entanglements between two consecutive branch points along the backbone (branch point spacing), Zs, ranged from well entangled, Zs ≅ 5, to values that were far less than one entanglement, Zs ≅ 0.1. Linear viscoelastic data including the zero-shear rate viscosity, η0, diluted modulus, GN,s0, and a new diluted modulus extracted from the van Gurp–Palmen plot, |G*| at δ = 60°, were analyzed as a function of the Mw of the combs. Scaling of η0 versus Mw revealed three different regions for increasing Nbr o...

Influence of molecular structure on the foamability of polypropylene: Linear and extensional rheological fingerprint

The foaming structure and rheological properties of four different isotactic homo-polypropylenes with various molecular weights and an isotactic long chain branched polypropylene were investigated to find a suitable rheological fingerprint for PP foams. The molecular weight distribution and thermal properties were measured using GPC-MALLS and differential scanning calorimetry, respectively. Small amplitude oscillatory shear data and uniaxial extensional experiments were analyzed using the frameworks of van Gurp-Palmen plot (δ vs. | G*|) and the molecular stress function model, respectively. These analyses were used to find a correlation between the molecular structure, rheological properties and foaming structures of linear and long chain branching polypropylenes. Two linear viscoelastic characteristics, | G*| at δ = 60° and | η*| at ω = 5 rad/s were used as criteria for foamability of these polymers, where decreasing of both parameters by increasing the long chain branching content results in smaller cell size and higher cell density. The molecular stress function model was able to quantify the strain hardening properties of long chain branching blends using small amplitude oscillatory shear data and two nonlinear material parameters, 1 ≤ β ≤ 2.2 and 1 ≤ [Formula: see text] ≤ 600, where the minimum and maximum values of these parameters belong to the linear and long chain branched polypropylene, respectively. Increasing the long chain branched polypropylene content of the PP blends increased strain hardening, and therefore improved the foaming characteristics significantly by suppressing the coalescence of cells. Dilution of linear PP with only 10 wt% of long chain branched polypropylene enhanced the cell density from 5.7 × 106 to 2.7 × 107 cell/cm3 and reduced the average cell diameter from 58 to 26 µm, respectively, while their volume expansion ratio remained in the same range of 2–3. Increasing of long chain branching to 50 and 100 wt% enhanced the V.E.R. to 6.2 and 7.8, respectively.