Z-average Molecular Weight Research Articles

A statistical approach towards determining the governing parameters in volume expansion behavior of polypropylene foams

This study delves into the complex relationship between molecular structures and properties within polypropylene (PP) foams, with a particular focus on how various material parameters influence foamability. Multiple linear regression was adopted to efficiently assess the impact of eleven material parameters on foam expansion behavior. A primary finding is the significant role of branching index (g'vis) in shaping the expansion profile (i.e., the foaming window, maximum expansion ratio (Φmax), and optimum foaming temperature (Toptimum)). Additionally, Z-average molecular weight (Mz) is identified as crucial factor influencing the foaming window. Furthermore, the Winter-Chambon parameter n, indicator of the relaxation behavior of a resin in the terminal zone, is distinguished as a key parameter in determining Φmax. The crystallization temperature (Tc) also plays a pivotal role, particularly in its relationship with Toptimum. The research further highlights the significance of long-chain branching (LCB) and suggests strategies for cost reduction by minimizing the degree of LCB without compromising foaming performance, achievable through the adjustment of Mz and n. This strategy was exemplified through the comparison of two LCB PP resins, PP-12 and PP-22, demonstrating the feasibility of achieving similar foamability with adjustments in material parameters. The findings offer a detailed assessment of these parameters' influence on foamability, presenting valuable guidelines for optimizing PP foam production and customizing material properties for targeted applications.

Fatigue-Crack Propagation of High-Density Polyethylene Homopolymers: Influence of Molecular Weight Distribution and Temperature

The present study focuses on the influence of the molecular weight distribution (MWD) on the crack-growth kinetics of fatigue-crack propagation in high-density polyethylene (HDPE) homopolymers. Compact-tension specimens of HDPE homopolymer grades, with polydispersities ranging from 2 to 45 and weight-averaged molar mass ranging from 49 to 450 kg/mol, are tested in cyclic loading at temperatures ranging between 23 and 92 °C. Through a variation of sample thickness, linear elastic-fracture mechanics is shown to apply for the chosen geometry (compact tension). It was found that the crack-propagation kinetics obey the Paris–Erdogan law, for which the Paris–Erdogan exponent m is (highly) similar for all grades tested (m = 3.9), implying that the Paris–Erdogan prefactor A is the governing parameter for the crack-growth kinetics. Relatively poor correlations are observed when the prefactor A is plotted as a function of both the tie-molecule fraction derived from the theoretical model by Huang and Brown, J. Mater. Sci. 1988, 23, 3648, and the average number of effective physical cross-links per chain as derived by Tervoort et al., Macromolecules 2002, 35, 8467. A far better correlation is observed between prefactor A and the weight-average molecular weight (Mw), which improved further when Mw is corrected for the width of the MWD, taking into account the z-average molecular weight Mz, through the ratio Mz/Mw. A power-law correlation of prefactor A with Mw and the width-corrected Mw reveals slopes of −3.4 and −3.3, respectively. Because a molecular slip within the fibrils would require chain transport through the crystalline blocks, the temperature dependence of the fatigue-crack-growth kinetics is investigated to identify the underlying molecular processes. This investigation reveals the existence of a high-temperature and a low-temperature deformation process, both of which can be related to chain-slip mechanisms through their respective activation energies (125 and 50 kJ/mole), as their activation energies are considerably lower than that required for chain scission (430 kJ/mol). This, combined with the power-law exponent of −3.4, would suggest a possible connection between the underlying failure mechanisms of craze fibrils and reptation-like dynamics. Furthermore, experiments at elevated temperatures on a selection of homopolymer grades suggest that the MWD has no influence on the temperature dependence of fatigue-crack propagation for HDPE homopolymers.

A Unified Theoretical Treatment on Statistical Properties of the Semi-batch Self-condensing Vinyl Polymerization System

We present a novel generating function (GF) method for the self-condensing vinyl polymerization (SCVP) system with any initial distribution of preexisted polymers. Such a method was proven to be especially useful to investigate the semi-batch SCVP system allowing a sequence of feeding operations during the polymerization. Consequently, the number-, weight-, and z-average molecular weights as well as dispersity index of hyperbranched polymers can be explicitly given, which are determined by predetermined feeding details and conversions in each polymerization step. These analytical results are further confirmed by the corresponding Monte Carlo simulations. Therefore, the present GF method has provided a unified treatment to the semi-batch SCVP system. Accordingly, hyperbranched polymers with desired properties can be prepared by designing feeding details and presetting conversions at each step based on the present GF method.

Fractal model of polymer electrolyte to investigate influence of high energy irradiation in molecular distribution and molar mass average

The present work is completely based on the theoretical investigation i.e. computer simulated study of the effect of gamma irradiation on the molecular weight distribution and the molar mass averages of solid polymer electrolytes which is relevant with the present trends of experimental works in this field. We propose a fractal model corresponding to polymer molecules by deterministic loop-less fractal (Vicsek). An initial un irradiated symmetrical molecular weight distribution has been considered. Application of high energy perturbation, for example gamma irradiation, affects the molecules mainly by two processes-scission and cross-linking of molecules which results morphological changes inside the system. A new parameter named as weight fraction, has been introduced to compare the structural modification of the sample with the experimental results. The four basic parameters representing the molar mass averages have been introduced in this context to analyze various structural properties such as intrinsic viscosity, number, weight and Z-average molecular weight etc. The results of our simulation work enables us an easy understanding about the nature of the response of solid polymer electrolyte to the external perturbation.

А new factor effecting gel strength of pectin polysaccharides

Pectin polysaccharides obtained from various raw materials have a different component composition and form gels with water, sugar and acid or calcium. In this study, an experimental approach the gelation properties of different pectin samples, varied from different sources, using new methods of hydrolysis and purification. Samples were obtained by hydrolysis of accelerated extraction of pectin and purified by diaultrfiltration, have a high gel strength. The highest gel strength have been found in series of high methoxyl (HM-) pectin samples of apple, peach, orange and low methoxyl (LM-) pectin samples of commercial citrus pectin and apple pectin obtained by new method. It is shown that in addition to the basic parameters (the content of galacturonic acid, degree of esterification, molecular weight and hidrodinamic radius macromolecule) to affect gel strength pectins aggregation of macromolecules, which is determined by the z-average molecular weight. There were observed a clear pattern of the influence of the molecular weight on hydrodynamic parameters for both HM- and LM- pectin samples on the gel strength. It were shown that a high values of molecular weight, intrinsic viscosity, and radius of gyration of pectin samples can significantly increase gel strength, while the value of Mz oppositely influenced the gel strength. As a result, a systematic analysis of this parameter and its relationship to the average molecular weight found that indeed the ratio Mz/Mw for pectin’s is an crucial to assess the quality of pectin at the study of gel strength for pectin polysaccharides.

Poly(vinylpyrrolidone) as dispersing agent for cerium-gadolinium oxide (CGO) suspensions

The behaviour of selected poly(vinylpyrrolidone) grades to act as dispersant for ethanol-based cerium-gadolinium oxide suspensions was investigated and related to the molecular weight characteristics. The number, weight, and z-average molecular weights M n, M w, and M z were determined by gel permeation chromatography and then used in a numerical method to evaluate the viscosity average molecular weight (M v) via an empirically modified Mark–Houwink–Sakurada (MHS) equation. The MHS equation parameters (a and K) and the polydispersity correction factor (q MHS) were also evaluated. Three grades with different molecular weight features were selected and further studied as dispersants by means of rheology. Despite the differences, only slight shifts in the amount of polymer required for achieving fully stabilized dispersions were observed, whereas comparable packing properties were obtained. This was explained as an effect of the polydispersity, expressed as q MHS.

In vivo oxidative degradation of polypropylene pelvic mesh

Commercial polypropylene pelvic mesh products were characterized in terms of their chemical compositions and molecular weight characteristics before and after implantation. These isotactic polypropylene mesh materials showed clear signs of oxidation by both Fourier-transform infrared spectroscopy and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). The oxidation was accompanied by a decrease in both weight-average and z-average molecular weights and narrowing of the polydispersity index relative to that of the non-implanted material. SEM revealed the formation of transverse cracking of the fibers which generally, but with some exceptions, increased with implantation time. Collectively these results, as well as the loss of flexibility and embrittlement of polypropylene upon implantation as reported by other workers, may only be explained by in vivo oxidative degradation of polypropylene.

Antihyperlipidemic and hepatoprotective activities of residue polysaccharide from Cordyceps militaris SU-12

Cordyceps militaris has been artificially cultivated in China, and the great amounts of produced medium residue were discarded after the harvest. The aims of this work were to analyze the structure of the residue polysaccharide (RPS) of C. militaris SU-12, and to investigate the pharmacological effects of RPS on lipid metabolism and oxidative stress. RPS was composed of glucose, arabinose and mannose with a ratio of 62:1.6:1 by gas chromatography analysis, and the Mw (weight-average molecular weight), Mn (number-average molecular weight) and Mz (z-average molecular weight) of RPS were 2.86×103, 6.85×102, and 1.97×104Da, respectively. The mice experiments demonstrated that RPS could reduce the levels of blood and liver lipid, and improve the glutamate pyruvate transaminase and antioxidant activity. The histopathological observations of mice livers indicated that RPS could attenuate liver cell injury. Results suggest that the RPS might be used as a potential antihyperlipidemic, hepatoprotective and antioxidant product.

Characterization of chain dimensions of poly(ε-caprolactone) diols in THF by size-exclusion chromatography coupled with multi-angle light scattering (SEC-MALS)

In this work, we studied the chain dimensions, shape, and thermodynamic characteristics of poly(e-caprolactone) diols (HO-PCL-OH) in solution. PCL diol samples of different molecular weights and architectures were synthesized using immobilized Yarrowia lipolytica lipase as catalyst. Gel permeation chromatography (GPC) with online right-angle laser-light scattering (RALLS), differential viscometer (DV), and interferometric refractometer IRS detectors offered a proper way to obtain information on thermodynamic characteristics and chain flexibility. The weight-average molecular weights of the PCL diol samples (M w ) ranged from 2,750 to 13,120 uma. The z-average radius of hydrodynamic volume (<R h 2 > z 1/2 ) vs. z-average molecular weight curve (M z ) could be satisfactorily fitted to a power-law equation. Mark–Houwink–Sakurada parameters (K = 2.74 × 10−3 dL/g and a = 0.64) were derived from the plots of [η] w against M w . The overall results clearly suggest that a flexible geometry is present in tetrahydrofuran (THF) solution of PCL at 33 °C. Unlike other PCL systems, PCL diols are more hydrophilic and expected to form associated species. They behave differently from common hydrophobic polymers and do not strictly conform to thermodynamic relationships generally used in Polymer Science. A more compact geometry is present for Mn lower than 4,000 Da. For higher molecular weights, the chain expands and become more elongated. Plots of ln [η] w against ln M w (MHS equation) and of log R hz against log M z suggest that PCL diols behave as flexible chains in a good solvent.

A Chromatographic Study of Shear Stability of Poly(styrene-co-alkyl methacrylate) Viscosity Modifier for Lubricating Oils

Shear stability of styrene, dodecyl methacrylate, and octadecyl methacrylate terpolymer of various molecular weights, as the rheology modifier of improved solubility, thermal and oxidation stability in mineral base oil, was investigated. Viscosity loss of the 5 wt% solutions caused by scission of macromolecules subjected to the high shear forces ranges between 15% and 27% for weight average molecular weights from 156000 to 252000. After the shear tests the number average molecular weights of polymer increases while weight and Z-average molecular weights decrease. As macromolecules of molecular weights above 700000 fully break the molar-mass dispersity decreases significantly, from starting at 2.34–2.79 down to below 1.8. A linear dependence between viscosity loss of terpolymer solutions and molecular weights was observed. The advantage of using the size exclusion chromatography to determine the stability of the polymer against mechanical shear directly and the viscosity loss indirectly was established.

Dynamic light scattering and small-angle neutron scattering studies on phenolic resin solutions

Solution properties of unfractionated phenolic resins prepared by polycondensation of phenol and formaldehyde using oxalic acid as a catalyst were investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The hydrodynamic radius, obtained by DLS experiments with 1 vol % solution in acetone, and the correlation length, ξ, of the Ornstein–Zernike equation, obtained by SANS experiments with 10 vol % solution in tetrahydrofuran, obey a power-law relation as a function of z-average molecular weight estimated by gel permeation chromatography, with scaling exponents of 0.57 and 0.27, respectively. These behaviors are unaffected by polymerization conditions, such as initial phenol-to-formaldehyde molar ratio in the range from 0.9 to 1.5, catalyst concentration with oxalic acid-to-phenol molar ratio from 0.01 to 0.1, and reaction time within the period in which the polymer remains soluble. SANS curves for polymers prepared under different conditions are sufficiently superimposed onto a single curve with the reduced variables, ξ−2I(q) and ξq. These results indicate that unfractionated phenolic resins have a self-similar structure with respect to the molecular weight.

Influence of electron beam irradiation on physicochemical properties of poly(trimethylene carbonate)

Electron beam (EB) irradiation of poly(trimethylene carbonate) (PTMC), an amorphous, biodegradable polymer used in the field of biomaterials, results in predominant cross-linking and finally in the formation of gel fraction, thus enabling modification of physicochemical properties of this material without significant changes in its chemical structure. PTMC films ( M w : 167–553 kg mol −1) were irradiated with different doses using an electron accelerator. Irradiation with a standard sterilization dose of 25 kGy caused neither significant changes in the chemical composition of the polymer nor significant deterioration of its mechanical properties. Changes in viscosity-, number-, weight-, and z-average molecular weights of PTMC for doses lower than the gelation dose ( D g ) as well as gel–sol analysis and swelling tests for doses above D g indicate domination of cross-linking over degradation. EB irradiation can be considered as an effective tool for increasing the average molecular weight of PTMC and sterilization of PTMC-based biomaterials.

Molecular Weight Distribution Evaluation of Polysaccharides and Glycoconjugates Using Analytical Ultracentrifugation

We review here the advances that have been made in methodology using the analytical ultracentrifuge for characterising polydisperse polymer systems with a quasi-continuous distribution of molecular weight. These advances include improved ways of defining the weight and z-average molecular weights of a distribution from sedimentation equilibrium experiments and hence the ratio Mz/Mw, off-line calibration of size exclusion chromatography by sedimentation equilibrium and conversion of a sedimentation coefficient distribution into a molecular weight distribution. Although these methods are applicable to other polymeric systems, we focus on polysaccharides, mucins and other glycoconjugates, systems which particularly benefit from the availability of recently available long optical path length cells for the minimisation of complications through thermodynamic non-ideality.

Ion‐specific modulation of protein interactions: Anion‐induced, reversible oligomerization of a fusion protein

Ions can significantly modulate the solution interactions of proteins. We aim to demonstrate that the salt-dependent reversible heptamerization of a fusion protein called peptibody A or PbA is governed by anion-specific interactions with key arginyl and lysyl residues on its peptide arms. Peptibody A, an E. coli expressed, basic (pI = 8.8), homodimer (65.2 kDa), consisted of an IgG1-Fc with two, C-terminal peptide arms linked via penta-glycine linkers. Each peptide arm was composed of two, tandem, active sequences (SEYQGLPPQGWK) separated by a spacer (GSGSATGGSGGGASSGSGSATG). PbA was monomeric in 10 mM acetate, pH 5.0 but exhibited reversible self-association upon salt addition. The sedimentation coefficient (s(w)) and hydrodynamic diameter (D(H)) versus PbA concentration isotherms in the presence of 140 mM NaCl (A5N) displayed sharp increases in s(w) and D(H), reaching plateau values of 9 s and 16 nm by 10 mg/mL PbA. The D(H) and sedimentation equilibrium data in the plateau region (>12 mg/mL) indicated the oligomeric ensemble to be monodisperse (PdI = 0.05) with a z-average molecular weight (M(z)) of 433 kDa (stoichiometry = 7). There was no evidence of reversible self-association for an IgG1-Fc molecule in A5N by itself or in a mixture containing fluorescently labeled IgG1-Fc and PbA, indicative of PbA self-assembly being mediated through its peptide arms. Self-association increased with pH, NaCl concentration, and anion size (I(-) > Br(-) > Cl(-) > F(-)) but could be inhibited using soluble Trp-, Phe-, and Leu-amide salts (Trp > Phe > Leu). We propose that in the presence of salt (i) anion binding renders PbA self-association competent by neutralizing the peptidyl arginyl and lysyl amines, (ii) self-association occurs via aromatic and hydrophobic interactions between the ..xxCTRWPWMC..xxxCTRWPWMCxx.. motifs, and (iii) at >10 mg/mL, PbA predominantly exists as heptameric clusters.

Dextranas em açúcares do estado de São Paulo

The characterization of dextran in sugars by size exclusion chromatography (SEC) has been carried out according to the number-average molecular weight (Mn), the weight-average molecular weight (Mw), the Z-average molecular weight (Mz), and the polydispersity (Mw/Mn). The results suggest that all the analyzed thirty sugar samples from Sao Paulo state were contaminated with two or three different dextran polymers. The collected data clearly point out that the total dextran content together with the mass distribution parameters Mw, Mn, Mz, and Mw/Mn should be considered during the evaluation of the quality of the sugar used for the cachaca sweeting process.

Influences of molecular weight and crystalline structure on fracture behavior of controlled-rheology-polypropylene prepared by reactive extrusion

The molecular weight of ethylene- block- co-polypropylene (co-PP) was adjusted by reactive extrusion with the incorporation of dicumyl peroxide (DCP), and the effect of molecular weight on the crystallization behavior, crystal morphology, and fracture behavior was investigated. It was found that, with increasing DCP content, the molecular weight (MW) decreased and the polydispersity ( M w/ M n) slightly decreased. After modification, the number of spherulites with obscure boundaries increased, and the size of the spherulites was more even due to increasing amount of grafting and micro-cross-linking structures, generated in co-PP degradation, which were acting as nucleating agents. Evaluated by essential work of fracture method, the specific essential work of fracture, w e, was found to be strongly dependent on the molecular weight, especially, on the number average molecular weight ( M n) linearly, while the specific non-essential work of fracture, βw p, was enhanced with decreasing z-average molecular weight ( M z), probably owing to the reduction of ultra-high molecular weight component in degraded co-PP.

Effects of high molecular weight species on shear-induced orientation and crystallization of isotactic polypropylene

In situ rheo-SAXS (small-angle X-ray scattering) and—rheo-WAXD (wide-angle X-ray diffraction) techniques were used to investigate the role of high molecular weight species on the evolution of oriented microstructure in isotactic polypropylene (iPP) melt under shear flow. The two iPP samples, designated as PP-A and PP-B, respectively, had the same number-average (Mn) but different weight-average (Mw) and Z-average (Mz) molecular weights. Molecular weight distribution (MWD) of PP-A and PP-B was such that for MW<105 the MWD curves overlapped; whereas in the high MW tail region, the amount of high molecular weight species was higher in PP-B than PP-A. Both samples were subjected to an identical shear condition (rate=60s−1, duration=5s, T=155°C). In situ 2D SAXS and WAXD images allowed the tracking of shear-induced oriented structures in the melt. It was found that the shish structures evolved much earlier, and the degree of crystal orientation and oriented crystal fractions were higher in PP-B than PP-A. Moreover, PP-B exhibited faster crystallization kinetics than PP-A. These results, along with the predictions of double reptation models of chain motion and experimental studies of chain conformation dynamics in dilute solutions under flow, suggest the following: When a polymer melt that consists of entangled chains of different lengths is deformed, the chain segments aligned with the flow eigenvector can undergo the abrupt coil-stretch-like transition, while other segments would remain in the coiled state. Since, flow-induced orientation decays much more slowly for long chains than for short chains, oriented high molecular weight species play a prominent role in formation of the stretched sections, where shish originates. Our experimental results are strong evidence of the hypothesis that even a small increase in the concentration of high molecular weight species causes a significant increase in the the formation, stability and concentration of the flow-induced oriented microstructure.

Recovery of mechanical properties of aged polystyrene after reprocessing

A combined procedure of thermal ageing followed by injection molding has been applied for ten times to simulate the repeated recycling. The processability of the recycled material was somewhat improved and the mechanical parameters were rather retained. Regular oscillations in strength characteristics of the successively aged and recycled samples have been registered. Namely, stress at break was repeatedly decreased and restored again after ageing and reprocessing steps, respectively. The very similar zig-zag pattern has been observed for elongation at break. Similarly, impact strength of the remolded samples shows on average better values than those of the aged samples. On the contrary, z-average molecular weight and melt flow rate were changed rather monotonically - a decrease and on increase, respectively. Considering the above, the observed phenomenon of alternating deterioration and recovery of the strength parameters has been attributed to material homoeenization under the reprocessing steps.

The Impact of Thermal Events on Amylose-Fatty Acid Complexes

The molecular behavior of amylose-lipid complexes was studied using differential scanning calorimetry. rapid viscoanalysis and texture analysis methods. Three amyloses were fractionated, one each from regular, 50% amylose and 70% amylose corn starches. High performance size exclusion chromatography, coupled with multiple angle laser light scattering, was used to determine amylose molecular weight profiles; fractions differed statistically (P<0.05) in their z-average molecular weights (M z ). Each amylose fraction was complexed with five different fatty acids. After 12 days of storage, amylose-lipid complexes had recrystallization percentages ranging from 42.7 to 98.2%. Cohesiveness (r = -0.84) and adhesiveness (r = -0.75) decreased with increasing M z of amyloses (P<0.05). An inverse relationship was obtained between fatty acid chain length and percent recrystallization (r = -0.84, P<0.05). Percent recrystallization decreased when fatty acid chain length increased from C16:0 to C18:0. All complex samples, when adjusted to an equal total starch basis, had decreased viscosities when pasted compared to their native starch or amylose counterparts. Shear thinning of complexes increased with increasing molecular weight (M z ) of amyloses (r = 0.71, P<0.05). Lower recrystallization rates and decreased viscosity properties could be accomplished complexing by amylose and fatty acids.

What Has Brought on the Effects of Number-Average Molecular Weight on the Spinodals in Polymer Mixtures?

On the basis of the thermodynamics of Gibbs, the spinodal for the quasibinary system was derived in the framework of the Sanchez−Lacombe lattice fluid theory. All of the spinodals were calculated based on a model polydisperse polymer mixture, where each polymer contains three different molecular weight sub-components. According to our calculations, the spinodal depends on both weight-average (Mw) and number-average (Mn) molecular weights, whereas that of the z-average molecular weight is invisible. Moreover, the extreme of the spinodal decreases when the polydispersity index (η = Mw/Mn) of the polymer increases. The effect of polydispersity on the spinodal decreases when the molecular weight gets larger and can be negligible at a certain large molecular weight. It is well-known that the influence of polydispersity on the phase equilibrium (coexisting curve, cloud point curves) is much more pronounced than on the spinodal. The effect of Mn on the spinodal is discussed as it results from the infuluence...