Lumped Time Distribution Function of Dynamic Equilibrium System and Its Application in Calculating Molecular Weight Distribution of Polymer

The lumped time distribution functions were proposed, which can be used for describing the dynamicsystems with two or more than two states of the end of growing polymer chain during chain addition polymerization.Numerical analysis of the lumped time distribution functions was carried out. The method for calculating molecularweight distribution of polymer in the stable free radical polymerization and more general cases was developed basedon the lumped time distribution functions.

Analysis of Molecular Weight Distribution and Antioxidant Activities of Cirrhinus molitorella Skin Collagen Hydrolysates

[Objective] The aim of this work was to identify molecular weight （MW） distribution and antioxidant activity of fish skin col agen hydrolysates. [Method] The MW distribution of hydrolysates was determined using both size exclusion chromatography and matrix-assisted laser desorption ionization time-of-flight mass spec-trometry （MALDI-TOF-MS）. Fish skin were treated by the alkaline protease 2709. [Result] The optional conditions for hyerolysis were time 3 h, temperature 55 ℃, pH 10.0, substrate concentration 80 g/L and E/S 4%. The results of both methods indi-cated that the molecular weight of col agen hydrolysates was from 400 to 1 800 Da, and the peptides’ molecular weight was less than 1 400 Da mostly. The reducing power and antioxidant/radical scavenging activity [1, 1-diphenyl-2-picryl-hydrazyl （DPPH） free radical scavenging activity] were determined. [Conclusion] The results reveal that the fishskin hydrolysate is a potential source of antioxidants.

Study on Enzymatic Hydrolysis of Gadus morrhua Skin Collagen and Molecular Weight Distribution of Hydrolysates

Process parameters on enzymatic hydrolysis and molecular weight （MW） distribution of collagen hydrolysates from Gadus morrhua skin were investigated. The optimal process parameters were obtained by the single-factor and orthogonal experiments. The molecular weight distribution of hydrolysates was determined using both Sephadex G25 partition and high speed liquid chromatography electricity spray mass spectrum （HPLC-ESI-MS）. Collagen hydrolysates were first gained by an alkaline protease ＂alcalase＂ for 3 h at temperature （50~C）, pH （10.0）, substrate concentration （75 g L-~）, and E/S （3%）. The molecular weight distribution of collagen hydrolysates ranged from 300 to 1 500 Da, and most of peptides were under 1 200 Da. Sephadex G25 partition and HPLC-ESI-MS should be successfully employed to determine the molecular weight distribution of collagen hydrolysates.

A HIGHLY ACTIVE NEODYMIUM CHLORIDE ISOPROPANOL COMPLEX/MODIFIED METHYLALUMINOXANE CATALYST FOR PREPARING POLYISOPRENE WITH HIGH CIS-1,4 STEREOSPECIFICITY AND NARROW MOLECULAR WEIGHT DISTRIBUTION

Neodymium chloride isopropanol complex （NdCl3.3＇prOH） activated by modified methylaluminoxane （MMAO） was examined in isoprene polymerization in hexane, with regards to Nd compounds, aluminum （Al） compounds, [Al]/[Nd] ratio, polymerization temperature and time. NdCl3＇3iprOH exhibited high activity producing polymers feasting high cis-l,4 stereospecificity （〉 96%）, very high molecular weight （Mn 〉 1.0 × 10^6） and fairly narrow molecular weight distribution （MWD, Mw/Mn 〈 2.0） simultaneously. In comparison, neodymium isopropoxide also showed high activity providing polymers with narrow MWD （Mw/Mn = 2.07）, but somewhat low cis-1,4 content （ca. 92%）, while neodymium chloride had no activity under present polymerization conditions. The Al compounds affected the polymer yield in the order of Al（i-Bu）3 〉 MMAO 〉 Al（i-Bu）2H. MMAO as cocatalyst afforded polyisoprene with high Mn over 1.0 × 10^6, whereas as stronger chain transfer agent than MMAO, AI（i-Bu）3 and AI（i-Bu）EH yielded polymers with low Mn （1.0 × 10^5-8.0 × 10^5）. NdCl3·3＇PrOH/MMAO catalyst showed a fairly good catalytic activity even at relatively low [Al]/[Nd] ratio of 30, and the produced polymer remained high cis-1,4 content of 95.8% along with high Mn over 1.0× 10^6 even at elevated temperatures up to 70℃. The polymerization rate is of the first order with respect to the concentration of isoprene. The mechanism of active species formation was discussed preliminarily.

Molecular Weight and Distribution of Cellulose and Cellulose Microspheres

[ Objective ] This study aimed to provide basic data for studying the relationship between structure and property of cellulose microspheres by measuring molecular weight of cellulose and cellulose microspheres with viscosity method and gel permeation chromatography （GPC） method. [ Method] In viscosity method, cadmium ethylenediamine was used as the solvent, intrinsic viscosity η of the solution was determined at 25 ℃ by using a Ubbelohde viscometer, to calculate the molecular weight of cellulose; in GPC method, 8% LiC1 / N, N-dimethylacetamide （LiC1/DMAc） was used as the solvent and 0.5% LiC1/DMAc was used as the mobile phase to determine the relative molecular weight and distribution of cellulose and cellulose microspheres. In addition, the determination results were analyzed to compare these two methods. [ Result ] Viscosity-average molecular weight Mr/ of cellulose and cellulose microspheres determined with viscosity method were 224,532 and 16,686, respectively; weight-average molecular weight Mw of cellulose and cellulose microspheres determined with GPC method were 284,196 and 22,345, respectively. [ Conclusion] The determination results of （;PC method are relatively close to the actual value and could truly reflect the characteristics of molecular weialat distribution of eellulose and cellulose mierosr, heres.

SUPPORTED ZIEGLER-NATTA CATALYSTS FOR ETHYLENE SLURRY POLYMERIZATION AND CONTROL OF MOLECULAR WEIGHT DISTRIBUTION OF POLYETHYLENE

The effect of chemical composition of highly active supported Ziegler-Natta catalysts with controlled morphology on the MWD of PE has been studied.It was shown the variation of transition metal compound in the MgCl_2-supported catalyst affect of MWD of PE produced in broad range:Vanadium-magnesium catalyst(VMC)produce PE with broad and bimodal MWD(M_w/M_n=14-21).MWD of PE,produced over titanium-magnesium catalyst(TMC)is narrow or medium depending on Ti content in the catalyst(M_w/M_n=3.1-4.8).The oxidation ...

Molecular Weight Distribution of Dissolved Organic Matter in Lake Hongfeng Determined by High Performance Size Exclusion Chromatography (HPSEC) With On-Line UV-Vis Absorbance and Fluorescence Detection

The molecular weight distribution (MWD) of dissolved organic matter (DOM) in lake waters from Lake Hongfeng was examined using high performance size exclusion chromatography (HPSEC) with UV-vis absorbance and fluorescence detection. The elution curves obtained by absorbance and fluorescence techniques expressed similar patterns, with the exception of diminishing of large fraction and the peaks behind several seconds in fluorescence chromatograms. According to its molecular weight (MW), DOM in water samples is divided into several fractions: large ({>3.5} kDa); medium-large ({3.5}-{2.0} kDa); medium ({2.0}-{1.0} kDa) and small ({<1.0} kDa). The average molecular weight was calculated using the elution curve detected by UV-vis absorbance and fluorescence detection techniques. The results showed that the weight-average molecular weight (Mw) and number-average molecular weight (Mn) calculated by UV-vis absorbance techniques range from 1750 to 2050 Dalton and from 1450 to 1850 Dalton, respectively. And the Mw and Mn obtained by fluorescence detection are lower by 50 to 400 Dalton. As a reference, the molecular weight of Fluka humic acid (FHA) is larger than that of water samples by about 200 Dalton. The average molecular weight of DOM for water samples collected in March and July was compared. The results revealed that the molecular weight is lower for water samples obtained in July than that obtained in March, indicating the ambient environment has an influence on the molecular weight, including photo-degradation and biological activity.

THE RELATION OF SEQUENCE DISTRIBUTIONS OF S-SBR TO ITS MOLECULAR WEIGHT DISTRIBUTIONS

The relationship between sequence distributions and molecular weight distributions of S-SBR, obtained from styrene and butadiene anionic copolymerization at various conversions with THF/Li^+ as an initiator has been studied by ^(13)C-NMR,GPC. The results showed that the molecular weight distributions of the copolymer couldbe correlated sophisticatedly to the binary sequcne distributions or the monomer unit distributions of the copolymer in a corrected Poisson's distribution from.

Effect of Molecular Weight and Molecular Distribution on Skin Structure and Shear Strength Distribution near the Surface of Thin-Wall Injection Molded Polypropylene

In this study, the relationship between skin structure and shear strength distribution of thin-wall injection molded polypropylene (PP) molded at different molecular weight and molecular distribution was investigated. Skin-core structure, cross-sectional morphology, crystallinity, crystal orientation, crystal morphology and molecular orientation were evaluated by using polarized optical microscope, differential scanning calorimeter, X-ray spectroscopic analyzer and laser Raman spectroscopy, respectively, while the shear strength distribution was investigated using a micro cutting method called SAICAS (Surface And Interfacial Cutting Analysis System). The results indicated that the difference of molecular weight and molecular weight distribution showed own skin layer thickness. Especially, high molecular weight sample showed thicker layer of the lamellar orientation and molecular orientation than low molecular weight sample. In addition, wide molecular distribution sample showed large crystal orientation layer.

The Relationship between Bulk Property and Property Distribution in Thin-Wall Injection Molded PP at Different Molecular Weight and Molecular Weight Distribution

Thin-wall injection molded parts have been paid much attention to the lightweight saving from viewpoints of natural resources saving. In the injection molding, skin-core structure can be found in the parts. This skin-core structure affects the property of completed injection molding parts (bulk property) even if in thin-wall injection molding. However, there is a few research about the relationship between bulk property and internal property distribution in the injection molding specimen. In this study, thin-wall injection molded parts of polypropylene (PP) were prepared by 4 different molecular weight and molecular weight distribution to reveal the relationship between bulk property and property distribution. These characteristics were investigated by using tensile test, fracture toughness characterized by Essential Work of Fracture (EWF) method for bulk property and film tensile test by sliced sample for tensile property distribution. The property distribution test results revealed that the highly bulk property sample had thicker highly mechanical property layer on its surface.

Determination and Temperature Dependence of Plateau Modulus for Polymerization of Propylene to Isotactic Polypropylene with Ultra-high Molecular Weight under Catalysis of Ziegler-Natta Catalyst

The viscoelastic behavior of isotactic polypropylene with ultra-high molecular weight(UHPPH) and broad molecular weight distribution(MWD), produced in the presence of Ziegler-Natta catalyst, was investigated by means of oscillatory rheometry at 180 and 200 ℃, whose loss modulus(G″) plots at 180 and 200 ℃ versus the natural logarithm of angular frequency(ω) present a pronounced maximum at 34.35 and 69.21 rad/s, respectively, and do not show a maximum peak at 0.01-100 rad/s for Ziegler-Natta catalyzing ethylene-propylene random copolymerization(PPR) with a conventional molecular weight and broad MWD. The fact indicates that the high molecular weight is responsible for a maximum peak of G″(ω) vs. lnω curves for UHPPH. This makes it possible to determine the plateau modulus(G 0_N) of UHPPH from a certain experimental temperature G″(ω) curve directly. For UHPPH, the G 0_N determined to be 4.28×10 5 and 3.62×10 5 Pa at 180 and 200 ℃, respectively, decreases with the increase of temperature and is independent of the molecular weight, which directly confirms reputation theoretical prediction that the G 0_N has no relation to the molecular weight.

Exact Statistical Distribution of the Body Mass Index (BMI): Analysis and Experimental Confirmation

Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to the square of the associated height (in meters), is one of the most widely discussed and utilized risk factors in medicine and public health, given the increasing obesity worldwide and its relation to metabolic disease. Statistically, BMI is a composite random variable, since human weight (converted to mass) and height are themselves random variables. Much effort over the years has gone into attempts to model or approximate the BMI distribution function. This paper derives the mathematically exact BMI probability density function (PDF), as well as the exact bivariate PDF for human weight and height. Taken together, weight and height are shown to be correlated bivariate lognormal variables whose marginal distributions are each lognormal in form. The mean and variance of each marginal distribution, together with the linear correlation coefficient of the two distributions, provide 5 nonadjustable parameters for a given population that uniquely determine the corresponding BMI distribution, which is also shown to be lognormal in form. The theoretical analysis is tested experimentally by gender against a large anthropometric data base, and found to predict with near perfection the profile of the empirical BMI distribution and, to great accuracy, individual statistics including mean, variance, skewness, kurtosis, and correlation. Beyond solving a longstanding statistical problem, the significance of these findings is that, with knowledge of the exact BMI distribution functions for diverse populations, medical and public health professionals can then make better informed statistical inferences regarding BMI and public health policies to reduce obesity.

Pharmacokinetics of fucoidan and low molecular weight fucoidan from Saccharina japonica after oral administration to mice

The brown seaweed,Sacchairna japonica,has been used in traditional Chinese medicine for over one thousand years.Oral administration of fucoidan or low molecular weight fucoidan(LMWF)from S.japonica could ameliorate kidney dysfunction in chronic kidney diseases and inhibit diabetic vascular complications.In many studies,LMWF was found to be more potent than fucoidan with high molecular weight.However,the pharmacokinetics of LMWF still remains unclear.The purpose of the research is to compare the pharmacokinetics of fucoidan with high molecular weight(136 kDa)with that low molecular weight(9.5 kDa)after oral administration to ICR mice.Since fucose is the main and representative monosaccharide of fucoidans,we evaluate the pharmacokinetics of fucoidan and LMWF by determining the fucose concentration in mice serum.Both fucoidan and LMWF were absorbed following oral administration.Fucoidan and LMWF were provided to mice by oral administration with 60 mg/kg and the maximum Concentration(C_(max))was found at 2.5 h(0.66±0.32 mg/L)for Fucoidan and 1.5 h(1.01±0.56 mg/L)for LMWF,respectively.It seems that LMWF had a higher area under the curve(AUC_(0–t))and was absorbed more quickly than fucoidan.The estimated bioavailability of LMWF was28.3%in the mice treated with a single dose of 30 mg/kg.In addition,LMWF was found widely spreaded into different tissues following oral administration and the highest concentration was found in kidney at 19.93±7.02μg/g.In this study,we first studied the pharmacokinetics of LMWF,in order to help to understand the function of LMWF.And our results shed light on the potential of development of drugs based on LMWF.

Molecular Weight Distribution of Polystyrene Produced in a Starved Feed Reactor

A starved feed reactor (SFR) is a semi-batch polymerization reactor where initiator and monomer are fed slowly into a fixed amount of solvent. The polymerization is carried out isothermally at elevated temperatures. The added initiator decomposes instantaneously and the added monomer polymerizes immediately. The molecular weight (MW) and molecular weight distribution (MWD) of the product polymer can be effectively controlled by the feed ratio of monomer to initiator. This paper presents a study on the MWD of styrene polymerization in a SFR. The MWD model parameters are regressed with experimental data. Although the solids fraction in the SFR is high (higher than 50%), viscosity is not too high and the 'gel effect' is weak due to the low molecular weight of the products. It is found that the termination rate constant is a power function of molecular weight, radicals terminate via 100% combination, the thermal initiation can be neglected even at high reaction temperature studied. And calculated results indicate that in the SFR, the validity of the long chain assumption becomes doubted. It appears that other alterative assumption should be found for an improved model.

Molecular Weight Distributions of Cotton Cellulose Treated with a Polycarboxylic Acid at Different pH

In last paper, the average molecular weight of a control cotton fabric and cotton fabrics treated with the polycarboxylic acid at different pH were measured. The result doesnt support the hypothesis that the pH of the finishing bath can affect the depolymerization of the finished cotton fabric. In order to understand more about it, the molecular weight distributions of the control and finished cotton fabrics were measured and the reason was fund. From the ratio and the molecular weight of the low molecular part one can see that the pH of the finishing bath can affect the depolymerization of the finished cotton fabrics. The phenomenon that the average molecular weights of the cotton fabric crosslinked with BTCA at different pH are almost same is attributed to that the crosslinks are not broken completely when treated with 0.5 M NaOH solution at 50℃ for 144 h.

New Indoor Accelerated Weathering Condition for Approximating Molecular Weight Distribution of Outdoor-Exposed LDPE

LDPE （low-density polyethylene） photo degraded through various accelerated weathering tests has the molecular weight distribution curves unlike that through outdoor exposure. The authors therefore developed new weathering test condition based on the existing accelerated weathering test using a xenon arc lamp. Samples of LDPE were photo degraded using various accelerated weathering test conditions and outdoor exposure. The physical properties and chemical structures of the photo degraded samples were studied through a tensile test, infrared spectroscopy, and gel chromatography. The authors found that the molecular weight distribution curve of a sample photo degraded using a xenon lamp at a higher BPT （black panel temperature） （73 ~C） was more similar to that of an outdoor-exposed sample than that of a sample photo degraded at the standard BPT （63 ~C）. It is considered that higher temperature accelerates radical recombination, consequently recreating molecular enlargement similar to the outdoor-exposed sample. Multiple regression analysis using newly introduced Mp （peak-top molecular weight） and Mw （weight-average molecular weight） as explanatory variables was conducted, which successfully enabled the authors to provide a simple explanation for the decrease in polymer tensile strength.

Studies in Molecular Weight Determination of Cottonseed and Melon Seed Oils Based Biopolymers

Six grades of biopolymers formulated to have oil content of 40% (M1), 50% (M2), and 60% (M3) melon seed oil (MESO) and 40% (C1), 50% (C2), and 60% (C3) cottonseed oil (COSO) respectively, were prepared with phthalic anhydride, and glycerol using alcoholysis-polycondensation process. The extend of polycondensation was monitored by determining the acid value of aliquots of the reaction mixture at various intervals of time. Molecular weight averages and polydispersity index (PDI) of the finished alkyds were determined by Rast method and end-group analysis. Molecular weight averages and PDI vary with differences in oil length of the alkyds, with samples M2 and C2 respectively exhibiting the highest PDI. Molecular weight average obtained from end-group analysis and those determined by Rast method in brackets are 1338.92 (597.00), 982.33 (696.25), 1316.09 (754.03), and 1160.57 (448.13), 765.96 (583.57), 1049.92 (696.25) for samples M1, M2, M3 and C1, C2, C3 respectively. Number molecular weight averages calculated from end-group analysis are larger than those obtained by Rast method for both MESO and COSO alkyds and seem to grossly overestimate their molecular weights. The mode of variation of these properties indicates that the synthesis of MESO and COSO alkyds are complex. Correlation of PDI with the quality of the finished alkyds shows that the higher the PDI value the better the quality of the alkyd. Performance properties such as rate of drying, film hardness and resistance to chemicals were optimum at 50% oil length for both triglyceride oil alkyds.

Effect of Temperature on the Molecular Weight Distribution in the Different Ranks of Coal during the On-Line Investigation of Coal Pyrolysis Gas Using Direct Photoionization Mass Spectroscopy

Coal pyrolysis gas from different ranks of coal was monitored on real time basis using photoionization mass spectroscopy. The molecular weight distribution of different products as a function of temperature from various coal ranks studied was observed. It was noted that the release of different classes of compounds like phenols, alkenes, alkylated aromatics and aromatic skeletons was temperature dependent. For all the coal ranks at lower temperatures phenols were the main component, with alkenes and alkylated aromatics at slight higher temperatures and aromatic skeletons were released at the highest temperatures studied.

Exact Statistical Distribution and Correlation of Human Height and Weight: Analysis and Experimental Confirmation

The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measurements and analyses, there has been no consensus on this relationship. The purpose of this article is to provide a definitive statistical distribution function from which all desired statistics (probabilities, moments, and correlation functions) can be determined. The statistical analysis reported in this article provides strong evidence that height and weight in a diverse population of healthy adults constitute correlated bivariate lognormal random variables. This conclusion is supported by a battery of independent tests comparing empirical values of 1) probability density patterns, 2) linear and higher order correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance correlation (dCor) values to corresponding theoretical quantities: 1) predicted by the lognormal distribution and 2) simulated by use of appropriate random number generators. Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that specifies conditions under which body mass index (BMI) can be a valid proxy of obesity. The consistency of the empirical data from a large, diverse anthropometric survey partitioned by gender with the predictions of a correlated bivariate lognormal distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or approximate, but may be a consequence of some underlying biophysical mechanism.

Weighted Gini-Simpson Quadratic Index of Biodiversity for Interdependent Species

The weighted Gini-Simpson quadratic index is the simplest measure of biodiversity which takes into account the relative abundance of species and some weights assigned to the species. These weights could be assigned based on factors such as the phylogenetic distance between species, or their relative conservation values, or even the species richness or vulnerability of the habitats where these species live. In the vast majority of cases where the biodiversity is measured the species are supposed to be independent, which means that the relative proportion of a pair of species is the product of the relative proportions of the component species making up the respective pair. In the first section of the paper, the main versions of the weighted Gini-Simpson index of biodiversity for the pairs and triads of independent species are presented. In the second section of the paper, the weighted Gini-Simpson quadratic index is calculated for the general case when the species are interdependent. In this instance, the weights reflect the conservation values of the species and the distribution pattern variability of the subsets of species in the respective habitat induced by the inter-dependence between species. The third section contains a numerical example.