Some inequalities for moments and coefficients of variation for a large class of probability functions

1979 ◽  
Vol 16 (3) ◽  
pp. 665-670 ◽  
Author(s):  
Burt V. Bronk
Keyword(s):  
Large Class ◽  
Average Molecular Weight ◽  
Empirical Measure ◽  
Number Average Molecular Weight ◽  
Positive Real ◽  
Coefficients Of Variation ◽  
Probability Densities ◽  
Rigorous Bounds ◽  
Illustrative Application

Some inequalities for moments and coefficients of variation of probability densities over the positive real line are obtained by means of simple geometrical relationships. As an illustrative application rigorous bounds are obtained for the ratio of weight average to number average molecular weight for a large class of distributions of macromolecules, giving a more precise characterization of this empirical measure of heterogeneity.

Some inequalities for moments and coefficients of variation for a large class of probability functions

1979 ◽  
Vol 16 (03) ◽  
pp. 665-670 ◽  
Author(s):  
Burt V. Bronk
Keyword(s):  
Large Class ◽  
Average Molecular Weight ◽  
Empirical Measure ◽  
Number Average Molecular Weight ◽  
Positive Real ◽  
Coefficients Of Variation ◽  
Probability Densities ◽  
Rigorous Bounds ◽  
Illustrative Application

Some inequalities for moments and coefficients of variation of probability densities over the positive real line are obtained by means of simple geometrical relationships. As an illustrative application rigorous bounds are obtained for the ratio of weight average to number average molecular weight for a large class of distributions of macromolecules, giving a more precise characterization of this empirical measure of heterogeneity.

Kinetic Studies on the Curing Reactions of Fluoroepoxy Oligomer and Cycloaliphatic Amine

2013 ◽  
Vol 747 ◽  
pp. 753-756 ◽  
Author(s):  
Thitinun Chongtum ◽  
Wunpen Chonkaew
Keyword(s):  
Average Molecular Weight ◽  
Gel Permeation Chromatography ◽  
Kinetic Studies ◽  
Equivalent Weight ◽  
Number Average Molecular Weight ◽  
Polymeric Systems ◽  
Acid Titration ◽  
Curing Kinetic ◽  
Gel Permeation

The curing kinetic analysis is an important technique for the characterization of the curing behavior of reactive polymeric systems. In this study, fluoroepoxy oligomer was synthesized from trifluoromethyl aniline and epichlorohydrin. The epoxide equivalent weight (EEW) and the number average molecular weight (Mn) of the systhesized fluroepoxy oligomer determined from acid titration and gel permeation chromatography were found to be 312.16 g/eq and 534 g/mol, respectively. The mixtures of the fluoroepoxy oligomer were mixed with the cycloaliphatic amine in various stiochiometric ratios (1:1, 1: 1.5 and 1:2). The effects of the stiochiometric ratio on the curing behaviors were studied using both isothermal and non-isothermal DSC methods. Ozawas, Kissingers and Friedmans methods were employed to investigate the kinetic parameters. The results showed that the peak temperature (Tp) increased with the increasing heating rate. The activation energy (Ea) calculated from Ozawas and Kissingers methods were much larger than that from Friedmans method.

Synthesis and Characterization of Coumarin–Trioxane–Urea Copolymers

1996 ◽  
Vol 8 (2) ◽  
pp. 295-300 ◽  
Author(s):  
D I Brahmbhatt ◽  
B R Hirani
Keyword(s):  
Molecular Weight ◽  
Elemental Analysis ◽  
Average Molecular Weight ◽  
Synthesis And Characterization ◽  
Number Average Molecular Weight ◽  
Molar Ratios

4-methyl-7-hydroxycoumarin trioxane urea (MHCTU) copolymers were prepared by copolycondensation of 4-methyl-7 hydroxycoumarin (MHC), trioxane (T) and urea (U) in the presence of 2 M HCl/H2SO4 as a catalyst with different molar ratios of reacting monomers. The copolymers were characterized by elemental analysis, IR spectral and TGA studies. The number average molecular weight ( Mn) of all the produced copolymers was determined by non-aqueous titrimetry.

scholarly journals Synthesis and Characterization of Colored Polyureas

2004 ◽  
Vol 1 (1) ◽  
pp. 51-56 ◽  
Author(s):  
M. G. Patel ◽  
K. R. Desai ◽  
H. S. Patel
Keyword(s):  
Electrical Conductivity ◽  
Molecular Weight ◽  
Room Temperature ◽  
Average Molecular Weight ◽  
Conductometric Titration ◽  
Spectral Studies ◽  
Synthesis And Characterization ◽  
Disperse Dyes ◽  
Number Average Molecular Weight

Various disperse dyes based onm-phenylenediamine have been prepared. These dyes then polycondensation with 4,4'-Diphenyl methane diisocyanate. The resultant colored polyureas were characterized by N content, IR spectral studies, Number Average Molecular Weight (Mn) estimation by nonaqueous conductometric titration and thermogravimetry. All the polyureas were subjected to measure electrical conductivity at room temperature.

CHARACTERIZATION OF SOME IRAQI ASPHALTS I. NUMBER AVERAGE MOLECULAR WEIGHT INVESTIGATION OF DORA AND QAIYARAH ASPHALTS

1986 ◽  
Vol 4 (3) ◽  
pp. 249-260 ◽  
Author(s):  
Mustafa M. F. Al-Jarrah ◽  
Hussain H. Al-Soufi ◽  
Rita L. Apikian ◽  
H. I. Al-Saleem ◽  
S. S. Naoom
Keyword(s):  
Molecular Weight ◽  
Average Molecular Weight ◽  
Number Average Molecular Weight

The Synthesis of Silicon-containing Polyester Directly from SiO2 and Characterization of Its Structure

2000 ◽  
Vol 661 ◽  
Author(s):  
Jianhua Song ◽  
Luyi Sun ◽  
Anhua Liu ◽  
Kecheng Gong
Keyword(s):  
Ir Spectra ◽  
Average Molecular Weight ◽  
Silicon Compound ◽  
Number Average Molecular Weight ◽  
Strong Absorption Band ◽  
Organic Silicon Compound ◽  
New Approach ◽  
Good Thermal Stability ◽  
Temperature Solution

ABSTRACTA new approach to the synthesis of a novel silicon-containing polyester by noncarbothermal method directly from SiO2 was studied. At first, a high reactive pentacoordinate organic silicon compound (KSi(OCH2CH2O)2(OCH2CH2OH)) was prepared by the reaction of the fumed silica with ethylene glycol (EG) and KOH. Then, a novel double hydroxy tetracoordinate silicon monomer (OCH2CH2O)Si(OCH2CH2OH)(OCH2CH2OCH2CH2OH) was synthesized by the reaction of ClCH2CH2OH with reactive pentacoordinate silicon compound. Finally, a silicon-containing polyester was synthesized by low temperature solution condensation between tetracoordinate silicon compound and p-phthaloyl chloride in dimethyl sulfoxide (DMSO). The product was characterized by FTIR, TG, GPC, etc. The IR spectra of polyester exhibited a characteristic strong absorption band for ester carbonyl in the 1722.2cm-1. IR spectra also showed absorption at 1124.6cm-1 due to the O-Si-O group. TG analysis showed its good thermal stability. GPC analysis showed that the number average molecular weight of this siliconcontaining polyester was about ninety thousand.

Preparation and characterization of novel soluble polyarylates derived from 9,9-bis[4-(4-chloroformylphenoxy)phenyl]xanthene with various bisphenols

2017 ◽  
Vol 30 (10) ◽  
pp. 1203-1209
Author(s):  
Yu-Ting Zhou ◽  
Shou-Ri Sheng ◽  
Chuan-Chao Tang ◽  
Cheng Song ◽  
Zhen-Zhong Huang ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Weight Loss ◽  
Room Temperature ◽  
Phase Transfer ◽  
Average Molecular Weight ◽  
Interfacial Polycondensation ◽  
Number Average Molecular Weight ◽  
Glass Transition Temperatures ◽  
Flexible Films

A series of new polyarylates bearing cardo xanthene groups were synthesized by phase-transfer-catalyzed interfacial polycondensation of 9,9-bis[4-(4-chloroformylphenoxy)phenyl]xanthene with various bisphenols containing the isopropylidene, hexafluoroisopropylidene, 1-phenylethylidene, diphenylmethane, cyclohexane, and xanthene structures. High-molecular-weight polyarylates with number-average molecular weight and polydispersity index in the range of 30,100–35,300 and 1.82–2.17, respectively, exhibited high glass transition temperatures ranged from 226°C to 261°C, and their 10% weight loss temperatures were in the range of 421–452°C with char yields above 45% at 700°C in nitrogen. All the polyarylates were amorphous and readily soluble in organic solvents such as dichloromethane, chloroform, tetrahydrofuran, meta-cresol, pyridine, N,N-dimethylformamide, N,N-dimethylacetamide, and 1-methyl-2-pyrrolidinone at room temperature and could be cast into tough, transparent, and flexible films with tensile strengths of 85.6–108.3 MPa, elongations at break of 2–3%, and tensile moduli of 7–9 GPa.

Synthesis and characterization of poly(coumarin-urethane)s

1994 ◽  
Vol 6 (3) ◽  
pp. 257-262
Author(s):  
D I Brahmbbatt ◽  
L Jayabalan ◽  
Harshad D Patel
Keyword(s):  
Molecular Weight ◽  
Elemental Analysis ◽  
Vapour Pressure ◽  
Condensation Reaction ◽  
Average Molecular Weight ◽  
Spectral Studies ◽  
Synthesis And Characterization ◽  
Molecular Weight Determination ◽  
Number Average Molecular Weight

Poly(coumarin-urethane)s (PCUs) were prepared by the condensation reaction of 3,3'-dihydroxy-6,6'-methylcnebiscoumarin (DHMBC) with various diisocyanates. All the poly(coumarin-urethane)s were characterized by elemental analysis, IR spectral studies, number average molecular weight determination (by vapour pressure osmometry), viscosity studies and thermogravimetry.

scholarly journals Synthesis of co-poly(eugenol sulfonate)-DVB from eugenol as a major component of Syzygium aromaticum oils

2004 ◽  
Vol 2 (2) ◽  
pp. 53-57 ◽  
Author(s):  
DESI SUCI HANDAYANI ◽  
TRIANA KUSUMANINGSIH ◽  
MARIA YULI
Keyword(s):  
Molecular Weight ◽  
Melting Point ◽  
Average Molecular Weight ◽  
Nitrogen Atmosphere ◽  
Capillary Viscometer ◽  
Syzygium Aromaticum ◽  
Number Average Molecular Weight ◽  
Solid Matter ◽  
Concentrated Sulfuric Acid

Cationic co-polymerization between eugenol and divinylbenzene (DVB) (2%, 4%, 6%, 8%, 10% and 12%) with BF3O(C2H5)2 as a catalyst at room temperature without media under nitrogen atmosphere has been investigated. Co-poly (eugenol sulfonate)-DVB has been synthesized by sulfonation of co-poly(eugenol-DVB). In the sulfonation, concentrated sulfuric acid was used as the reagent and Ag2SO4 as a catalyst. Structure and characterization of co-poly (eugenol-DVB) and Co-poly(eugenol sulfonate)-DVB were analyzed by Infra Red (IR), Differential Thermal Analysis) DTA and UV-Vis. Measurement of the number-average molecular weight (Mn) of copolymer was used Ostwald capillary viscometer. The yields of co-polymerization of eugenol-DVB were solid matter and the highest result was found on a copolymer of 10% of DVB. Its melting point was 69.33oC. The increasing of mole of DVB increase the number-average molecular weight (Mn) of co-poly (eugenol sulfonate)-DVB. A copolymer of 12% of DVB gave the highest molecular weight, Mn = 2984 g/mole. Synthesized of co-poly (eugenol sulfonate)- DVB were solid matter too and the highest result was found on a copolymer of 12% of DVB. Its melting point was 95.5oC.

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