Use of χ As a Function of Volume Fraction of Rubber to Determine Crosslink Density by Swelling

2003 ◽  
Vol 76 (4) ◽  
pp. 832-845 ◽  
Author(s):  
William L. Hergenrother ◽  
Ashley S. Hilton
Keyword(s):  
Carbon Black ◽  
Metal Oxides ◽  
13C Nmr ◽  
Crosslink Density ◽  
Volume Fraction ◽  
Good Measure ◽  
Noticeable Effect ◽  
Wide Range ◽  
The Relationship

Abstract A technique is described allowing a relatively simple determination of χ as a function of vr from swelling in heptane. A good measure of the true νe of the cured elastomer at all values of vr was demonstrated by substituting this relationship for χ in the Flory-Rehner (F-R) equation. The relationship was established over a wide range of vr values by using samples that had the νe of the cured elastomer determined by tensile retraction (TR). Applying this function to samples treated using the thiol probe method of Campbell gave an improved measure of the types of crosslinks present in sulfur-cured stocks. An identical equation describing χ as a function of vr in heptane was obtained with NR, EPDM and SBR containing up to a 0.31 volume fraction of carbon black (CB) and other fillers. The presence of up to 10 % of clay, talc, silica, resins or metal oxides in the CB had no noticeable effect on the relationship measured. However, when the filler contained about 50% silica a distinctly different slope in the relationship was found. The percent S1, S2 and Sx distribution measured was contrasted between measurements made by 13C NMR, swelling with χ = constant or χ as a function of vr.

Effect and Detection of Loose Chain Ends in Crosslinked Polyurethane Elastomers

1971 ◽  
Vol 44 (1) ◽  
pp. 152-165 ◽  
Author(s):  
A. E. Oberth
Keyword(s):  
Crosslink Density ◽  
Volume Fraction ◽  
Present Theory ◽  
Swelling Ratio ◽  
Polyurethane Elastomers ◽  
Equilibrium Volume ◽  
Equilibrium Swelling ◽  
Volume Swelling

Abstract The effect of loose chain ends on tensile properties and equilibrium swelling of crosslinked polyurethane rubbers is studied. As in plasticized elastomers, tensile strength and elastic modulus are reduced approximately by a factor (1−νE,P)2, where νE,P is the volume fraction of loose chain ends, plasticizer, or both. This effect is much larger than predicted by present theory. Also the equilibrium volume swelling ratio, V0/V, of rubbers having terminal chains or an equal volume of plasticizer is the same, provided they do not differ in crosslink density. However, the volume fraction of “network rubber” in the equilibrium swollen specimen, ν2, differs owing to the non-extractability of terminal chains. On this basis a method is proposed which allows experimental determination of the volume fraction of loose ends. Elastomers abounding in loose chain ends show markedly less long term stress relaxation. This effect is not clearly understood but is useful to detect the presence of non load-bearing network.

Carbon Black. I—A Study of Its Volatile Constituents

1928 ◽  
Vol 1 (3) ◽  
pp. 485-497 ◽  
Author(s):  
C. R. Johnson
Keyword(s):  
Carbon Black ◽  
Volatile Matter ◽  
Original Sample ◽  
Missing Information ◽  
Volatile Constituents ◽  
Vulcanized Rubber ◽  
Rates Of Evolution ◽  
Temperature And Pressure ◽  
The Relationship

Abstract The rates of evolution of gas from carbon black with variation of time, temperature, and pressure have been determined. Complete analyses have been made of five types of carbon black, which involve an organic combustion of the original sample, an organic combustion of the sample after the gases have been removed, a determination of the loss in weight represented by the gases removed, analyses of the gases removed, and finally a complete accounting, or balance, of the carbon in the steps considered. In an attempt to supply some missing information not revealed by the foregoing, some special gas analyses under varying conditions were made. The relationship between the amount and composition of volatile matter evolved from carbon blacks and the properties imparted to vulcanized rubber when compounded with these blacks has been studied.

Structural Characterization of Filled Vulcanizates Part 1. Determination of the Concentration of Chemical Crosslinks in Natural Rubber Vulcanizates Containing High Abrasion Furnace Black

1967 ◽  
Vol 40 (3) ◽  
pp. 866-882 ◽  
Author(s):  
M. Porter
Keyword(s):  
Carbon Black ◽  
Natural Rubber ◽  
Volume Fraction ◽  
Exponential Relationship ◽  
Furnace Black ◽  
Simple Linear Relationship ◽  
Chemical Crosslinks ◽  
Natural Rubber Vulcanizates

Abstract The degree to which HAF black restricts the swelling of natural rubber vulcanizates in n-decane has been determined using a vulcanizing system in which the stoichiometry of crosslinking is unaffected by the carbon black. The dependence of the degree of restriction, as measured by the ratio of the volume fractions of rubber in the filled and unfilled vulcanizates swollen to equilibrium, on the concentration of carbon black follows an exponential relationship previously proposed by Lorenz and Parks. This is found to be equivalent to a simple linear relationship between the apparent and actual crosslink concentrations: napparent/nactual=1+Kϕ, where K is a constant characteristic of the filler and φ is its volume fraction in the vulcanizate. The relation has been used to determine actual crosslink concentrations in filled natural rubber vulcanizates. HAF black is found to cause increases of up to 25 per cent in the yield of polymer to polymer crosslinks in conventional sulfur vulcanizing systems, accompanied by changes in rate of cure and of crosslink reversion. All these are small compared with the effect of the filler on many physical properties.

Experiments on the Determination of the Activity of Carbon Black by Its Power of Adsorbing Carbon Tetrachloride Vapor

1940 ◽  
Vol 13 (2) ◽  
pp. 437-440
Author(s):  
T. Patryn
Keyword(s):  
Aqueous Solution ◽  
Carbon Tetrachloride ◽  
Carbon Black ◽  
Reliable Method ◽  
High Ratio ◽  
Point Of View ◽  
Adsorptive Capacity ◽  
The Relationship ◽  
Very High

Abstract On the basis that a material like carbon black must, because of its very high ratio of surface area to volume, possess very high adsorptive capacity, several investigators have attempted to establish the relationship between the adsorptive capacity of carbon black and its activity in rubber. Spear and Moore used aqueous solutions of malachite green, Victoria blue and hexamethylenetetramine; Beaver and Keller used iodine in aqueous potassium iodide; Goodwin and Park used iodine in carbon tetrachloride and also an aqueous solution of methylene blue; Carson and Sebrell used iodine, benzoic acid, mercaptobenzothiazole and diphenylguanidine. All these workers tested various types of carbon black. If one examines critically the data of these several investigators from the point of view of the relation between the adsorptive capacity of a carbon black and its activity in rubber, it will be evident that the investigations do not lead to any reliable method whereby the behavior of carbon black in rubber can be judged by its adsorptive capacity.

scholarly journals CHARACTERIZATION OF THE MULLINS EFFECT OF CARBON-BLACK FILLED RUBBERS

2011 ◽  
Vol 84 (3) ◽  
pp. 402-414 ◽  
Author(s):  
Yannick Merckel ◽  
Julie Diani ◽  
Mathias Brieu ◽  
Pierre Gilormini ◽  
Julien Caillard
Keyword(s):  
Carbon Black ◽  
Crosslink Density ◽  
Volume Fraction ◽  
Damage Parameter ◽  
Hencky Strain ◽  
Filler Volume Fraction ◽  
Filled Rubbers ◽  
Styrene Butadiene ◽  
Linear Expression

Abstract Several carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method or the tangent modulus at zero stress. The proposed parameter is used to study the effects of crosslink density and filler amount on the Mullins softening. The latter is shown to remain unaffected by a change of crosslink density and to increase with an increase of filler amount. The damage parameter exhibits mere linear dependences on the maximum Hencky strain applied and on the filler volume fraction. A simple linear expression is given finally to predict the Mullins softening of filled rubbers. The parameter also provides an objective analysis for the Mullins softening that supports comments on a better understanding of this effect.

scholarly journals Determination of the Degree of Homogeneity for n Ge Crystals by Measurements of Magnetoresistance in Classically Weak Magnetic Fields

2015 ◽  
Vol 16 (3) ◽  
pp. 469-474
Author(s):  
G. P. Gaidar ◽  
P. I. Baranskii
Keyword(s):  
Spatial Distribution ◽  
Magnetic Fields ◽  
Crystallographic Orientation ◽  
Qualitative Assessment ◽  
Weak Magnetic Fields ◽  
Wide Range ◽  
The Relationship ◽  
Range Of Values ◽  
Degree Of Heterogeneity

In a wide range of values of the resistivity 0.0212 £ r £ 35 Ohm×cm for n‑Ge crystals with known crystallographic orientation the ratio , which was predicted by the theory, was experimentally confirmed. The experimentally measured deviations from the relationship , which are associated with the heterogeneity of the crystals, it is proposed to use for qualitative assessment of the degree of heterogeneity in the spatial distribution of dopants in the samples.

A numerical analysis of relationship between ductility and nucleation and critical void volume fraction parameters of Gurson–Tvergaard–Needleman model

2013 ◽  
Vol 227 (11) ◽  
pp. 2634-2646 ◽  
Author(s):  
M Hadj Miloud ◽  
A Imad ◽  
N Benseddiq ◽  
B Bachir Bouiadjra ◽  
A Bounif ◽  
...  
Keyword(s):  
Fracture Strain ◽  
Volume Fraction ◽  
Void Volume ◽  
Critical Volume Fraction ◽  
Experimental Parameters ◽  
Three Stages ◽  
Bar Test ◽  
The Relationship ◽  
Critical Void

Gurson–Tvergaard–Needleman model is widely used to describe the three stages of ductile tearing: nucleation, growth and the coalescence of micro-voids. The aim of this article is to study the relationship between volume fraction of voids and the fracture strain ɛf. The effects of the volume fraction of nucleation, fN, and the critical volume fraction, fc, were analysed. These parameters play crucial roles in the process of ductile damage. A phenomenological analysis is carried out to study the relationship between the different void volume parameters and the fracture strain ɛf. A method is proposed for the determination of fN and fc, knowing the experimental fracture strain ɛf. The experimental parameters are extracted from the load–diametric contraction curve of an axisymmetric notched tensile bar test AN2.

Determination of Polymer Composition of Rubber Vulcanizates

1971 ◽  
Vol 44 (5) ◽  
pp. 1278-1281
Author(s):  
D. W. Carlson ◽  
H. C. Ransaw ◽  
A. G. Altenau
Keyword(s):  
Carbon Black ◽  
Polymer Composition ◽  
Infrared Analysis ◽  
Pyrolysis Products ◽  
Nmr Spectrum ◽  
Quantitative Measurements ◽  
Infrared Studies ◽  
The One ◽  
The Relationship

Abstract Various methods exist for the quantitative determination of the polymer composition in vulcanized stocks. These methods consist of dissolving the vulcanizates in boiling o-dichlorobenzene, removal of the carbon black by filtration, and then infrared determination of the polymer. Pyrolysis of the stock followed by infrared analysis of the products has also been used. This technique had the disadvantages of requiring an analysis of products other than the original polymer or polymers. The infrared calibration based on polymers would no longer be valid. There may also be some uncertainty about changes in the relationship between the original microstructure and the pyrolysis products. Other infrared studies have been made but no quantitative measurements were reported. Recently an NMR method was published for vulcanizate analysis. The method consisted of dissolving the vulcanizate in hexachlorobutadiene, recording the NMR spectrum of the solution, and determining the total amount of butadiene, styrene, and natural rubber from the spectrum. Good results were obtained on a variety of vulcanizates. The one disadvantage of the method was that only a limited amount of microstructure data could be obtained. This was due to the lack of resolution of the 60-megacycle NMR. We have now developed a technique which allows enough of the rubber to dissolve in carbon disulfide for infrared analysis. This solution is free of carbon black. Infrared analysis provides microstructure data on the butadiene and/or isoprene portions as well as the total styrene content.

YIELD STRESS OF FRACTAL AGGREGATES

Fractals ◽  
2015 ◽  
Vol 23 (03) ◽  
pp. 1550028 ◽  
Author(s):  
YUE XI ◽  
JINJIAN CHEN ◽  
YONGFU XU ◽  
FEIFEI CHU ◽  
CHUANXIN LIU
Keyword(s):  
Fractal Dimension ◽  
Yield Stress ◽  
Power Law ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Published Data ◽  
Proposed Model ◽  
Wide Range ◽  
The Relationship ◽  
Theory And Experiments

A model for the yield stress of aggregates is presented that incorporates fractal dimension taking into account the solid volume fraction and the aggregate diameter. The model shows the yield stress (σy) of aggregates increases with the solid volume fraction (ϕs) as a power law, and is given by [Formula: see text], where the exponent (m) is related to fractal dimension (D), and σy0 is a referenced parameter. The relationship between exponent (m) and fractal dimension is validated by published data of aggregates and represents the measured data very well, over a wide range of the solid volume fractions. The referenced parameter (σy0) is calibrated from experiments of yield stress using power law fittings. The agreement between theory and experiments supports the idea that yielding is ultimately caused by the rupture of a few interparticle bonds within aggregates. In addition, the proposed model for the yield stress of aggregates is found to match better with experiments by comparing with all models in literature.

Microwave Diagnosis of Carbon Black Rubber Compounds and Porosity Estimation in Composites

1994 ◽  
Vol 347 ◽  
Author(s):  
Reza Zoughi ◽  
S. I. Ganchev ◽  
J. Bhattacharyya ◽  
S. Gray ◽  
D. Radford
Keyword(s):  
Dielectric Properties ◽  
Carbon Black ◽  
Volume Fraction ◽  
Wide Frequency Range ◽  
Model Material ◽  
Volume Percentage ◽  
Measurement Analysis ◽  
Rubber Compounds ◽  
Wide Range ◽  
5 Ghz

ABSTRACTThe results of an in depth study of the dielectric properties of various rubber compounds at different microwave frequencies are discussed. Subsequently, the influence of carbon black volume percentage on the dielectric properties of rubber is studied in a wide frequency range (5 -24 GHz). The results show that the real and imaginary parts of rubber dielectric constant increase as a function of increasing carbon black percentage. Frequencies around 5 GHz show more sensitivity to small changes in the carbon volume content. The presence of curatives in uncured rubber samples is detected, which is an indication of the sensitivity of microwaves to the chemical reaction triggered by these curatives. Similar approach is used to measure the air content in specially prepared model material (plastic microbaloon-filled epoxy) samples with varying degrees of uniformly distributed air inclusion. The results of these measurements for a wide range of frequencies is also reported. Measurement analysis resulted in detecting variation in the air volume fraction of around 1.5%. The results confirm the utility of microwave NDE techniques for local porosity detection and evaluation in dielectric composites.

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