Molecular Processes during Deformation of Rubberlike Elastic Bodies

1946 ◽  
Vol 19 (3) ◽  
pp. 525-533
Author(s):  
Kurt H. Meter ◽  
A. J. A. Van Der Wyk
Keyword(s):  
Structural Data ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Chain Molecule ◽  
Molecular Processes ◽  
Chain Molecules ◽  
Elastic Bodies ◽  
Vulcanized Rubber ◽  
Chain Links ◽  
Made In

Abstract It has been demonstrated that the elastic force of a moderately vulcanized rubber kept at a constant stress is proportional to the absolute temperature, T, in the region of medium elongations. In this respect, rubber behaves somewhat like an ideal gas, the pressure of which at constant volume is also proportional to T. By applying the first and second laws of thermodynamics, it can be shown that the internal energy of isothermally stretched rubber changes as little as that of an ideal gas if its volume is increased or decreased isothermally. In both cases, however, the entropy of the system changes. Meyer, Susich, and Valkó, Karrer, and Busse explain this behavior in the following way. All rubberlike substances consist of long, flexible, chain molecules whose links are thermally mobile. In the undeformed amorphous rubber, the molecules represent randomly coiled chains ; as a result of the deformation their shape is changed, e.g., partly stretched by elongation. Thus a thermo-dynamically less probable shape is forced on them ; the thermal agitation tends to eliminate it ; because of the reciprocal felting and intertwining of the molecules, a return to the thermodynamically more probable state is possible only if the deformation can be reversed. The thermally mobile chain links are referred to as kinetic units or chain segments. In the present paper, we shall discuss the molecular processes taking place in the course of deformation, in particular such questions as: “How is the deforming force transferred to an individual chain molecule and its segment?” “How does the molecule react to this force?” After having discussed these questions, we shall examine how far the requirements are complied with for a quantitative theory such as the derivation of an equation to calculate the modulus of elasticity from structural data. We shall also discuss the attempts known to have been made in this direction so far.

scholarly journals The torsional flexibility of aliphatic chain molecules

1940 ◽  
Vol 174 (956) ◽  
pp. 137-144 ◽  
Keyword(s):  
Room Temperature ◽  
Threshold Energy ◽  
Chain Molecule ◽  
Aliphatic Chain ◽  
Chain Molecules ◽  
Distortion Effect ◽  
A Chain ◽  
Single Bonds ◽  
Long Chain ◽  
Made In

The rotation of the CH 3 groups round the single C—C bond in ethane is associated with a threshold energy of about 3000 gcal./gmol. or 2 x 10 -13 erg/mol. (Schäfer 1938; Kistiakowsky, Lacher and Strutt 1939). In an aliphatic CH 2 chain where the carbon atoms are linked together by single bonds the corresponding energy must be of the same order and is most likely rather smaller. Supposing we consider any particular C—C bond in the chain and treat the two parts at each side of this bond as rigid rotators, then their kinetic energy would be 2 x 1/2 kT which at room temperature amounts to about one-fifth of the threshold energy. It seems very likely under these circumstances that a chain molecule of say ten to twenty carbon atoms should already at room temperature show signs of distortion due to internal rotation. If this is true, then the previously observed increase of the crystal symmetry at the melting-point of paraffins (Müller 1930, 1932) and the corresponding changes of the polarization of long-chain ketones (Müller 1937, 1938) can no longer be ascribed entirely to a rotation of the molecule in the field of the surrounding molecules but must at least partly be due to this internal distortion. It is clear that a distortion of this type tends to destroy the anisotropy of the molecule and to give an apparent isotropy to the crystal. The present experiments were made in order to obtain an estimate of the magnitude of the distortion effect. It is found to be surprisingly large.

scholarly journals The Tensile Strength of Rubber and Rubber Molecule

1950 ◽  
Vol 23 (3) ◽  
pp. 581-586
Author(s):  
Chullchai Park ◽  
Usaburo Yoshida
Keyword(s):  
Tensile Strength ◽  
Low Temperature ◽  
Room Temperature ◽  
Chain Molecule ◽  
Chain Molecules ◽  
Vulcanized Rubber ◽  
A Chain

Abstract The tensile strengths of crystallized crude rubber and vulcanized rubber are remarkably different from each other at room temperature, but are found to be almost the same at the temperature of liquid air. By assuming that the tensile strength of crystallized rubber at this low temperature is entirely due to its chain molecules, the forced needed to break a chain molecule of rubber at its weakest point is estimated.

Thermoelasticity

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Equation Of State ◽  
Elastic Deformation ◽  
Additional Assumption ◽  
Polymer Network ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Constant Volume ◽  
Conformational Energy ◽  
Network Chain ◽  
Constant Deformation

The important postulate that intermolecular interactions are independent of extent of deformation leads directly to the conclusion that such interactions cannot contribute to an energy of elastic deformation ΔEel at constant volume. In the earliest theories of rubberlike elasticity, it was additionally assumed that, intramolecular contributions to ΔEel were likewise nil. In this idealization that the total ΔEel is zero, the elastic retractive force exhibited by a deformed polymer network would be entirely entropic in origin. At the molecular level, this would correspond, of course, to assuming all configurations of a network chain to be of exactly the same conformational energy and thus the average configuration to be independent of temperature. Under these circumstances, the dependence of stress on temperature is strikingly simple, as shown, for example, by the equation . . . f* = υkT/V (〈r2〉i/〈r2〉0)(α – α-2) . . . . . . (9.1) . . . that characterizes a polymer network in elongation where, it should be recalled, 〈r2〉i3/2 is proportional to the volume of the network. This additional assumption that 〈r2〉0 is independent of temperature would lead to the prediction that the elastic stress determined at constant volume and elongation α is directly proportional to the absolute temperature. Such network chains would be akin to the particles of an ideal gas, which would obey the equation of state p = nRT(1/V) and thus exhibit a pressure at constant deformation (1/V) likewise directly proportional to the temperature.

Molecular processes during deformation of rubberlike elastic bodies

1946 ◽  
Vol 1 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Kurt H. Meyer ◽  
A. J. A. Van Der Wyk
Keyword(s):  
Molecular Processes ◽  
Elastic Bodies

Rubber Elasticity and Gas Elasticity

1939 ◽  
Vol 12 (2) ◽  
pp. 124-129
Author(s):  
H. Mark
Keyword(s):  
Polyvinyl Alcohol ◽  
Room Temperature ◽  
Absolute Temperature ◽  
Rubber Elasticity ◽  
Chain Molecules ◽  
Internal Mobility ◽  
Higher Temperature ◽  
Coefficient Of Elasticity ◽  
Polyacrylic Ester ◽  
High Degree

Abstract All substances which are composed of long mobile chains show one peculiar property, highly reversible elasticity. Even though the range of temperature of this property may be notably variable (in the case of polyvinyl alcohol and rubber at about room temperature, in the case of polystyrene, sulfur, or Thiokol only at a higher temperature) still it is to be noted that for rubber-like elasticity the presence of long flexible chains is an indispensable factor. Thus, typical rubber elasticity occurs in polyvinyl alcohol (Vinarol), polybutadiene (Buna), polymethyl-butadiene (methyl rubber), polyacrylic ester and also in its mixed polymerisate with vinyl chloride. This type of elasticity occurs also in sinew fibrin and muscle fibrin, in polychlorobutadiene (Neoprene, Sovprene), in polyethylene sulfide (Thiokol, Baerite), polyphosphornitrile chloride and finally in vulcanized oils (factice) and also in elastic sulfur. In the cases so far examined (natural rubber, Buna, methyl rubber), it has been found that the coefficient of elasticity increases proportionally to the absolute temperature, and that during the stretching heat is evolved. This behavior is contrary to that of normal elastic materials, steel, quartz, glass, etc. It is striking that the substances which have this property of highly reversible (rubber-like) stretching are widely different chemically. This tempts one to ascribe that property to the similarity of their construction. For example, all the substances mentioned consist of long chain-molecules, which display a high degree of internal mobility. The number of members in these chains varies from 102 to 104 and their mobility is due to the kind of linkage between the members, mostly simple C—C bonds.

Permanent Set in Vulcanized Rubber

1949 ◽  
Vol 22 (4) ◽  
pp. 1036-1044 ◽  
Author(s):  
L. Mullins
Keyword(s):  
Plastic Flow ◽  
Room Temperature ◽  
Elastic Recovery ◽  
The Other ◽  
Initial Length ◽  
Chain Molecules ◽  
Permanent Set ◽  
Vulcanized Rubber ◽  
Rate Of Recovery ◽  
Long Chain

Abstract The residual extension which remains after a sample of rubber has been stretched for some period, then released and allowed to recover, is popularly called permanent set. This set, however, is far from being permanent since it continuously decreases with the period of recovery; furthermore, after the rate of recovery has become exceedingly slow and is no longer readily observable, an increase in temperature will usually result in a sharp increase in the rate of recovery. It has been usual to identify this set with irreversible plastic flow, but it will be immediately evident that this can rarely be justified for, owing to incomplete high-elastic recovery, the measured value of set is a combination of both plastic flow and high-elastic deformation which has not completely recovered. Thus before any attempt is made to discuss the interpretation of the results of set tests, a study must be made of the significance of set. Treloar has investigated this phenomenon in raw natural rubber and has shown that entanglements or cohesional linkages may form while the rubber is stretched, and these oppose recovery; further, although van der Waals forces between the long-chain molecules largely control the rate and the amount of recovery, the crystallization of rubber produced by stretching may profoundly influence the set. On the other hand Tobolsky has studied the set which results from stretching rubber vulcanizates at high temperatures ; in such cases the amount of set is controlled by two processes which take place while the rubber is stretched; one of these involves the oxidative breaking of network chains, the other the oxidative cross-linking of network chains. Although these ideas are well founded, they do not provide a completely satisfactory basis for the understanding of set, and the purpose of this work is to extend these ideas and to explain the significance of the results of normal set tests ; in these tests rubber samples were extended at room temperatures to moderate elongations for relatively short periods of time. Most of the tests performed in this investigation were made on dumbbell shaped samples, which were extended by 200 per cent of their initial length for fifteen minutes at room temperature and then allowed to recover for one hour at room temperature; the residual extension was then noted and expressed as a percentage of the initial length. These tests will be referred to as normal set tests. In some tests various periods and temperatures of extension and recovery were used.

Determination of the Resistance of Vulcanized Rubber to Tearing

1938 ◽  
Vol 11 (4) ◽  
pp. 689-705
Author(s):  
D. J. van Wijk
Keyword(s):  
Vulcanized Rubber ◽  
Complete Survey ◽  
Side Walls ◽  
First Cause ◽  
Made In ◽  
Tear Resistance

Abstract By the resistance to tearing of a material is meant the resistance shown by the material, while under tension, to tearing completely apart after a split has been made in the surface by any means whatsoever. Without question, the destruction of rubber articles can in many cases be traced to tearing. The initial tears can be regarded as the result of a splitting of the inelastic oxidized skin or of injury to the surface. Tears on the side walls of a tire, for example, can be attributed to the first cause; the wear on the tread is attributable to the second cause mentioned above. Resistance to tearing should therefore be regarded as one of the most important properties of rubber. The numerous and widely different methods which have been proposed and used for determining resistance to tearing are proof of this. A complete survey of the literature to 1932 was published by Lefcaditis and Cotton. These authors described about twelve different methods for determining resistance to tearing, proposed a modified form of the method of Heidensohn, and determined the tear-resistance of various mixtures by this method. Subsequently, Lefcaditis studied this method further, and determined the effect of fillers and of mastication on resistance to tearing.

Isothermal and Adiabatic Stress-Strain Curves of Vulcanized Rubber

1939 ◽  
Vol 12 (1) ◽  
pp. 64-70 ◽  
Author(s):  
V. Hauk ◽  
W. Neumann
Keyword(s):  
Chemical Nature ◽  
Absolute Temperature ◽  
Strain Diagram ◽  
Stress Strain ◽  
Isothermal Conditions ◽  
Adiabatic Conditions ◽  
Vulcanized Rubber ◽  
The Subject ◽  
The Difference ◽  
Thermodynamic Interpretation

Abstract The stress-strain diagram of rubber has been the subject of a large number of investigations, including those of Röntgen, Gough, and Joule in the nineteenth century, those on isothermal phenomena by Meyer and Ferri, and Wiegand and Snyder, and most recently those on adiabatic phenomena of Ornstein, Eymers, and Wouda. The investigations of Meyer and Ferri are concerned chiefly with the dependence of the stress-strain phenomena on the temperature, and they confirm experimentally the hypothesis that within a certain range of temperature and with highly vulcanized samples, the stress is proportional to the absolute temperature, i. e., S=aT+b. At lower states of vulcanization this proportionality does not hold true. The work of Ornstein and his collaborators, which is frequently cited in the literature, is concerned with the phenomena which take place when raw rubber and weakly vulcanized rubber are stretched adiabatically; that of Wiegand and Snyder is concerned chiefly with a thermodynamic interpretation of stress-strain curves obtained experimentally. Now in spite of the fact that stress-strain curves of rubber have been determined so frequently, particularly under isothermal conditions, these measurements are for the most part of limited value, since the chemical nature of the types of rubber employed is not described definitely. Then again in most cases little attention was paid to the difference between isothermal and adiabatic stretching. In view of these facts, it seemed desirable to throw further light on the problem by obtaining stress-strain curves of one particular well-defined material. The object of the present work was then: 1. To obtain true isothermal stress-strain curves as a function of the degree of vulcanization and as a function of the temperature, and thus to study stresses as a function of temperature. 2. To obtain data on the same vulcanizates under adiabatic conditions. 3. To compare the stress-strain results under isothermal conditions with those under adiabatic conditions.

An Overview of Ovarian Cancer: Molecular Processes Involved and Devel-opment of Target-based Chemotherapeutics

2020 ◽  
Vol 20 ◽  
Author(s):  
Basheerulla Shaik ◽  
Tabassum Zafar ◽  
Krishnan Balasubramanian ◽  
Satya P. Gupta
Keyword(s):  
Ovarian Cancer ◽  
Drug Resistance ◽  
Western World ◽  
Advanced Stage ◽  
Molecular Processes ◽  
Common Cause ◽  
The Past ◽  
Theoretical Approaches ◽  
Statistical Studies ◽  
Made In

: Ovarian cancer is one of the leading gynecologic diseases with a high mortality rate worldwide. Current statistical studies on cancer reveals that over the past two decades the fifth most common cause of death related to cancer in females of the western world is this ovarian cancer. In spite of significant strides made in genomics, proteomics and radiomics, there has been little progress in transitioning these research advances into effective clinical administration of ovarian cancer. Consequently, researchers have diverted their attention to find various molecular processes involved in the development of this cancer and how these processes can be exploited to develop potential chemotherapeutics to treat this cancer. The present review gives an overview of these studies which may update the researchers where we stand and where to go further. Un-fortunate situation with ovarian cancer that still exists is that most patients with it do not show any symptoms until the disease has moved to an advanced stage. Undoubtedly, several targets-based drugs have been developed to treat it, but drug-resistance and the recurrence of this disease is still a problem. For the development of potential chemotherapeutics for ovarian cancer, however, some theoretical approaches have also been applied. A description of such methods and their success in this direction is also covered in this review.

scholarly journals The emission constants of metals in the near infra-red

1933 ◽  
Vol 142 (847) ◽  
pp. 466-490 ◽  
Keyword(s):  
Cross Section ◽  
Specific Resistance ◽  
Wave Length ◽  
Electromagnetic Theory ◽  
Absolute Temperature ◽  
Restricted Range ◽  
Electron Theory ◽  
Long Wave ◽  
Infra Red ◽  
Made In

In the far infra-red, the reflecting power, R, of a metal at a wave-length, λ, is connected with its specific resistance, ρ, by the Hagen-Rubens relation, 1 - R = k √ρ/λ, where k is a constant with the value 0·365 when λ is measured in μ., and ρ is the resistance of a rod of the metal 1 metre in length and 1 sq. mm. in cross-section. The relation has only a restricted range of validity: for it is based theoretically on the electromagnetic theory, which does not embody the modern conceptions of the electron theory; and a restriction for a lower wave-length limit is made in the deduction of the formula itself. Hagen and Rubens have subjected the formula to a rigid test by a series of emission measurements. At wave-lengths of 25·5 and 8·85 μ, the calculated and observed emissivities agreed usually to within about 10%. Further experiments at the same wave-lengths showed, moreover, that the emissivity changed with temperature in the manner demanded by the relation. It follows that the emissivity of a metal at sufficiently long wave-lengths is roughly proportional to the square-root of its absolute temperature.

Sign in / Sign up

Export Citation Format

Share Document