摘要:

AbstractThe molecular mechanism of stress relaxation in a linear polymeric material is conceived of as a process of diffusion in phase space of molecular configuration. The analysis is an extension of the Rouse theory of linear visco‐elasticity to finite, three‐dimensional deformations. A molecule, either open end or crosslinked, is treated as a chain of submolecules, each just long enough that its net length follows approximately the Gaussian distribution law. Variables are separated by transformation to normal coordinates, and diffusion equations are obtained of the form\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\partial \rho _n}}{{\partial t}} = - D_n \frac{\partial}{{\partial u_{jn}}}\left({\frac{{\partial \rho _n}}{{\partial u_{jn}}} + 2bu_n \rho _n} \right) $\end{document}where ρnis the density in configuration space of then‐mode of molecular configuration, andDnis the diffusion constant characteristic of the mode. An exact solution exists in the form\documentclass{article}\pagestyle{empty}\begin{document}$ \rho _n = \frac{1}{{\beta _n}}\left({\frac{b}{\pi}} \right)^{1/2} \exp \left\{{- bu_n^2 /\beta _n^2} \right\} $\end{document}\documentclass{article}\pagestyle{empty}\begin{document}$ \beta _n^2 = 1 + (\alpha ^2 - 1)\exp \left\{{- bD_n t} \right\} $\end{document}Here βn− 1 is the measure of the recoverable strain in theundirection of then‐mode, the instantaneous value of the corresponding partial stress being proportional to βn2− 1. Any partial stress obeys the Boltzmann superposition law, but the total stress does not. The transform equations connecting such pairs of functions as creep and relaxation in the linear theory are here not valid; but, as in the linear theory, in a given case of a single imposed strain the stresses are expressed in terms of a distribution function of relaxation times. Expressions are obtained for the tangential and normal stressed in continuous simple shear at a finite rate. To explain non‐Newtonian viscosity it is necessary to postulate either that the intertangling of the molecules is reduced or that rheological flow units develop in the material which are larger than the indi

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412741

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractIt is well known that the modulus and equilibrium swellling of long‐chain polymers are both related to degree of crosslinking. Modulus theory normally assumes that chain segments are completely free at all points except the junctions of chains (crosslinks). In practice, however, there are trapped entanglements and other steric restrictions on the freedom of chains in highly crosslinked polymers. In addition, real polymers may not conform entirely with the Gaussian distributions assumed by elasticity theory. The present paper discusses these effects, including a steric effect whose contribution to modulus is dependent on chain flexibility and on linkage concentration. Similar but smaller modifications appear necessary in the case of equilibrium swelling in solvent. The molecular weight of the polymer is taken into account by an adaption of Flory's theory, and a simple correction is proposed to take account of entanglements. The relation between modulus and equilibrium swelling is considered for natural rubber when vulcanized by peroxides or by sulfur, and an assessment is made of the relative effects of steric hindrance on modulus and equilibrium swelling. This is converted to an absolute estimate of steric effects by calculations based on Moore and Watson's chemical determinatios of crosslinking. The equations derived have a convenient form in which there is a parameter ω to take account of steric effects. The contribution which this makes to the modlulus is not constant because it is determined by the magnitude of ω relative to the molecular weightMcbetween crosslinks. The reciprocal of ω is taken to be a measure of chain flexibility. By measurements of modulus and equilibrium swelling over a wide range of crosslinking a measure of the molecular flexibility can be obtained, together with an estimate of the solubility parameter μ for the polymer and solvent. For peroxide cures it is found thatd that μ is roughly constant when toluene is the solvent, but for sulfor vulcanizates this appears to be true only at low states of cure. The evidence suggests that μ changes from 0.42 to 0.45 when a high proportion of sulfur is combined with the rubber. Therefore peroxide cures should be used for comparing the chain flexibility of polymers. For sulfur vulcanizates these changes in μ make swollen modulus the most reliable methode of measuring crosslinking. It is estimated that eight atoms of sulfur are combined for every crosslink that is formed in the early stages of vulcanization. The work described should assist studies of curative agents and of the difference between

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412742

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractGraft copolymers have been prepared from natural rubber latex and methyl methacrylate using visible, ultraviolet, and γ‐radiation. The influence of monomer concentration, temperature, radiation intensity, and, in the case of photoinitiation, photosensitizer concentration, on polymerization rates and molecular weights have been studied. The proportion of graft polymer is very high initially but falls with conversion and with increase in monomer concentration. Photoinitiated grafting depends on the photosensitizer and on temperature, but with γ‐initiation the fraction grafted is independent of temperature. In the latter case the high proportion of graft cannot be explained in terms ofthe relative G values and concentrations of monomer and rubber. The fall‐off in proportion of graft with conversion is thought to result from microscopic heterogeneous regions formed during polymerization, which are believed to increase in size as polymerization proceeds, thereby reducing further the possibility of grafting. Degradation of previously grafted polymer by prolonged irradiation is not of consequence in this case. Molecular weights of grafted and ungrafted polymers are very similar, except at low monomer concentrations, and a marked feature of this system is their constancy with change in all reaction conditions other than monomer concentration. Estimates of the utilization of radiation energy have been made and it is concluded that on an energy basis γ and photoinitiated reactions are of comparable ef

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412743

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractThe production of crosslinks and of sites for grafting in solid high polymers can be achieved by hydrogen abstraction. This hydrogen abstraction reaction can be carried out by means of far ultraviolet light (200–300 mμ). The rate of the reaction is tremendously increased if certain sensitizers are incorporated into the plastic. A comparative study of various aromatic carbonyl compounds has been made to determine which are effective sensitizers. Crosslinking is accompanied by a photolysis of the sensitizer. Sensitizers which are effective for crosslinking are also effective for grafting. For the same degree of crosslinking the high density polyethylenes have greater strength at 150°C. than have the low density polyethylenes. The ultraviolet method differs from the ionizing radiation method in that the dosages required for crosslinking by the former method are the same regardless of the degree of crystallinity of the polyethylene. A further difference is that whereas with the ionizing radiation method extensive Degradation occurs with certain polymers, in the ultraviolet method crosslinking is the predominant react

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412744

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractThe catalytic and autocatalytic hydroperoxidations of the surface of filaments and laminae of isotactic and stereoblock poly‐α‐olefins have been studied. The peroxidation of atactic and stereoblock polymers in solution has also been examined. Peroxidized polymers have been used as radical initiators in the polymerization of vinyl monomers to achieve their grafting on poly‐α‐olefin chains. Some properties of these graft polymers, e.g., antishock properties of polystyrenes grafted on poly‐α‐butene, have

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412745

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractThe mastication of polymers brought into a rubbery state by admixture with monomers causes polymerization of the monomer. The reaction shows dependence on rate of shearing, temperature, and monomer concentration expected for a mechanism of mechanical rupture of the polymer to free radicals which initiate polymerization. Fractional precipitation methods for separating block polymers of polymethyl methacrylatepolystyrene from the homopolymers are applied to the products after masticating both initial polymer‐monomer combinations. The products of reaction indicate that the block polymer does not contain many segments of each polymer. When the two polymers are present either as free or block polymers, the polymethyl methacrylate is preferentially ruptured to form initiation site

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412746

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractThe orientation of the crystals and the amorphouse regions of polyethylene occurring during stretching has been studied using the combined techniques of x‐ray diffraction, infrared dichroism, and birefringence. The state of orientation is expressed in terms of the position of a point on a triangular “orientation diagram.” It is found that the a and b crystallographic axes orient differently. The degree of crystalline orientation is greater at a given elongation for a sample oflower degree of crystallinity than higher. An appreciable amount of amorphous orientation occurs, and appears greater in the more crystalline samples. Orientation oflarger crystalline aggregates has been studied using the light scattering technique and is found to parrallel that of the crystallites. A model consistent with these various types of experimental studies is pro

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412747

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractBei der Kristallisation von Niederdruckpolyäthylen aus Lösung in dünnsten Filmenerhält man lamellen‐bzw.fibrillenartige Einkristalle, in denen nach Elektronenbeugungsmessungen die Molekülketten senkrecht zur Lamellenbene bzw. zur Längsrichtung der Fibrillen stehen. Die Moleküle müssen also gefaltet sein. Bei sehr verschidener Wachstumsgeschwindigkeit der kristallographischen Ebenen entarted die Lamellen zu stäbchenartigen Fibrillen. Auch bei der Kristallisation von Lösungs‐ und Schmelzfilmen (bulk‐material) kann die Lamellenstruktur nachgewiesen werden. Lamellen bzw. Fibrillien stellen also eine unter sehr verschiedenen Kristallisationsbedingungen entstehende morphologische Grundform dar. Elektronenoptisch und genetisch sind sie Einkristalle. Zur Erklärung der Molekülfaltung sowie der Entstehung von Lamellen konstanter Dicke wird ein bestimmter Keimbildungsmechanismus diskutiert. Bei der Kristallisation von Polyurethan aus dem Glaszustande zeigen die elektronenmikroskopischen Versuche, dass auch hier morphologische Grundformen entstehen. Ihre Ausbildung kann auch im Röntgenkleinwinkeldiagramm verfolgt werden. Amorphes, glasklares Terylen zeigt schon beim Tempern bei 110° Sphärolithe, deren Wachstum lichtmikroskopisch beobachtbar ist. Die Molekülketten müssen also bereits weits unterhalb des Schmelzbereiches eine viel grössere Kettenbeweglichkeit besitzen, als bisher angenommen. Genügend teif abgeschrecktes Polyurethan ist im Elektronenmikroskop strukturlos und zeight auch keinerlei Kleinwinkelstreuung. Auch hier zeight sich zwischen der Ausbildung morphologischer Strukturen und den scharfen Röntgenkleinwinkelinterferenzen ein enger Zusammenhang. Das alte Bild des Kristallin‐amorphen Gefüges vermag die hier geschilderten Ers

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412748

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractAlthough crystallization under stress occurs in nearly all synthetic fiber making, giving fine fibrillar fiber structures, it has been relatively little studied; and the literature, centered mainly round coarser spherulitic crystallization, does not take us very far in understanding it. However, a simple experiment shows that it is very important. If a filament of amorphous polyethylene terephthalate is stretched over a hot plate between two roller moving at different speeds, stretching can take place either without crystalization at low tension, or with considerable crystallization at high tension, at the same temperature and speed, simply according to the method of starting the machine. A model visco‐elastic theory based on Maxwell's equation is, therefore, developed to describe this behaviour using the simplest possible assumptions. Further experiments then show that this simple and partly empirical theory fits the observed behaviour of polyethylene terephthalate reasonably well, and the simple assumptions made, therefore, seem to give a first approximation to the course of strain induced crystallization. They correspond with the idea of exremely rapid crystallization from a nucleus to a small structural unit, the density of nucleation being dependent on the stress. Parallel work on the streching of spherulitic structures is then mentioned, and it is finally suggested that stress induction and rapid growth to a small structural unit may be common to both spherulitic crystallization under internal stresses, and fibrillar crystallization under an externally applied stres

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412749

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY

摘要:

AbstractIn the course of our investigations into the relation between draw ratio (i.e., the permanent extension ratio imparted during manufacture) and birefringence of man‐made fibers, we found that the relation published by Kordeset al.for Perlon (nylon 6) has equivalents for several different fibers that may be considered as special cases of one general empirical relation. This empirical relation, expressed in differential form, reads\documentclass{article}\pagestyle{empty}\begin{document}$ d(\Delta n)/d(\ln \lambda) = m + p\Delta n $\end{document}where Δn= specific birefringence of the fiber, In λ = the natural logarithm of the permanent extension ratio, reckoned from the isotropic state, andmandpare constants. The constantmcan assume positive or negative values, according to the sign of the birefringence of the fiber. The values found forpappear also to be characteristic of the polymer. It also appears that the experimental results can be described within experimental error by taking forpmultiples of 1/2. This opens the possibility for a comparatively simple way of plotting the results. Thus, apart from the valuep= −1/2 corresponding to Kordes' relation, forpthe following values, which are multiples of 1/2,viz., −1, −1/2, +1/2, +1, have been found by us (e.g., respectively for nylon 66, polyethylene, polyethylene terephthalate, viscose rayon). These seem to be preferred values ofp. So far no case has been found of the valuesp= 0 andp>±1. As yet there is no theory forthcoming to explain the empirical relation in its general form nor the apparent rule of preference for the above‐mentione

ISSN:0022-3832    

DOI:10.1002/pol.1959.1203412750

出版商:Interscience Publishers, Inc.    

年代:1959

数据来源: WILEY