Optical and calorimetric analysis of stress-induced crystallization in natural rubber networks

Stress-induced crystallization of natural rubber networks is studied. The analysis is carried out using two different experimental techniques and the results are compared. In particular, the microcalorimetric and photoelastic results seem to be in disagreement, but the disagreement can be resolved by assuming that organization phenomena take place even at strains less than the critical value at which thermally detectable crystallization occurs. It is believed that such organization phenomena give rise to highly defective crystallites which behave as nucleation agents in the crystallization process that is induced at larger strains.     

Study on the relationship between the mechanical properties and processing for self-reinforced polymers. Part 1: A theory of stress-induced crystallization for entangled polymer networks

A new theory of stress-induced crystallization for entangled polymer networks is presented. It is based on the theory of viscoelasticity with constraints of trapped entanglements and crystallites using a model of fibrillar and lamellar morphology engendered by the extended and folded-chain crystallization. The probability distribution function of the end-to-end vector for two kinds of constituent chains and the viscoelastic free energy of deformation for two kinds of networks have been calculated. The relationships of stress to strain for four types of deformation were derived. The theory is successful in relating the equilibrium degree of crystallinity and the melting temperature to the extension ratio for networks with stress-induced crystallization. Furthermore, the theory provides a theoretical foundation for studying the dependences of tensile modulus and strength on the processing and testing conditions for self-reinforced polymers.Nomenclature A initial cross-section - a _j radius ofjth spheres - a _k radius ofkth spheres - a _kj radius of different spheres - B _cr structure factor for the folded-chains in the crystallite aggregate-polymer chain networks - B _ef structure factor for the folded-chains in the trapped entanglement networks - C ₁ material constant for the folded-chains in entanglement or/and crosslink networks - C _1c material constant for the folded-chains in entanglement or/and crosslink networks with stress-induced crystallization - C _100cr material parameter for the folded-chains in the crystallite aggregate-polymer chain networks - C _100ef material parameter for the folded-chains in the trapped entanglement networks - C ₂ material constant for the entanglement chains in the entanglement or/and crosslink networks - C _2c material constant for the entanglement chains in the entanglement or/and crosslink networks with stress-induced crystallization - C ₃ material constant for the extended-chains in the entanglement or/and crosslink networks - C _3c material constant for the extended-chains in the entanglement or/and crosslink networks with stress-induced crystallization - C _200cr material parameter for the extended-chains in the crystallite aggregate-polymer chain networks - C _200ef material parameter for the entanglement chains in the trapped entanglement networks - C _cr structure factor for the extended-chains in the crystallite aggregate-polymer chain networks - C _ef structure factor for the extended-chains in the trapped entanglement networks - C _020ef material parameter for the entanglement chains in the trapped entanglement networks - C _000cr material parameter for the crystal-lite aggregate-polymer chains in connection with changing volume - D _cr structure factor for the crystallite aggregate-polymer chains in connection with changing volume - D _ef structure factor for the entanglement chains in the trapped entanglement networks - dv volume element - F elastic free energy of deformation - F _crT elastic free energy of deformation for the crystallite aggregate-polymer chain networks - F _cT free energy of crystallization for the crystallite region - F _eT elastic free energy of deformation for the trapped entanglement networks - F _TT total free energy for the crystallizable entangled or/and crosslinked networks with stress-induced crystallization - F _TT ⁰ change in free energy of deformation from a deformed state to a free state for entangled networks with a given crystallinity - F ⁰ net change in free energy of deformation at a free state - f force - f _cr number of chains emanating from a crystallite aggregate in the crystallite aggregate-polymer chain networks - (1–f) fraction of trans-isomers on the extended and folded-chains in the constituent chains by crystallite aggregates - G _c total number of the extended and folded-chains in the crystalline region - G _c number of the folded-chains in the crystalline region - G _c number of the extended-chains in the crystalline region - G _c ⁰ total number of the crystallizable extended and folded-chains in the crystallite aggregate-polymer chain networks - H _u heat of fusion per link of polymer - H _u heat of fusion per gram of polymer - k Boltzmann constant - k _h rate constant for the change of constituent chain by crystallite aggregates - k _g rate constant for the change of constituent chains by entanglement - number average molecular weight - r the end-to-end vector length of the chain in a conjected state - r ⁰ coordination number - r _i the end-to-end vector length ofith chains in conjected state - r _j vector length from the center of crystallite aggregate to thejth chain end in the conjected state - r _k vector length from the center of crystallite aggregate to thekth chain end in the conjected state - t time of drawing - T incipient melting temperature of the deformed materials - T _m ⁰ melting temperature of the undeformed materials - t _x stress alongx direction - t _y stress alongy direction - t _z stress alongz direction - u change in energy of the rotational isomers - W(r) probability that the center of the constituent chains with different dimensions lies in the spherical shellr andr+dr - W degree of crystallinity - W ₀ Nagai function of the end-to-end vector for a chain - draw ratio - _g coefficient of relaxation time for the constituent chains by entanglement - _g interface factor for the constituent chains by crystallite aggregate - _x y _z components of alongx, y andz directions - ₀ ² parameter for a chain in free state - _0j ² parameter for thejth chains of the trapped entanglement networks in free state - _0k ² parameter for thekth chains of the crystallite aggregate-polymer chain networks in free state - _rj ² parameter for therj-th chain of the trapped entanglement networks in conjected state - _rk ² parameter for therk-th chains of the crystallite aggregate-polymer chain networks in conjected state - _rj ² parameter forrj-th chains of the trapped entanglement networks in conjected state - _k ² parameter for k-th chains of the crystallite aggregae-polymer chain networks in conjected state - _crk dimension of thekth constituent chains by crystallite aggregate in the crystallite aggregate-polymer networks - _edk dimension of thekth constituent chains by the extended-chain crystallite aggregate in the extended-chain crystallite aggregate-polymer chain networks - _ef dimension of thejth constituent chains by entanglement in the trapped entanglement networks - _fc j dimension of thejth constituent chains by folded-chain crystallite aggregate in the folded-chain crystallite aggregate-polymer chain networks - _{crkx crky crkz} components of _crk alongx, y, z directions - _crk number of the constituent chains with dimension _crk - _crT total number of the constituent chains by crystallite aggregate in the crystallite aggregate-polymer chain networks - _efi number of the constituent chains with dimension _efi - _efT total number of the constituent chains by entanglement in the trapped entanglement networks - _crT total number of chains in the crystallite aggregate-polymer chain networks - _efT total number of chains in trapped entanglement networks - _cr total number of elastic chains in the crystallite aggregate-polymer chain networks - stress - _n normal stress - _s shear stress - degree of constrained severity by crystallite aggregate in the crystal-lite aggregate-polymer chain networks - degree of constrained severity by entanglement in trapped entanglement networks - _r front factor in the crystallite aggregate-polymer chain networks - _r front factor in the entanglement networks - number of conformations     

Inclusion of mobile crosslinks and lateral crystallite growth in the theory of stress-induced crystallization

The theory of stress-induced crystallization is broadened to include a reshuffling of crosslink positions as a result of changing sizes of crystalline domains and multiple crystallites of varying lateral dimensions (i.e., lateral growth). A continuous state of equilibrium throughout the amorphous component of the stretched network is postulated and, consequently, effected by requiring crosslinks to anchor about their most probable locations, which vary continuously as crystallization changes. Such features incorporated into Flory's model of stress-induced crystallization broaden its theoretical base, placing it on a stronger, more realistic foundation.     

A thermodynamic approach to the stress-induced crystallization in cross-linked rubbers

The thermodynamic treatment of crystallization phenomena in a prestretched rubber was undertaken. Emphasis was put on defining conditions for the thermodynamic stability of the extendedor folded-chain crystal structure. The extended-chain structure is found to be stable thermodynamically at temperatures higher than the isotropic melting point of un-cross-linked polymer T in the stretched state, while the folded chain one is not. Below T, the stretch ratio of the network structure determines which crystal structure is more stable. The relation among the critical stretch ratio for the extended/folded crystalline structure transition, temperature, and molecular weight is also discussed. The crystallinity predicted by this work becomes zero at a temperature of T, the isotropic melting point of a cross-linked system. The value of T decreases with increasing cross-link density, and this is consistent with the experimental data reported in the literature.     

Optical studies of the stress-induced crystallization of rubber

The low-angle light scattering by films of stretched natural and synthetic rubbers was investigated. Intense V_v scattering is found under conditions when crystallization occurs which is characteristic of the scattering from aggregates of dimensions comparable with the wavelength of visible light. These were identified with the γ fibrils described by Andrews. The dependence of scattering was studied as a function of light polarization direction, orientation direction, elongation, temperature, degree of swelling, type of swelling liquid, and degree of crosslinking. It was concluded that the scattering unit consists of an assembly of crystals with their chain axes parallel to the stretching direction, but (in the case of natural rubber at high elongations) with the fibril axis at a slight angle to the stretching direction. The scattering is not affected much by swelling but is decreased upon increasing the temperature. Upon recooling the scattering returns, but does so over several hours, indicating that much of the scattering arises from secondary crystallization.     

A shape-persistent polymeric crystallization template for CaCO3

Alanyl-alanine-derived poly(isocyanide)s possess a helical structure that persists even in aqueous media. These rigid macromolecules possess a regular distribution of carboxylic acid-terminated side chains which for the first time allows the study of the templating process involved in biomineralization using a shape-persistent polymeric template. It is demonstrated that in the case where the polymer derived from l-Ala-d-Ala is used the formation of apple core-type calcite crystals is controlled both by nucleation of the (01.1) face and subsequent adsorption of the polymer to the {hk.0} faces of the growing crystal. A small change in the secondary structure of the template that is introduced by using the polymer derived from l-Ala-l-Ala is directly reflected in the lower degree of control over the crystallization process.     

Chitosan-g-poly(acrylic acid) hydrogel with crosslinked polymeric networks for Ni2+ recovery

In this study, chitosan-g-poly(acrylic acid) (CTS-g-PAA) hydrogel with crosslinked polymeric networks was prepared from an aqueous dispersion polymerization and then used as the adsorbent to recover a valuable metal, Ni2+. The adsorption capacity of CTS-g-PAA for Ni2+ was evaluated and the adsorption kinetics was investigated using Voigt-based model and pseudo-second-order model. In addition, the effects of pH values and coexisting heavy metal ions such as Cu2+ and Pb2+ on the adsorption capacity were studied. The results indicate that the as-prepared adsorbent has faster adsorption rate and higher adsorption capacity for Ni2+ recovery, with the maximum adsorption capacity of 161.80 mg g(-1). In a wide pH range of 3-7, the adsorption capacity keeps almost the same, and even under competitive conditions, the adsorption capacity of CTS-g-PAA for Ni2+ is observed to be as high as 54.47 mg g(-1). Finally, the adsorption performance of CTS-g-PAA for Ni2+ in real water sample and the reusability of the as-prepared adsorbent were evaluated, and also the controlled adsorption mechanism was proposed.     

Chitosan-g-poly(acrylic acid) hydrogel with crosslinked polymeric networks for Ni recovery

In this study, chitosan-g-poly(acrylic acid) (CTS-g-PAA) hydrogel with crosslinked polymeric networks was prepared from an aqueous dispersion polymerization and then used as the adsorbent to recover a valuable metal, Ni²⁺. The adsorption capacity of CTS-g-PAA for Ni²⁺ was evaluated and the adsorption kinetics was investigated using Voigt-based model and pseudo-second-order model. In addition, the effects of pH values and coexisting heavy metal ions such as Cu²⁺ and Pb²⁺ on the adsorption capacity were studied. The results indicate that the as-prepared adsorbent has faster adsorption rate and higher adsorption capacity for Ni²⁺ recovery, with the maximum adsorption capacity of 161.80 mg g⁻¹. In a wide pH range of 3–7, the adsorption capacity keeps almost the same, and even under competitive conditions, the adsorption capacity of CTS-g-PAA for Ni²⁺ is observed to be as high as 54.47 mg g⁻¹. Finally, the adsorption performance of CTS-g-PAA for Ni²⁺ in real water sample and the reusability of the as-prepared adsorbent were evaluated, and also the controlled adsorption mechanism was proposed.     

Strain-induced crystallization of swollen,crosslinked polyethylene

The kinetics of strain-induced crystallization of swollen polyethylene networks have been measured using dynamometry coupled with optical birefringence. Fibers were prepared by gel-spinning ultrahigh-molecular-weight polyethylene followed by crosslinking in dicumyl peroxide and swelling in xylene. Retractive force on crystallization was monitored at various temperatures and draw ratios. Fiber visualization was achieved using optical illumination coupled with video recording and digital analysis of the in situ transformation. Avrami plots of the transformation data showed good linear fits for low draw ratios in the range α < 1.2 and moderate undercoolings (60 < T_c < 70°C). Time exponents of unity were found, indicating a one-dimensional, heterogeneous growth mechanism whose temperature dependence could be described by a formalism similar to that recently used for flow-induced growth.     

Rapid stress-induced crystallization in natural rubber

Stress-induced crystallization in a rapidly stretched natural rubber gum vulcanizate has been studied using thermal techniques to follow the development of crystallinity. A special-purpose analog computer has been assembled and used on-line to process the thermal and mechanical data obtained in high speed tensile testing. Roughly first-order room temperature crystallization kinetics curves were obtained having time constants of 50–60 msec in the range of 400–540% extension. While the rate of this rapid, presumably primary crystallization appears rather insensitive to elongation in this limited range, the extent of crystallization at 400 msec increases smoothly from zero at 340% elongation to around 18% at 540% elongation. It is shown that our high-speed tensile tester can stretch this vulcanizate fast enough that most of the crystallization takes place after extension has been completed. Stress-strain curves obtained at this high rate are compared with those obtained at lower rates where crystallization takes place during the stretching.     

A reconsideration of polymer crystallization theory

Summary Two polymer crystallization theories are reviewed and discussed against the background of a revision of general nucleation theory, given in a preceding paper. Since crystallization nuclei, as usually defined, do not exist, the free energy of formation of a nucleus, such as it is applied for the calculation of nucleation frequency or rate of crystal growth, is a misleading concept. The latter quantities must be described as functions of parameters governing the attachment of polymer segments to, and their separation from, the growing crystal. The crystallization of polymers is supposed to proceed via attachment of segments of one or a few polymer repeating units rather than by steps of a whole fold length at once. Chain folding as aprerequisite for crystallization must be rejected as being highly improbable; it may be theresult of crystallization. One cannot decide from data on polymer-crystallization kinetics alone which theory is right or wrong, since it is the derived interfacial free-energy parameters that are actually the adjustable parameters of the theory.

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Zusammenfassung Zwei Theorien der Polymerkristallisation werden kurz wiedergegeben und diskutiert auf der Grundlage einer Revision der allgemeinen Keimbildungstheorie, wie in einer vorhergehenden Veröffentlichung dargelegt. Da Kristallisationskeime, wie sie üblicherweise definiert werden, nicht existieren, ist die freie Energie zur Keimbildung, wie sie zur Berechnung der Keimbildungs-häufigkeit oder Kristallwachstumsgeschwindigkeit herangezogen wird, ein irreführender Begriff. Diese Größen sind in Abhängigkeit von Parametern zu beschreiben, die die Angliederung von Polymersegmenten an die wachsenden Kristalle bzw. deren Abtrennung von diesen beherrschen. Es wird jetzt angenommen, daß die Kristallisation von Polymeren durch Angliederung von Segmenten erfolgt, die aus einem einzigen oder einigen wenigen Monomereinheiten bestehen, statt durch einzelne Schritte von ganzen Faltungslängen. Kettenfaltung alsVorbedingung zur Kristallisation wird als höchst unwahrscheinlich verworfen; sie könnte alsErgebnis der Kristallisation auftreten. Kinetische Daten der Kristallisation von Polymeren allein geben keinen Schlüssel zur Frage, welche die richtige Theorie ist, da die hergeleiteten Parameter der freien Grenzflächenenergie im wesentlichen die freien Parameter der Theorie sind.

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With 5 figures in 7 details     

Characterization of dimethacrylate polymeric networks: a study of the crosslinked structure formed by monomers used in dental composites

The resin phase of dental composites is mainly composed of combinations of dimethacrylate comonomers, with final polymeric network structure defined by monomer type/reactivity and degree of conversion. This fundamental study evaluates how increasing concentrations of the flexible triethylene glycol dimethacrylate (TEGDMA) influences void formation in bisphenol A diglycidyl dimethacrylate (BisGMA) co-polymerizations and correlates this aspect of network structure with reaction kinetic parameters and macroscopic volumetric shrinkage. Photopolymerization kinetics was followed in real-time by a near-infrared (NIR) spectroscopic technique, viscosity was assessed with a viscometer, volumetric shrinkage was followed with a linometer, free volume formation was determined by positron annihilation lifetime spectroscopy (PALS) and the sol–gel composition was determined by extraction with dichloromethane followed by ¹H NMR analysis. Results show that, as expected, volumetric shrinkage increases with TEGDMA concentration and monomer conversion. Extraction/¹H NMR studies show increasing participation of the more flexible TEGDMA towards the limiting stages of conversion/crosslinking development. As the conversion progresses, either based on longer irradiation times or greater TEGDMA concentrations, the network becomes more dense, which is evidenced by the decrease in free volume and weight loss after extraction in these situations. For the same composition (BisGMA/TEGDMA 60–40 mol%) light-cured for increasing periods of time (from 10 to 600 s), free volume decreased and volumetric shrinkage increased, in a linear relationship with conversion. However, the correlation between free volume and macroscopic volumetric shrinkage was shown to be rather complex for variable compositions exposed for the same time (600 s). The addition of TEGDMA decreases free-volume up to 40 mol% (due to increased conversion), but above that concentration, in spite of the increase in conversion/crosslinking, free volume pore size increases due to the high concentration of the more flexible monomer. In those cases, the increase in volumetric shrinkage was due to higher functional group concentration, in spite of the greater free volume. Therefore, through the application of the PALS model, this study elucidates the network formation in dimethacrylates commonly used in dental materials.     

Analysis of stress-induced crystallization in high-cis-1,4-polybutadiene

Stress-induced crystallization of a crosslinked polybutadiene with a high 1,4-cis content is investigated, at room temperature. The change in the fraction of crystallinity with deformation is evaluated by two different methods. The first is based on simultaneous measurement of birefringence and stress. The second is based on calorimetric analysis. The data on crystallinity obtained by these two methods are in good agreement in the range of low deformations, while, in the range of higher deformation (λ > 5), the degree of crystallinity obtained by calorimetry is higher than that obtained by the optical method. Qualitative information on the crystallization was also obtained by optical analysis of the hysteresis behavior. The hysteresis data show the presence of ordering phenomena at deformations at which there seems to be no crystallinity according to both quantitative methods.     

A hierarchical model of crystallization in polymeric gels and porous solids

A kinetic model of the crystallization of substances in the volume of an agglomerate of many microparticles or in a polymeric gel in solution with a given composition and temperature was formulated. The model takes into account the diffusion of the crystallizing substance from outside into the space between microparticles in an agglomerate or between polymeric globules in a gel and then from this space into the volume of microparticles (globules) with the simultaneous nucleation and growth of microcrystals of the crystallizing substance. The possibility of simultaneous diffusion of several crystallizing substances, which chemically react with each other to produce product microcrystals, heating of the gel (solid) by the heat of crystallization, pushing the solution out from the space between microparticles, and changes in the volume of the gel (solid) as a result of crystallization is considered. The model was used to develop a classification of crystallization types in gels and porous solids and interpret several phenomena described in the literature. A hypothesis was advanced concerning some unknown phenomena related to crystallization.     

Non-isothermal crystallization kinetics of graphite-reinforced crosslinked high-density polyethylene composites

Journal of Thermal Analysis and Calorimetry - Crosslinked high-density polyethylene (PEX) composites containing various amounts of graphite particles (1, 2.5 and 5 mass% or 0.479, 1.206 and 2.445...     

Glass transitions in crosslinked epoxy networks

Epoxy resins of DGEBA type were thermally cured with diaminodiphenylmethane as crosslinking agent, and then analysed by Differential Scanning calorimetry (DSC) at various heating rates in order to determine the glass transition temperatureT _g of the final networks. First it was shown that during cyclingT _g is shifted towards higher values up to a maximum or . Such a change is attributed to an increasing extent of cure which develops during the thermal analysis, and also to relaxation processes thermally activated inside the polymeric matrix. Then the dependence of on the heating rateq imposed by the DSC apparatus was presented forq changing from 0.1 to10C min^–1. At heating rates exceeding 3C min^–1 only the classical temperatureT _g was detected, but at smallerq values, an additional endothermic transition was revealed, located at higher temperature and linked to a physical aging-like phenomenon, which takes place at low heating rates. The plot of against logq is divided into two quasi-linear parts on each side ofq=3C min^–1. In conclusions, an equation was given to describe the vs. logq function.     

A probabilistic theory on the time to fracture of amorphous crosslinked polymers

The energy probability theory of fracture proposed by Valanis has been extended to apply to the global fracture of a large material region and has been generalized to take into account the probabilistic distribution among bonds of the free energy of the region. In contrast to the theory of fracture initiation of the first author, it is assumed, in the present paper, that global fracture is brought about by the fracture of a critical number N_cr of primary bonds. Whereas this condition alleviates some of the problems encountered in the application of the theory to fracture initiation and propagation—such as determination of the local energy field at the root of a developed crack—it introduces the difficulty that N_cr may, in general, depend on the geometry of the specimen and the directionality of the stress field, though it was found to be relatively insensitive to the rate of deformation, as corroborated in this paper. The theory is used in this work to predict the time of global fracture, under conditions of constant load, constant strain, and constant strain rate.     

Birefringence of semicrystalline polymeric networks

A simple theoretical development is proposed to explain the variation of birefringence with degree of crystallization for crosslinked, stretched polymer networks. The model adopted for the calculations is one proposed by Flory in order to calculate the thermodynamic properties of such systems and hence is restricted to the special case of network orientation prior to the onset of crystallization. Our findings are briefly discussed and possible applications of the results are considered.     

Crystallization under stress: A theory of fibrillar crystallization

A theory of crystallization in stretched polymer networks is developed. In it, four principal features are incorporated: (i) crosslinks are displaced by growing crystallites, (ii) network chains are constrained to positions compatible with fixed sample shape and volume, (iii) some network chains remain amorphous, and (iv) the relative direction of a chain through a crystallite may not be the same for all chains. The derived network force exhibits a V or U shape with changing temperature in the crystallization zone that is a close replica of the behavior of gutta percha networks. Postulates of fibrillar-lamellar transitions are not introduced into the calculations.