Viscoelastic characterization of polyethylacrylate.Polyethylacrylates are oil-resistant and high-temperature resistant rubbers [refs. 1 and 2]. The commercial products are offered in various grades; the variation may be in the processability, in the chemical nature of the cure-site or in the copolymer copolymer: see polymer. designed for the lower temperature application [ref. 3]. The underlying interest of this work is the processability; however, the processability depends upon not only the characteristics of a given rubber but also various other factors such as a processing machine, a formulation, a manner of charging into a machine and the operating condition of the machine. We intend to characterize the various grades of polyethylacrylate in a manner free from the factors other than the properties of rubber itself A standard method of characterizing a polymer sample is a use of the dilute solution techniques [ref. 4] for the determination of the average molecular weights, molecular weight distribution, long branching and so on. It is not widely recognized that this method is often useless for characterizing rubber samples because of the presence of gel. The gel in this case is a fraction of polymer, which swells but does not dissolve in the solvent. Therefore, the gel is filtered out before the dilute solution technique is applied. On the other hand the gel fraction has a significant and often decisive influence on the processability. Therefore, the characterization of a rubber must begin with the determination of the gel-content [ref. 5]. Subsequent observation must treat a whole sample including the gel-fraction. Previously such a characterization method was developed by using viscoelastic Adj. 1. viscoelastic - having viscous as well as elastic properties natural philosophy, physics - the science of matter and energy and their interactions; "his favorite subject was physics" measurements. The method was applied to various commercial samples including NBR NBR Number NBR Nightly Business Report (PBS show) NBR National Business Review (New Zealand weekly business newspaper) NBR National Bureau of Asian Research NBR National Board of Review , SBR SBR - Spectral Band Replication , polyisobutylene, polyethylacrylate, polyepichlorohydrin and EPDM EPDM Ethylene-Propylene-Diene-Monomer EPDM Enterprise Product Data Management EPDM Ethylene Propylene Dimonomer (industrial/commercial piping/plumbing components) EPDM Engineering Product Data Management [refs. 6 and 7]. With the NBR, representative grades had been selected and an extensive characterization was performed [refs 8-10]. However, with other rubbers only limited examples were examined. Polyethylacrylate is quite different from NBR in that it has a saturated backbone and much more polar group along the chain. In addition, polyethylacrylate has 73% of its molecular weight in its pendant group A pendant group or side group is a group of molecules attached to a backbone chain of a long molecule. Usually, this molecule would be a polymer.[1] such that it is a relatively short and fat chain for a given molecular weight. It is the objective of this study to develop a viscoelastic characterization method for polyethylacrylate, a method similar to the one previously developed for the commercial NBRs. Formation and characterization of gel Polyethylacrylate is made in the emulsion polymerization Emulsion polymerization is a type of radical polymerization that usually starts with an emulsion incorporating water, monomer, and surfactant. The most common type of emulsion polymerization is an oil-in-water emulsion, in which droplets of monomer (the oil) are emulsified (with with a free-radical initiator [refs. 1 and 2]. The mechanisms of polymerization polymerization Any process in which monomers combine chemically to produce a polymer. The monomer molecules—which in the polymer usually number from at least 100 to many thousands—may or may not all be the same. include chain-transfer reaction, which generates long branches. The probability of chain-transfer is higher for the larger molecules. This leads to the branched molecules becoming more and more branched [refs. 13 and 14]. As more polymer chains are formed within the emulsion emulsion: see colloid. emulsion Mixture of two or more liquids in which one is dispersed in the other as microscopic or ultramicroscopic droplets (see colloid). Emulsions are stabilized by agents (emulsifiers) that (e.g. droplets the probability of the chain-transfer to polymer increases. At a high degree of conversion there is a significant fraction of polymers having many long branches. These highly branched molecules are insoluble insoluble /in·sol·u·ble/ (in-sol´u-b'l) not susceptible of being dissolved. in·sol·u·ble adj. Not soluble. in a solvent, although they swell in it, i.e. gels. Sometimes these molecules are said to be crosslinked. However, they are not crosslinked in a sense of forming a network. After coagulation coagulation (kōăg'y lā`shən), the collecting into a mass of minute particles of a solid dispersed throughout a liquid (a sol), usually followed by the precipitation or of latex latex, emulsion of a polymer (e.g., rubber) in water (see colloid). Natural latexes are produced by a number of plants, are usually white in color, and often contain, in addition to rubber, various gums, oils, and waxes. , washing and
drying, the rubber is made into a bale bale1. a package of wool in a wool pack weighing 150-250 lb depending largely on whether it is greasy or scoured. 2. a compressed bundle of hay, either about 100 lb tied with wire or twine, or large, round, untied bales, as big as a small hay stack and referred to as 'big bales'. . The bale containing a significant amount of the highly branched gel behaves as if the whole bale is crosslinked. After removal of the soluble fraction [ref. 5] we can see the gel particle remaining on a screen. The gel in this case is sometimes called "macrogel" in order to differentiate it from the "microgel" which is a crosslinked latex particle. The latter is made by copolymerizing with a difunctional comonomer co·mon·o·mer n. One of the compounds that constitute a copolymer. , resulting in a crosslinked network. The microgel-containing NBR is available commercially [refs. 9 and 10]. An example of microgel containing polyethylacrylate was examined before [ref. 11]. The present work does not include the microgel. However, in general for a given sample it is necessary to distinguish the presence of macrogel from that of microgel, because they affect processability differently. The determination of the gel content requires solvent-extraction of the soluble fraction and filtration. The fraction left on the filter is considered to be the gel. This poses a serious problem; that is, the gel-content depends upon the poresize of the filter. A standard procedure uses a screen having 300 [mu]m opening [ref. 5], whereas a filter used before the GPC (1) A PC that uses the Linux-based gOS operating system. See gOS. (2) (GPC Group) Originally the Graphics Performance Characterization committee of the NCGA, the GPC Group is now part of Standard Performance Evaluation Corporation (SPEC) and oversees the following measurement is 0.1 [mu]m. The gel-content of an EPDM determined with these. filters was significantly different [ref. 7]. Another problem in the gel-determination is the sample size, which is usually very small, e.g. 0.4 g. At such a size level the bale of rubber is not as uniform with respect to the gel-content. Therefore, the gel-content of a given rubber has a certain range of values. In this study the gel-content is used as a supplementary information and the quantitative characterization is sought in the viscoelastic measurements. Viscoelastic method of structural analysis Molecular architectural features, which have significant influence on the viscoelastic properties of an amorphous Unorganized or vague. A lack of structure. For example, the amorphous state of a spot on a rewritable optical disc means that the laser beam will not be reflected from it, which is in contrast to a crystalline state which will reflect light. See crystalline. elastomer elastomer (ĭlăs`təmər), substance having to some extent the elastic properties of natural rubber. The term is sometimes used technically to distinguish synthetic rubbers and rubberlike plastics from natural rubber. , are molecular weights, molecular weight distribution, long-branching and gel. An implication is that viscoelastic measurements may be used for analyzing these structures. However, there are several difficulties in using viscoelastic methods for structural analysis; they are: * Each structural category cannot be identified with a unique marker such as a peak in spectroscopic spec·tro·scope n. An instrument for producing and observing spectra. spec tro·scop analyses.* Viscoelastic techniques do not involve separation, which is a common method in the dilute solution property measurements, e.g. GPC. * Viscoelastic contributions from different structural categories overlap upon each other and the relative degree of contribution changes depending upon the measuring conditions. * In addition there are difficulties in precisely defining the structure of long-branching and gel [ref. 15]. We will use the following approach to overcome these difficulties: the first step is to obtain the linear viscoelastic properties over as wide a time-scale as possible: an emphasis must be placed on extending the data towards the longer time-scale, where the difference in molecular structure is usually magnified [ref. 7]. In this work we obtain shear storage modulus See modulo. , G', and shear loss modulus, G", as functions of angular frequency In physics (specifically mechanics and electrical engineering), angular frequency ω (also referred to by the terms angular speed, radial frequency, and radian frequency) is a scalar measure of rotation rate. , [omega]. In order to expand the frequency range, the measurements were made at several temperatures and the time-temperature superposition su·per·po·si·tion n. 1. The act of superposing or the state of being superposed: "Yet another technique in the forensic specialist's repertoire is photo superposition" is used [ref. 16] to construct a master curve. In the master curve one characteristic of the polymer structure becomes apparent; that is, how far towards the longer time scale the relaxation times relaxation time n. Physics The time required for an exponential variable to decrease to 1/e (0.368) of its initial value. Noun 1. of a sample are distributed. From this we know, relatively speaking, how far towards the larger size the molecular size distribution is extended, although it is not known whether the larger size comes from a linear molecule, a branched molecule or a gel. The second step is to contrast G' data with G" data. This indicates the relative degree of long branch and gel, although these two cannot be distinguished from each other [ref. 17]. It is convenient to construct a master-curve of a locus of G' and G" taken at the same value of [omega]. Such a master-curve may be presented as a log G"-log G' curve. Compared at the same value of G" the more branched and the higher gel-content samples give a higher G'. In this presentation the macrogel and microgel cannot be differentiated. The same data may be presented as the absolute value of complex viscosity, [vertical bar] [[eta].sup.*][vertical bar], (henceforth From this time forward. The term henceforth, when used in a legal document, statute, or other legal instrument, indicates that something will commence from the present time to the future, to the exclusion of the past. called complex viscosity), as a function of [omega]. With most of the commercial rubbers the Newtonian value of viscosity is not observed even at very low frequencies. However, a relative ranking of the molecular weight may easily be found from [vertical pipe][[eta.sup.*][vertical pipe] values towards the low frequency region. This is very helpful, because for the gel-containing samples a rigorous definition of the average molecular weight becomes obscure and yet we need some indication of the molecular weight level. In the above characterization scheme, the long branch and gel are not differentiated. Neither the molecular weight distribution is treated. These questions may be addressed from the point of view of the polymerization mechanism. As discussed before, the gel-formation in polyethylacrylate is an extreme case of branch-formation. Therefore, the long branch and gel may be considered to be one structural category. Because the branch-formation is the dominant cause for altering the molecular weight distribution, it is not necessary to consider the molecular weight distribution separately. In summary. gel together with long-branching are the only structural features which need to be considered. This interpretation is not necessarily valid, if the mechanisms of polymerization and those of branch-formation are different from the present case. The remaining problem is to distinguish macrogel from microgel. This is done with tensile tensile, adj having a degree of elasticity; having the ability to be extended or stretched. stress-strain measurements, because it is already known that the macrogel-containing rubber behaves differently from microgel-containing or gel-free rubbers in the large tensile deformation deformation /de·for·ma·tion/ (de?for-ma´shun) 1. in dysmorphology, a type of structural defect characterized by the abnormal form or position of a body part, caused by a nondisruptive mechanical force. 2. [ref. 15]. Even though the present study does not include microgel containing samples, we will perform the tensile deformation studies, because the rubber-processing involves large deformation [ref. 19]. The material behavior observed in large deformation is usually quite different from that of the small deformation. Therefore, the characterization of commercial rubbers should include large deformation. In order to treat the tensile data systematically, we use the strain-time correspondence principle [ref. 18]. Strain-time correspondence principle and analysis of macrogel The presence of long branch and gel affects the shape of stress-strain curve of gum rubbers. Qualitatively it is possible to detect these structures sometimes. However, quantitative measure is not readily available. The strain-time correspondence principle as will be explained later provides a means of quantitatively analyzing these curves. The tensile modulus, E, is in general as a function of strain, [epsilon] and strain rate, [epsilon], E ([epsilon], [epsilon]) = [sigma][alpha]/[epsilon] (1) where [sigma] is the stress based on the undeformed cross-section, [alpha] is the extension ratio and therefore, [sigma][alpha] is the true stress. Usually the tensile measurements are performed with a constant strain rate; therefore, E ([epsilon], t) = [sigma][alpha]/[epsilon] (2) where the time, t, is t = [epsilon]/[epsilon] (3) In equation 2 the modulus is a function of both strain and time; this contrasts with the linear viscoelastic modulus, which is a function of time-scale only. The strain-time correspondence principle is a linearization In mathematics and its applications, linearization refers to finding the linear approximation to a function at a given point. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential scheme, where the reduced time, [alpha]t, is used instead of t, E ([alpha]t) = [sigma][alpha]/[epsilon] (4) where [alpha] is the extension ratio, [alpha] = [epsilon] + 1 (5) This reduction scheme is similar to the time-temperature correspondence. The latter arises from a thermal excitation excitation Addition of a discrete amount of energy to a system that changes it usually from a state of lowest energy (ground state) to one of higher energy (excited state). For example, in a hydrogen atom, an excitation energy of 10. whereas the former from a mechanical excitation [ref. 20]. Equation 4 was found to be applicable to gel-free rubber, microgel containing rubber and rubber containing a relatively small amount of macrogel, e.g. up to 8%. With a significant amount of macrogel, the strain-hardening was observed requiring an additional linearization scheme, E ([alpha]t) = ([sigma]/[alpha])/[tau] ([alpha]) (6) The function, [tau] ([alpha]) is a modulus-shift and a measure of the strain-hardening [ref. 21]. Previously, [tau] ([alpha]) was found to have the following form, [tau] ([alpha]) = [[alpha].sup.n] (7) where n is larger for the higher gel-content. If the above reduction scheme is successful in linearizing the nonlinear A system in which the output is not a uniform relationship to the input. nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input. data and if Poisson's ratio When a sample of material is stretched in one direction, it tends to get thinner in the other two directions. Poisson's ratio (ν, ), named after Simeon Poisson, is a measure of this tendency. is one half, then, the
linearized tensile modulus and the shear modulus shear modulusSee under modulus of elasticity. must agree with each other with a factor of three, E ([alpha]t) = 3 [vertical bar][G.sup.*][vertical pipe] ([omega]) (8) Such a comparison may be made in terms of viscosity also, [[eta].sub.T]/3 = E ([alpha]t [multiplied by] [alpha]t/3 = [vertical pipe][[eta].sup.*][vertical pipe] ([omega]) (9) where [[eta].sub.T] is a viscosity evaluated from tensile measurements. The agreement with equation 9 was found with gel-free and microgel containing NBRs. Polyethylacrylates even though the sample was gel-free [[eta].sub.T] was higher than [vertical bar] [G.sup.*][vertical pipe]. The [[eta].sub.T] values being evaluated from large deformation, a polar association similar to the strain-induced crystallization Crystallization The formation of a solid from a solution, melt, vapor, or a different solid phase. Crystallization from solution is an important industrial operation because of the large number of materials marketed as crystalline particles. was postulated pos·tu·late tr.v. pos·tu·lat·ed, pos·tu·lat·ing, pos·tu·lates 1. To make claim for; demand. 2. To assume or assert the truth, reality, or necessity of, especially as a basis of an argument. 3. to be the cause of the disagreement [ref. 22]. When a steady shear deformation is imposed on a rubber sample, initially the stress-growth is observed before reaching the steady state. The stress-growth curve may be treated as a shear stress-strain curve, G ([gamma],[gamma]) = [tau]/[gamma] (10) where r is the shear stress shear stress n. See shear. shear stress A form of stress that subjects an object to which force is applied to skew, tending to cause shear strain. , [gamma] shear strain shear strain or shearing strain See under strain. , [gamma] shear strain-rate and G shear modulus. When [gamma] is very low, e.g. in an order of 0.01 [s.sup.-1], a smooth curve may be obtained easily. The nonlinear modulus may be linearized similarly to equations 4 and 5. G ([alpha]t) = [tau]/[gamma] (11) with [alpha] = [gamma] - (1/[gamma]) (12) The shear stress-strain measurements are also performed in this study. In addition the steady state viscosity measurements with a rotational and a capillary capillary (kăp`əlĕr'ē), microscopic blood vessel, smallest unit of the circulatory system. Capillaries form a network of tiny tubes throughout the body, connecting arterioles (smallest arteries) and venules (smallest veins). rheometer rhe·om·e·ter n. An instrument for measuring the flow of viscous liquids, such as blood. will be made in order to observe the sample-to-sample differences. Experimental Samples Six samples of this work are listed in table 1. They were supplied by Zeon Chemical Co.
Table 1 - samples
Sample Gel % Mooney Remarks
index
A 0 43 Cement grade, gelled in
solution
B 0 36 Cement grade, not gelled
C 48 48 General purpose
D 5 48 General purpose
E 48 51 General purpose
F 3 No cure-site
The cement grade is made for the application of its solution as a rubber cement. Sample A makes a very high viscosity solution In mathematics, the viscosity solution concept was introduced in the early 1980's by Pierre-Louis Lions and Michael Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). and is difficult to make it flow, i.e. gelled. Sample B makes an easy-flowing solution. Samples C and E were made a year apart but are similar as far as the gel-content and Mooney index are concerned. Sample D has a Mooney index similar to C and E, but a low gel-content. Samples A to E are all commercial products supplied as bales. They have the same cure-site, which is a chlorine-type. Sample F was prepared in a pilot plant without the cure-site comonomer in order to observe the effect of cure-site or the absence of it on the gum-rubber properties. It is supplied as coagulated co·ag·u·late v. co·ag·u·lat·ed, co·ag·u·lat·ing, co·ag·u·lates v.tr. To cause transformation of (a liquid or sol, for example) into or as if into a soft, semisolid, or solid mass. v.intr. crumbs CRUMBS is an improvisational theatre duo based in Winnipeg, Manitoba, Canada. The duo consists of two actors, Stephen Sim, and Lee White. Other members include videographers, musicians, photographers, webmasters, illustrators, producers, agents, publicists, graphic . Specimen preparation For the dynamic and tensile measurements the samples were compression molded into sheets at 160[degrees]C for 22 minutes. After removing the mold from the press the mold containing the elastomer sheets were placed under a 6 kg weight for three days in order to relax out the molding stresses. For the steady state and transient shear measurements the bales of rubber or crumb are cut into small pieces and charged into the instruments. Gel measurements Gel measurements were made with samples as supplied and with the compression molded sheets. A small piece of rubber, about 0.4g, was placed in 100 ml of methylethylketone. The solution was kept in the dark for 48 hours at room temperature. Then, it was filtered through a Whatman No. 4 filter paper. Instruments and operation Dynamic mechanical measurements A Rheometrics mechanical spectrometer spectrometer Device for detecting and analyzing wavelengths of electromagnetic radiation, commonly used for molecular spectroscopy; more broadly, any of various instruments in which an emission (as of electromagnetic radiation or particles) is spread out according to some (RMS (1) (Record Management Services) A file management system used in VAXs. (2) (Root Mean Square) A method used to measure electrical output in volts and watts. 1. RMS - Record Management Services. 2. - 800) was operated with 25 mm parallel plates in a shear oscillatory oscillatory characterized by oscillation. oscillatory nystagmus see pendular nystagmus. mode. In addition to the calibration suggested by the instrument manufacturer, a silicone rubber Noun 1. silicone rubber - made from silicone elastomers; retains flexibility resilience and tensile strength over a wide temperature range synthetic rubber, rubber - any of various synthetic elastic materials whose properties resemble natural rubber (PDMS (Product Data Management System) See PDM. SE-30) was used as a calibration standard. Before the measurements with polyethylacrylates were performed, the silicone standard was run at 25[degrees]C for the angular frequency range of [10.sup.-1] to [10.sup.2] rad/s to ascertain that the data are in good agreement with the previous ones. For each polyethylacrylate sample, the storage modulus, G', and the loss modulus, G", were measured as a function of frequency at five temperatures from 36 to 141[degrees]C. The strain amplitude was taken in the linear region of the response, 3~4%. The measurements were made over the frequency range of [10.sup.-2] to [10.sup.2] rad/s at 100[degrees]C and lower, and [10.sup.-1] to [10.sup.2] rad/s at higher than 100[degrees]C. The frequency sweep was made from the lower to the higher frequency and then reversed. This is to see if the lower frequency data agree between the up-sweep and the down-sweep. If the degradative crosslinking has occurred during the measurement, the down-sweep data show higher moduli In theoretical physics, moduli are scalar fields whose different values are equally good (each one such scalar field is called a modulus). The reason is that the potential energy for moduli is constant, which can be guaranteed, for example, by supersymmetry (with . A slight degradation was observed at 160[degrees]C. Transient and steady state shear measurements A variable-speed Mooney rheometer with a biconical rotor was used for the observation of the transient and the steady state behavior at 100[degrees]C. The shear-rate range was from 0.025 to 1.1 [s.sup.-1] and the torque-time curves were recorded in the strip chart. The edge corrections were not made because our present interest is on the relative values of the viscoelastic data. Also, a capillary rheometer, Monsanto Processability Tester (MPT MPT Maryland Public Television MPT Modern Portfolio Theory (investing) MPT Ministry of Posts and Telecommunications MPT Message-Passing Toolkit MPT Master of Physical Therapy MPT Mitochondrial Permeability Transition ), was operated at 100[degrees]C with dies having L/D L/D Labor and Delivery L/D Lethal Dose L/D Lift/Drag (ratio) L/D Low Dynamic L/D Limiter/Discriminator L/D Loading / Discharging Rate (shipping) ratios of 5, 10 and 20. The shear rate Shear rate is a measure of the rate of shear deformation: ![]() For the simple shear case, it is just a gradient of velocity in a flowing material. range was from 3.6 to 36 [s.sup.-1]. Tensile stress-strain measurements A Monsanto Tensometer 500 with an extensometer ex·ten·som·e·ter n. An instrument used to measure minute deformations in a test specimen of a material. [extens(ion) + -meter. was used at room temperature and at strain rates of 0.075, 016 and 0.25 [s.sup.-1]. The measurements were made in triplicate and the results were averaged. Results and discussion Gel content The gel content before and after compression molding Compression molding is a method of molding in which the molding material, generally preheated, is first placed in an open, heated mold cavity. The mold is closed with a top force or plug member, pressure is applied to force the material into contact with all mold areas, and heat are listed in table 2. The compression molding did not increase the gel content in a significant way, as it is recognized that the error of the measurement is about [+ or -] 5%.
Table 2 - gel content
Sample Gel content Gel content Gel content
before before after
compression compression compression
molding molding molding
(wire mesh) (Whatman filter) (Whatman filter)
A 0 32 34 B 0 3 11 C 48 77 75 D 5 50 53 E 48 61 62 F 3 42 47 The gel data supplied by Nippon Zeon are also shown in the table. They were determined using a 300 [mu]m wire mesh wire mesh, wire netting n → tela metálica whereas we used a Whatman No. 4 filter paper having a pore pore (por) a small opening or empty space. alveolar pores openings between adjacent pulmonary alveoli that permit passage of air from one to another. size of 20-25 [mu]m. The effect of the pore size of the filter on the gel-determination is quite significant. Dynamic mechanical measurements The results of the time-temperature superposition are shown in figures 1 and 2. A modulus-shift was made, if required for the best superposition, but was very small or entirely unnecessary. As shown the data of G's are higher than those of G" over the entire frequency range of the observation, indicating the rubbery behavior. With sample B, figure 1, the G' and G" curves come very close to each other towards the lower frequencies, indicating a crossover Crossover The point on a stock chart when a security and an indicator intersect. Crossovers are used by technical analysts to aid in forecasting the future movements in the price of a stock. In most technical analysis models, a crossover is a signal to either buy or sell. . This suggests that at the frequency lower than this observation the sample B is in the flow region. The curves of A, C, D and F are similar to those of E in that the G' and G" are far apart even at the lowest frequency of the observation. The unique behavior of sample B is attributable to the very low gel-content. Shown in figure 3 are the plots of the absolute values of the complex viscosity. Looking at the data at frequencies lower than 0.01 rad/s, samples A and B, the cement grades, have viscosities distinctly lower than those of other samples. Both A and B have the gel-content lower than others. At the lowest frequency of the observation the ranking of viscosities is in accord with the gel-contents, although the differences are rather small. The WLF WLF Washington Legal Foundation WLF Wallis and Futuna (ISO Country code) WLF Waist Level Finder (camera viewfinder type) WLF Viva La Figa (MotoGP motorcycle races) constants [C.sub.1.sup.0] and [C.sub.2.sup.0], evaluated from the temperature shift factor, [a.sub.T], are given in table 3. The reference temperature is 36[degrees]C. The fractional free volume, [f.sub.g]/B and the coefficient of thermal expansion coefficient of thermal expansion, n See expansion, thermal coefficient. of free volume [alpha.sub.f]/B at the glass transition temperature The glass transition temperature is the temperature below which the physical properties of amorphous materials vary in a manner similar to those of a solid phase (glassy state), and above which amorphous materials behave like liquids (rubbery state). were calculated from the values of [C.sub.1.sup.0] and [C.sub.2.sup.0] and are shown in table 4. Concerning the [f.sub.g], sample C has a much lower value (0.026) compared to the other samples which have values of [f.sub.g] within the range of 0.034 to 0.039. Comparing the values of [[alpha.sub.f] sample C has the lowest value (0.9 x [10.sup.-4] [K.sup.-1]) followed by sample E (2.8 x [10.sup.-4] [K.sup.-1]). All other samples have values that lie in the range of 4.6 - 5.6 x [10.sup.-4] [K.sup.-1].
Table 3 - WLF constants
[C.sub.1.sup.0] and [C.sub.2.sup.0] at a reference
temp. of 36[degrees[C
Sample [C.sub.1.sup.0] [C.sub.2.sup.0] A 6.5 118 B 7.3 119 C 14.0 335 D 7.4 128 E 9.1 171 F 7.0 123 Table 4 - fractional free volume and coefficient of thermal expansion of free volume at the glass transition temperature of -14[degrees]C (259[degrees]K)
Sample Fractional Coefficient of thermal
free volume expansion of free volume
[f.sub.g]/B [alpha.sub.f]/B[[deg.sup.-1] x [10.sup.4]
A 0.039 5.6 B 0.035 5.0 C 0.026 0.9 D 0.036 4.6 E 0.034 2.8 F 0.036 5.0 Relating the values of [f.sub.g] and [alpha.sub.f] to the gel content, above a certain gel content (62%), the value of [f.sub.g] decreases with increasing gel content. At gel contents greater than 47%, the value of [alpha.sub.f] decreases with increasing gel content. The data of G" and G' are read at the same frequency from the master curve and plotted as log G" vs. log G' in figure 4. At a fixed value of G" (e.g.[10.sup.4] Pa) the magnitude of G' increases in the following order, B < A < F < D < E < C. This is the order of the increasing gel content. At a fixed value of G' (e.g. [10.sup.5] Pa) the magnitude of G" increases in the following order, F < C < E < D < A < B. Relating the observed behavior to the gel content in table 2, the magnitude of G" increases with decrease in gel content. The exception is sample F. It does not have the highest gel content but has the lowest value of G". This may be attributable to the chemical difference in the chain structure. Transient and steady state shear measurements Figure 5 (a) is representative of the torque-time curves obtained for samples A to F at a shear rate of 0.024 [s.sup.-1]. Figures 5 (a) and (b) are representative of the torque-time curves obtained for samples A and B over the available shear rate range of the rheometer (0.02-1.05 [s.sup.-1]) For these samples, as the shear rate is imposed the torque initially increases smoothly with or without stress overshoot o·ver·shoot n. A change from steady state in response to a sudden change in some factor, as in electric potential or polarity when a cell or tissue is stimulated. , eventually reaching a steady value. Figures 6 (a) and (b) are representative of the behavior observed with samples C to F at the shear rates higher than 0.024 [s.sup.-1]. For these samples the initial increase of torque is similar to that of samples A and B, but does not reach a steady value: instead, it fluctuates severely and continues to increase with time. For sample D this behavior occurred at shear rates greater than 0.55 [s.sup.-1]. The higher gel-content samples, C, D, E and F, evidently did not flow at the higher shear rates. The fluctuation of the torque may be a slip-stick in the course of the increasing deformation. The data at the shear rate of 0.024 [s.sup.-1] have been converted to the viscosity, ([tau][gamma])[alpha]t as a function of the deformation rate, 1/[alpha]t and are shown in figure 7. The level of the viscosity is related to the gel-content of the sample, except for sample F, which shows the viscosity somewhat higher than expected from the gel-content. Figures 8 and 9 represent the recorder traces of the pressure drop as a function of time for samples B and C. The pressure drops were recorded as the material was extruded across a die having a L/D ratio of five at a shear rate of 21.5 [s.sup.-1]. Figure 8 is representative of the nature of the pressure drop for samples A and B over the entire shear rate range. Figure 9 is representative of the fluctuations in pressure drop recorded for samples C to F. Figure 10 is a schematic A graphical representation of a system. It often refers to electronic circuits on a printed circuit board or in an integrated circuit (chip). See logic gate and HDL. of the grossly distorted extrudate obtained on extruding samples C to F. For samples A and B the extrudate was less distorted. Due to the severe fluctuations in pressure drop for samples C to F the viscosity could not be calculated. For these samples the average pressure drop has been recorded in table 5 as a function of the volumetric flow rate In fluid dynamics and hydrometry, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m3 s-1 and the L/D ratio of the die. For all the samples the pressure drop increases with the increase in flow rate. Among the samples, the average pressure drop increases in the following order: D - F < E < C, which is the increasing gel-content. Shear viscosity from dynamic, steady and transient measurements Figure 11 shows the complex viscosity, [absolute value of eta*] (from RMS-800 data) the transient viscosity, ([tau][gamma])[alpha]t (from transient Mooney data) and the steady shear viscosity [eta] (from steady state Mooney and the MPT) for sample A at 100[degrees]C. The nature of the curves obtained for sample B are similar to those in figure 11. However, for samples C to F the viscosity data could not be obtained from the MPT measurements because of the severe fluctuations in pressure drop. Neither could the steady shear viscosity be obtained from the measurements with the Mooney rheometer at shear rates greater than 0.25 [s.sup.-1]. For sample D the steady shear viscosity data could not be obtained at shear rates greater than 0.55 [s.sup.-1]. For samples A and B there is a good agreement between [absolute value of eta*] (from RMS-800) and [eta] (from MPT). Here the empirical Cox-Merz rule is applicable. Although ([tau][gamma])[alpha]t (from transient Mooney) is in good agreement with the [eta] (from steady state Mooney), they are higher than [absolute value of eta*]. A probable reason is the edge effect in the Mooney rheometer. Tensile stress-strain measurements In figure 12 the stress-strain curves of samples A to F are compared at a strain rate of 0.075 [s.sup.-1]. The stress in this figure is the true stress (based on the deformed de·formed adj. Distorted in form. cross-sectional area). The slopes of the stress-strain curves increase in the following order: B < A < D < F < E < C, which is the order of the increasing gel content. In figures 13 and 14 the tensile modulus, [delta][alpha]/[epsilon], is plotted as a function of reduced time, [alpha]t; that is the application of the strain-time correspondence principle. Figure 13 is representative of the type of curve obtained for samples A and B. For both these samples a master curve was obtained. Figure 14 is representative of the type of curve obtained for samples C to F. For these samples a master curve was not obtained. For samples C to F the modulus shift, [Gamma] ([alpha]) was made to construct the master curve. An example is shown in figure 15 for sample D. Similarly master curves were obtained from samples C to F. In figure 16 log [Gamma]([alpha]) is plotted as a function of log [alpha] for samples C to F. The plots are not linear as the previous observations (ref. 21). In this figure, sample C requires a modulus shift at values of [alpha] > 2. For samples D, E and F a modulus shift was required at values of [alpha] > 3. The magnitude of the modulus shift increases in the order of the increasing gel content: D - F < E < C. Moduli from dynamic shear and tensile measurements In figures 17 and 18 the shear moduli obtained from dynamic measurements, are compared to the shear equivalent moduli, ([delta][alpha]/3[epsilon])/[Gamma]([alpha]) obtained from tensile measurements for samples B (figure 17 andC (figure 18). None of the samples (A to F) the [absolute value of G*] and([delta][alpha]/3[epsilon])/[Gamma]([alpha]) data is in agreement. Figure 18 is representative of the type of curves obtained from samples A, C, D, E and F. In the previous studies (ref 6) the above two viscosities were in agreement for SBR, NBR and polyisobutylene samples. However, the disagreements similar to the above were found with polyethylacrylates and polyepichlorohydrin. A "strain-induced polar association" similar to the strain-induced crystallization was postulated. The dynamic measurements being performed at small strains, the strain-induced polar association did not occur. Conclusions The viscoelastic properties of the commercial polyethylacrylate rubbers were found to be primarily related to the gel content, which is determined with a filter of 25 [mu]m openings. Specific properties Specific properties of a substance are derived from other intrinsic and extrinsic properties (or intensive and extensive properties) of that substance. For example, the density of steel (a specific and intrinsic property) can be derived from measurements of the mass of a steel bar and the methods of presentations are as follows: dynamic shear storage and loss moduli and their plot as log G" vs. log G'; the absolute value of the complex viscosity as a function of the angular frequency; the stress-growth curves at the very slow rotational-speed of the Mooney rheometer; tensile stress-strain behavior and the application of the strain-time correspondence principle; also the application of the modulus-shift for the case of the strain hardening hardening, in metallurgy, treatment of metals to increase their resistance to penetration. A metal is harder when it has small grains, which result when the metal is cooled rapidly. . These represent shear and tensile properties at small, moderate and large deformation. Because the measurements were made over the temperature ranges of the practical interests, the material behavior described here corresponds to that at the processing conditions. The implication is that the gel content is not only the primary variable in the viscoelastic properties but also that in the processability. This conclusion is the same as that reached for the commercial NBRs (ref 9). However, one observation was new and different from that with the NBRs. With the higher gel-content samples, the steady shear behavior was not observed at 100[degrees]C except for the very low deformation rate of 0.024 [s.sup.-1]. The large irregular oscillation Oscillation Any effect that varies in a back-and-forth or reciprocating manner. Examples of oscillation include the variations of pressure in a sound wave and the fluctuations in a mathematical function whose value repeatedly alternates above and below some of the stresses indicated a fracture and possibly the slip-stick behavior. This did not occur with the NBRs. The viscoelastic properties of two high-gel samples made at different times are not exactly the same although the Mooney values and the gel content were reported to be similar. The finer filter must be used to distinguish their gel contents. Two samples having the same Mooney values but different gel contents had very different viscoelastic properties. Significance of this observation is the that the gel content is the important variable and the standard Mooney measurement alone is capable of neither detecting gels nor representing processability. The sample made without the cure-site did not show any peculiarity; it fitted in the above conclusion that the gel-content was the primary variable. Apparently the cure-site comonomer did not participate in the gel-formation in the significant manner. This is different from our previous study with a rubber made with ethylidene norbornene curesite comonomer (ref. 11). References [1.] P. Fram, Encycl Polym. Sci. and Tech. 1, 226 (1964). [2.] T.M. Vial vial a small bottle. , Encycl. Chem. Tech. 8, 459 (1979). [3.] R.D. DeMarco, Rubber Chem. Technol. 52, 173 (1979). [4.] P.A. Small, Adv. Polym. Sci., 18, 1 (1975). [5.] ASTM ASTM abbr. American Society for Testing and Materials D3616, American Society for Testing and Materials. [6.] N. Nakajima, J.J. Scobbo, Jr. and E.R. Harrell, Rubber Chem. Technol., 60, 742 (1987). [7.] N. Nakajima and E.R. Harrell, J. Rheol. 26 (5), 427 (1982). [8.] N. Nakajima and E.A. Collins, Rubber Chem. Technol., 49, 52 (1976). [9.] N. Nakajima, Polym. Eng. Sci. 19, 215 (1979). [10.] N. Nakajima, E.R. Harrell, P.R. Kumler, D.A. Seil and A.H. Jorgensen, Adv. Polym. Tech. 4, 267 (1984). [11.] N. Nakajima, R.A. Miller and E.R. Harrell, Intern intern /in·tern/ (in´tern) a medical graduate serving in a hospital preparatory to being licensed to practice medicine. in·tern or in·terne n. . Polym. Process, 2, 88 (1987). [12.] ASTM D1646, American Society for Testing and Materials. [13.] W.O. Baker, Rubber Chem. Technol., 22, 935 (1949). [14.] P.J. Flory, "Principles of polymer chemistry Polymer chemistry or macromolecular chemistry is a multidisciplinary science that deals with the chemical synthesis and chemical properties of polymers or macromolecules. " chapt. 9, Cornell University Cornell University, mainly at Ithaca, N.Y.; with land-grant, state, and private support; coeducational; chartered 1865, opened 1868. It was named for Ezra Cornell, who donated $500,000 and a tract of land. With the help of state senator Andrew D. Press, Ithaca, New York
For other places or objects named Ithaca, see Ithaca (disambiguation). , 1953. [15.] N. Nakajima and E.R. Harrell, Rubber Chem. Technol., 53, 14 (1980). [16.] J. D. Ferry, "Viscoelastic properties of polymers," John Wiley John Wiley may refer to:
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of , 1980. [17.] N. Nakajima and E.R. Harrell, in "Current topics in polymer science Polymer science or macromolecular science is the subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics. The field of polymer science includes researchers in multiple disciplines including chemistry, physics, and engineering. , Vol. II, rheology and polymer processing/multiphase systems," Otterbrite/Utracki/Inoue, Eds., Hanser pub., New York, 1987, pp. 149-166. [18.] N. Nakajima and E.R. Harrell, Rubber Chem. Technol., 56, 1019 (1983). [19.] N. Nakajima, Rubber Chem. Technol., 53, 1088 (1980). [20.] B. Bernstein and A. Shokooh, J. Rheol 24(2) 189 (1980). [21.] N. Nakajima, J. Appl. Polym. Sci., Appl. Polym. Symp. 50, 79 (1992). [22.] N. Nakajima, C.D. Huang, J.J. Scobbo, Jr. and W.J. Shieh, Rubber Chem. Technol., 62, 343 (1989). |
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lā`shən)
tro·scop
), named after Simeon Poisson, is a measure of this tendency. 
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