Average Stretch Research Articles

Diffusion of a polymer chain in porous media

Using an off-lattice Monte Carlo bead-spring model of a chain in a random environment, we study chain conformations and dynamic scaling of diffusivity and relaxation times with chain length N and density of the host matrix ${\mathrm{C}}_{\mathrm{obs}}$. Our simulational results show that with growing ${\mathrm{C}}_{\mathrm{obs}}$ the mean size (gyration radius) of the polymer, ${\mathrm{R}}_{\mathrm{g}}^{2}$, initially slightly decreases and then rapidly increases as the macromolecule exceeds the size of the average entropic wells and stretches through bottlenecks into neighboring wells. The chain dynamics changes from a Rouse-like one into a reptational one as the permeability of the matrix decreases. Although at variance with some previous treatments [M. Muthukumar, J. Chem. Phys. 90, 4594 (1989)], these findings agree well with a recent analytic approach (S. V. Panyukov, Zh. \'Eksp. Teor. Fiz. 103, 1287 (1993) [Sov. Phys. JETP 76, 631 (1993)]) to chain conformations in random media. We also suggest a simple scaling analysis, based on a ``blob'' representation of the polymer chain, whereby the blob size is governed by the size of the cavities in the host matrix and yields a faithful description of our computer experiments.

Flame stretch measurements during the interaction of premixed flames and Kármán vortex streets using PIV

Flame stretch measurements in a premixed, lean methane-air, V-flame interacting with a Kármán vortex street have been made using a particle image velocimeter. The flame curvature and strain rate along the flame have been measured over the range of −2.0–1.0 mm −1 and −175-175 s −1, respectively, which corresponds to a range of flame stretch from −475-200 s −1. Results indicate that the curvature and strain rate are statistically independent. Flame stretch statistics based on individual flames are also considered since each flame represents a particular phase within the regular and periodic interaction cycle studied. These results indicate that for a particular flame the average stretch rate becomes independent of the average flame strain rate. A comparison among PIV measurements, OH planar laser-induced fluorescence (OH-PLIF) measurements, and numerical simulation reveals similar flame stretch statistics. Qualitative measurements concerning flame shape and the relative location of vortices within the reactant flow are also discussed.

Mechanical and muscular factors influencing the performance in maximal vertical jumping after different prestretch loads

The objective of the present work was to study the interaction between the tendon elasticity, the muscle activation-loading dynamics, specific actions of the biarticular muscles, preloading and jumping performance during maximal vertical jumping. Six male expert jumpers participated in the study. They performed maximal vertical jumps with five different preloads. The kinematics and dynamics of the jumping movements were analysed from force plate and high speed film recordings. The amount of elastic energy stored in the tendons of the leg extensor muscles was calculated by a generalised tendon model, and the muscle coordination was analysed by surface EMG. The best jumping performances were achieved in the jumps with low preloads (counter movement jumps and drop jumps from 0.3 m). A considerable amount of the energy imposed on the legs by prestretch loading was stored in the tendons (26 ± 3%), but the increased performance could not be explained by a contribution of clastic energy to the positive work performed during the push off. During the preloading, the involved muscles were activated at the onset of the loading. Slow prestretches at the onset of muscle activation under relatively low average stretch loads, as observed during counter movement jumps and drop jumps from 0.3 m, prevented excessive stretching of the muscle fibres in relation to the tendon length changes. This consequently conserved the potential of the muscle fibres to produce positive work during the following muscle-tendon shortening in concert with the release of the tendon strain energy. A significant increase in the activity of m. rectus femoris between jumps with and without prestretch indicated a pronounced action of m. rectus femoris in a transport of mechanical energy produced by the proximal monoarticular m. gluteus maximus at the hip to the knee and thereby enhanced the transformation of rotational joint work to translational work on the mass centre of the body. The changes in muscle activity were reflected in the net muscle powers. Vertical jumping is like most movements constrained by the intended direction of the movement. The movements of the body segments during the prestretches induced a forward rotation and during the take off, a backward rotation of the body. A reciprocal shift in the activities of the biarticular m. rectus femoris and m. semitendinosus indicated that these rotations were counteracted by changes in the direction of the resultant ground reaction vector controlled by these muscles. The rotational actions around the mass centre of the body should be minimised in maximal vertical jumping because the muscle work used to control these actions is lost for the achievement of jumping height.

The origin of the C2 term in rubber elasticitya)

A unifying stress–strain model for physical networks (polymer melts) and for permanent networks (rubbers) is presented. It is based on three assumptions: (1) the uncrossability condition of real chains can be modeled by the tube concept; (2) the tube diameter is a function of the average stretch; and (3) the tube volume is invariant with respect to deformation. The model predicts that stress–strain behavior of dry and swollen rubber networks is completely determined by four material constants: the equilibrium modulus G∞ of the bulk network; the critical entanglement modulus G*e, which is equivalent to the plateau modulus GN of the un‐crosslinked parent melt; a finite extensibility parameter α; and a solvent‐polymer interaction exponent β. Predictions are compared with experimental data in elongation, and agreement is excellent. The Mooney–Rivlin constant C2 of unswollen networks with high crosslink densities is limited to roughly GN/2, and the origin of the C2 term is shown to be due to nonaffine deformat...

Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders

The kinematics of viscous and viscoelastic liquid flows transverse to periodic arrays of circular cylinders have been studied experimentally at Reynolds numbers ranging from 0.039 to 0.5. Streak photography was used to observe the flow of a dilute polyisobutylene solution in polybutene, through square and hexagonal arrays with a porosity of 70%. Unsteady flow patterns were observed at Deborah numbers above 0.5 for the hexagonal array and at Deborah numbers above 1.5 for the square array. In the case of the square array, the asymmetry of the particle paths was particularly striking. The flow resistance corresponding to each photograph has been recorded; progressively increasing flow resistance is seen to correspond to progressively increasing unsteadiness and asymmetry in the flow patterns. The velocity profiles along selected streamline segments of another concentrated solution of polyisobutylene in decalin flowing through the same arrays, were recorded with a laser Doppler velocimeter. The Reynolds number was less than 0.01 in all the runs. At Deborah numbers up to one within the square array, the average stretch rate between rows of cylinders, determined experimentally and normalized with the nominal strain rate, increases by up to 50%. At Deborah numbers of 1–2 within the hexagonal array, the average stretch rate measured between stagnation points is the same as the corresponding value for the Stokes field. The flow field becomes unsteady with this fluid also, at Deborah numbers where the fRe product increases for both arrays.

Rubbers and polymer melts: Universal aspects of nonlinear stress–strain relations

Uniaxial elongation and compression data of linear and branched polymer melts as well as of crosslinked rubbers are analyzed with respect to their nonlinear strain measure. This is found to be the result of two contributions: (1) affine orientation of network strands, and (2) isotropic strand extension. Network strand extension is caused by an increasing restriction of lateral movement of polymer chains due to deformation, and is modeled by a molecular stress function f, which in the tube concept of Doi and Edwards is the inverse of the relative tube diameter. Up to moderate strains, f2 is found to be linear in the average stretch for melts as well as for rubbers, which corresponds to a constant volume of the tube. At large strains, melts show maximum molecular tension depending on the degree of long‐chain branching, while rubbers show maximum extensibility. The influence of crosslink density on the strain measure is considered.

The nonlinear strain measure of polymer melts and rubbers: A unifying approach

AbstractUniaxial elongation and compression data of linear and branched polymer melts as well as of rubbers are analyzed with respect to their nonlinear strain measure. This is found to be the result of two contributions: (1) affine orientation of network strands, and (2) isotropic strand extension. Network strand extension is caused by an increasing restriction of lateral movement of polymer chains due to deformation, and is modelled by a molecular stress function f, which in the tube concept of Doi and Edwards is the inverse of the relative tube diameter. At small strains, f2 is found to be linear in the average stretch for melts as well as for rubbers, which corresponds to an affine deformation of the tube. At large strains, melts show maximum molecular tension depending on the degree of long‐chain branching, while rubbers show maximum extensibility.

The slip-link model: A constitutive equation for general biaxial extension of polymer melts

Starting from a slip-link model, we derive a general strain measure for polymer melts. Predictions are compared to experimental data of uniaxial, planar, ellipsoidal, and equibiaxial extensions of a polyisobutylene (PIB) melt. The data do not support Doi's assumption that the tube diameter remains unchanged by deformation. The relative tube diameter and its inverse, the molecular stress function, can be extracted directly from the data. At small strains, the relative cross section of the tube is inversely proportional to the average stretch of the tube.

Relationship Between Radiation Stability and Molecular Structure of Nitramine Explosives

AbstractThe radiation stabilities of the nitramine explosives 1,4-dinitroglycolurile (DINGU), 1,4-dimethyl-2,5-dinitroglycolurile (DMD) and hexanitrohexaazaisowurtzitane (HNIW) have been determined using XPS. Samples were exposed to x-rays for times up to eight hours while photoelectron spectra were recorded in the carbon, oxygen, and nitrogen Is energy regions and mass spectra were recorded of gases evolved during the decomposition process. These data are compared to the previously determined stabilities for cyclotrimethylene trinitramine (RDX) and cyclotetramethylene tetranitramine (HlMX). The N1s spectra of the irradiated materials show the NO2 peak decreases relative to the total nitrogen signal while low binding energy peaks grow. The rate of loss of the NO2 peak was fit to first order kinetics and the rate constants obtained show some correlation with the N-N bond strength as measured by the average N-N bond distance and the average NO2 asymetric stretch frequency. Despite the differences in structure of these molecules (DINGU and DMD are bicyclic rings, RDX and HMX are rings and HNIW is a cage) the radiation stability appears to be controlled by the strength of the N-N bond.

Nonlinear strain measures for general biaxial extension of polymer melts

Starting from the idea of equilibration, i.e., assuming that all molecular tensions are evenly distributed onto short and long chains in polydisperse polymer melts, we derive a general strain measure from a slip‐link model. By specifying disentanglement and slip of polymer chains, the strain measures of Lodge, Wagner, Doi, and Marrucci are shown to be special cases of this general strain measure. Predictions are compared to experimental data of uniaxial, planar, ellipsoidal, and equibiaxial extensions of a well‐characterized polydisperse polyisobutylene melt. The data do not support Doi’s assumption that the tube diameter remains unchanged by deformation. The relative tube diameter and its inverse, the molecular stress function, can be extracted directly from the data. The tension of the average polymer chain increases with increasing deformation, i.e., the polymer chain is stretched. At small strains, the relative cross section of the tube is inversely proportional to the average stretch of the tube.

Vibrational fluctuations of hydrogen bonds in a DNA double helix with alternating TA type inserts

The Green's function technique is applied to a study of breathing modes in a DNA double helix which contains a region of different base pairs from the rest of the double helix. The calculation is performed on an alternating poly(dC-dG).poly(dC-dG) helix in the B conformation with four consecutive base pairs replaced by a model of a biological promoter region with four alternating T-A,A-T base pairs, henceforth referred to as (TATA)2. The average stretch of interbase hydrogen bonds is found to be amplified around the insert. This is likely related to the (TATA)2 insert having a lower stability against hydrogen bond melting than the two semi-infinite poly(dC-dG).poly(dC-dG) helices. The insert region may be considered to be a site of enhanced tendency to melt in such a helix. The results show that an alternating AT insert of four base pairs has a larger average hydrogen bond stretch inside and outside the insert region than the average hydrogen bond stretch inside and outside an insert of four consecutive A-T base pairs, henceforth referred to as (AAAA).(TTTT). Calculations are performed which show that the enhancement of the average hydrogen bond stretch around an alternating TA type insert is greatly dependent upon the local modes and not the inband modes. The amount of local mode enhanced average stretch is explored as a function of insert size.

Vibrational fluctuations of hydrogen bonds in a DNA double helix with nonuniform base pairs

The Green's function technique is applied to a study of breathing modes in a DNA double helix which contains a region of different base pairs from the rest of the double helix. The calculation is performed on a G-C helix in the B conformation with four consecutive base pairs replaced by A-T. The average stretch in hydrogen bonds is found amplified around the A-T base pair region compared with that of poly(dG)-poly(dC). This is likely related to the A-T regions lower stability against hydrogen bond melting. The A-T region may be considered to be the initiation site for melting in such a helix.

Note: Strain Invariants Expressed as Average Stretches

Note: Strain Invariants Expressed as Average Stretches

Stretching of a fine cylindrical fluid filament having lengthwise viscosity variation

The stretching of a fine cylindrical filament of power-law fluids having arbitrary lengthwise variations in viscosity was studied analytically. A very simple analytical solution expressing the cross-sectional area profile along the filament is available in Lagrangian coordinates for any arbitrary initial viscosity profile. Variation in cross-sectional area caused by a 1% variation in viscosity is independent of the wave length of the viscosity variation and increases monotonically with increasing average stretch ratio.

A Scholar's Wittgenstein

The starry heavens above, the moral law within, and the work this volume represents fill me with awe.' Its 786 pages examine the Philosophical Investigations paragraph by paragraph, line by line and sometimes word by word, and fairly bulge with scholarly findings, as to where Wittgenstein expressed a similar or related view, where earlier formulations of the same point are to be found, where a remark has been lifted from one setting and used in a different context, what earlier doctrines it is to be contrasted with, how Wittgenstein's views developed in subtle stages through various manuscripts, sample writings of other philosophers expressing views Wittgenstein was opposing, comments on Miss Anscombe's translations, locations of Wittgenstein's undocumented references to such people as James, Ramsey and Frege, or of such literary allusions as to Adelheid and the Bishop-and much, much else besides. The book has much the form of Black's Companion to the Tractatus: there is a general introduction, followed by a division of the Investigations into forty-one parts, for each of which there is a general commentary followed by a detailed commentary on paragraphs, phrases and words. There is an appendix on what Wittgenstein read, and a bibliography. It seems fair to assume that the chief ambition of a book of this kind would be to help us make sense of the fine detail of the Philosophical Investigations, and most of my comments will be as to how successful it is in this regard; but at the same time it must be confessed there is room for doubt as to whether Hallett had that ambition at all. He almost never gives any explicit indication that he finds something puzzling, does not pose questions and. try to answer them, treats some of the most bewildering sections as if they needed no explanation, never confesses any failure to understand, and never betrays the least uncertainty as to the soundness of his observations. He does not come across as a puzzled man, actively engaged in posing and working out solutions to problems of interpretation. The questions that an average stretch

Reduction of the stretch modulus of human cervical tissue by prostaglandin E2

Samples of cervical tissue were obtained from women immediately following term delivery from spontaneous labor or oral PGE2-induced labor and from a small number of nonpregnant women in the reproductive years undergoing hysterectomy for benign gynecologic disease. The measured strips were placed in a well-oxygenated bath at 37°C. containing Ringer's solution and stretched at a constant rate while continuously recording length and tension. The data were converted to stress-strain diagrams. Each curve contained a long linear portion which allowed one to compute a stretch modulus for each sample. A total of 71 strips from 23 patients was used. The average stretch modulus from the oral PGE2-induced patients was significantly lower than the spontaneous labor group (p < 0.005), which, in turn, was significantly lower than the stretch modulus of the nonpregnant cervical tissue. It was also noted that the yield point was lower in the PGE2 series when compared to the spontaneous labor series (p < 0.05). The effect of the PGE2 at a bath concentration of 10−5 to 10−6 Gm. per cubic centimeter was to materially reduce the stretch modulus within 5 to 15 minutes of the drug addition in both the PGE2-induced and spontaneous labor series. The results of these experiments indicate that PGE2 has the effect of reducing cervical stiffness.