Knots “Choke Off” Polymers upon Stretching

Long polymer chains inevitably get tangled into knots. Like macroscopic ropes, polymer chains are substantially weakened by knots and the rupture point is always located at the “entry” or “exit” of the knot. However, these phenomena are only poorly understood at a molecular level. Here we show that when a knotted polyethylene chain is tightened, most of the stress energy is stored in torsions around the curved part of the chain. The torsions act as “work funnels” that effectively localize mechanical stress in the immediate vicinity of the knot. As a result, the knot “chokes” the chain at its entry or exit, thus leading to bond rupture at much lower forces than those needed to break a linear, unknotted chain. Our work not only explains the weakening of the polymer chain and the position of the rupture point, but more generally demonstrates that chemical bonds do not have to be extensively stretched to be broken.     

Bond rupture in highly oriented crystalline polymers

The strength-limiting process in the fracture of semicrystalline fibers and highly oriented films is the rupture of tie molecules connecting the folded chain lamellae in the machine direction. This view is supported by the data on stress and temperature dependence of lifetime of fibers under load and on radical formation during the fracture experiment. The observed tensile strength, however, is about 10 times smaller and the number of fractured chains between 100 and 1000 times larger than expected on the basis of the known number of tie molecules in the fracture plane. This discrepancy is a consequence of the inhomogeneity of the micromorphology of fiber structure, which causes a much larger stress concentration on the most unfavorably located tie molecules than the average value one would expect in the case of perfectly uniform stress distribution on identical tie molecules. The fluctuation of amorphous layer thickness, of number and length of tie molecules, produces such a high stress concentration on some tie molecules throughout the sample that they rupture long before the average stress concentration is sufficient for chain fracture. By accumulation of damage caused by gradual chain rupture the weakening of the sample locally proceeds so far that at the maximum damage concentration, microcracks start to form, and the fiber breaks.     

Radical formation during tensile deformation of highly drawn crystalline poly[p-(2-hydroxyethoxy)benzoic acid] fibers

The micromechanism of tensile deformation of poly[p-(2-hydroxyethoxy)benzoic acid] fibers is discussed on the basis of a detailed esr study of radical formation. The concentration of primary phenoxy radicals, which were detected during deformation at room temperature as a direct indicator of main-chain rupture, was determined by extrapolating the radical decay curves at various strains to zero time. The relation between the initial radical concentration and the strain is well expressed by the cumulative normal distribution curve. By use of this relation and a model of fiber structure, the distribution of the contour length of tie chains was determined. No radicals were detected during a second stretching cycle until the maximum strain in the first run was exceeded. The deformation model which includes alternating crystalline and amorphous regions connected by tie chains, a distribution of contour lengths of tie chains, and a phase transformation of molecular chains in the crystalline region accounted fairly well for the observed stress–strain behavior of monofilaments in first and second stretching cycles. The comparison between the observed and the calculated radical concentration suggests that statistical factors and other deformation mechanisms have to be taken into account.     

Macroscopic,microscopic and molecular aspects of fracture in polymers

The distribution of stress at macroscopic and molecular levels can dramatically affect mechanical properties. This paper explores both these aspects. In the first part, quenching operations for polycarbonate and polystyrene were shown to develop favorable residual stresses as well as structural alterations (as manifested by changes in density, hardness, DSC results, etc.). The changes in these glassy polymers can be accompanied by as much as an order of magnitude increase in impact strength and fatigue life. In the other phase of our study, various analytical methods were used to investigate phenomena associated with fracture in oriented semi-crystalline polymers. In the studies reported here, the combined effects of stress and environmental agents on mechanical strength of nylon, polyethylene, and Kevlar fibers were measured. These results, in conjunction with investigations of bond rupture kinetics, suggest that fracture in these materials involve thermally activated chain scission in which the activation energy is aided by stress and the chemical environment. Different mechanisms appear to dominate fracture in spherulitic forms of chemically similar polymers.     

Molecular conformation and craze fracture

A craze may fracture either by the breaking of covalent bonds or by a process of “viscous rupture” involving the movement of bulk material in the craze. In the latter case it is necessary that the majority of the chain ends of the polymer molecules passing through the craze-matrix interface terminate within the craze. We have therefore calculated the probability of a polystrene macromolecule spanning a thin craze and shown that for viscous rupture a craze in a normal commercial polystyrene must be something more than 40 nm thick. As the measured craze thicknesses have generally exceeded 100 nm, a viscous fracture process is clearly possible, though, of course, chain rupture is not excluded by the argument. More difficulties arise when fracture occurs within a specified region of the craze and the possibility of a bond fracture under these circumstances is briefly discussed.     

Rupture force of single supramolecular bonds in associative polymers by AFM at fixed loading rates

Atomic-force-microscopy-based single-molecule force spectroscopy (AFM-SMFS) was used to study the bond strength of self-complementary hydrogen-bonded complexes based on the 2-ureido-4[1H]-pyrimidinone (UPy) quadruple H-bond motif in hexadecane (HD). The unbinding force corresponding to single UPy-UPy dimers was investigated at a fixed piezo retraction rate in the nonequilibrium loading rate regime. The rupture force of bridging supramolecular polymer chains formed between UPy-functionalized substrates and AFM tips in the presence of a bis-UPy derivative was found to decrease with increasing rupture length. The rupture length was identified as the chain length of single, associating polymers, which allowed us to determine the number of supramolecular bonds (N) at rupture. The rupture force observed as a function of N was in quantitative agreement with the theory on uncooperative bond rupture for supramolecular linkages switched in a series. Hence, the value of the dimer equilibrium constant Keq=(1.3+/-0.5) x 10(9) M(-1), which is in good agreement with previously estimated values, was obtained by SMFS of supramolecular polymers at a single loading rate.     

Monte Carlo simulation studies of the interfaces between polymeric and other solids as models for fiber-matrix interactions in advanced composite materials

As a coarse-grained model for dense amorphous polymer systems interacting with solid walls (i.e., the fiber surface in a composite), the bond fluctuation model of flexible polymer chains confined between two repulsive surfaces is studied by extensive Monte Carlo simulations. Choosing a potential for the length of an effective bond that favors rather long bonds, the full temperature region from ordinary polymer melts down to the glass transition is accessible. It is shown that in the supercooled state near the glass transition an “interphase” forms near the walls, where the structure of the melt is influenced by the surface. This “interphase” already shows up in static properties, but also has an effect on monomer mobilities and the corresponding relaxation behavior of the polymer matrix. The thickness of the interphase is extracted from monomer density oscillations near the walls and is found to be strongly temperature dependent. It is ultimately larger than the gyration radius of the polymer chains. Effects of shear deformation on this model are simulated by choosing asymmetric jump rates near the moving wall (large jump rate in the direction of motion, and a small rate against it). It is studied how this dynamic perturbation propagates into the bulk of the polymer matrix.     

NMR study of the tie-chain length distribution in oriented polymers

Wide-line NMR has been used in an investigation of noncrystalline (amorphous) regions in oriented semicrystalline polymers. Nylon 6 was chosen as a model material. The tie-chain length distribution function, the fraction of tie chains in the total number of chains in the crystallite cross section, and the relative number of taut tie chains have been determined. The data on the tie-chain length distribution are used in discussing specific features of vitrification of the amorphous regions in oriented polymers and in prediction macroscopic mechanical properties.     

A polarizable ellipsoidal force field for halogen bonds

The anisotropic effects and short‐range quantum effects are essential characters in the formation of halogen bonds. Since there are an array of applications of halogen bonds and much difficulty in modeling them in classical force fields, the current research reports solely the polarizable ellipsoidal force field (PEff) for halogen bonds. The anisotropic charge distribution was represented with the combination of a negative charged sphere and a positively charged ellipsoid. The polarization energy was incorporated by the induced dipole model. The resulting force field is “physically motivated,” which includes separate, explicit terms to account for the electrostatic, repulsion/dispersion, and polarization interaction. Furthermore, it is largely compatible with existing, standard simulation packages. The fitted parameters are transferable and compatible with the general AMBER force field. This PEff model could correctly reproduces the potential energy surface of halogen bonds at MP2 level. Finally, the prediction of the halogen bond properties of human Cathepsin L (hcatL) has been found to be in excellent qualitative agreement with the cocrystal structures. © 2013 Wiley Periodicals, Inc.     

Thermal degradation of unstrained single polymer chain: non-linear effects at work

We examine the thermally induced fracture of an unstrained polymer chain of discrete segments coupled by an anharmonic potential by means of molecular dynamics simulation with a Langevin thermostat. Cases of both under- and over-damped dynamics are investigated, and a comparison with recent studies of bond scission in model polymers with harmonic interactions is performed. We find that the polymer degradation changes qualitatively between the inertial regime and that of heavily damped dynamics. The role of bond healing (recombination) is also studied and probability distributions for the recombination times and overstretched bond lengths are obtained. Our extensive simulations reveal many properties of the scission dynamics in agreement with the notion of random breakdown of independent bonds, e.g., the mean time of chain rupture, <τ> follows an Arrhenian behavior with temperature T, and depends on the number of bonds N in the polymer as <τ> ∝ N(-1). In contrast, the rupture rates of the individual bonds along the polymer backbone indicate clearly the presence of self-induced inhomogeneity resulting from the interplay of thermal noise and nonlinearity. Eventually we examine the fragmentation kinetics during thermolysis. We demonstrate that both the probability distribution function of fragment sizes as well as the mean length of fragments at subsequent times t characterize degradation as predominantly a first order reaction.     

Studies of tensile failure in oriented polymeric fibers by quantitative fractography

For some fibers, such as the nylon monofilaments studied here, quantitative information may be obtained from scanning electron micrographs of fracture surfaces. On these surfaces the segment of the cross section that supports the load at the instant of rupture is seen distinctly, and its area can be measured. Normalizing breaking load by this area provides a breaking stress characteristic of the final supporting segment. “Ultimate” breaking stresses calculated in this way indicate (i) For notched filaments, the ultimate breaking stress is almost constant with notch depth and also with strain rate. (ii) For un-notched filaments, there is an increase of breaking load with strain rate, due in part to the extent of the slow cleavage that precedes failure; however, the ultimate breaking stress increases as rate of strain decreases. These two findings are incompatible with mechanisms of failure based on growth of microcracks by heat- and stress-activated chain breakage. A possible explanation involves rearrangement of microfibrils within the fiber which alters their strength distribution. (iii) The apparent strength reduction on wetting nylon filaments in water is due to a faster rate of growth of the slow-cleavage area; the ultimate breaking stress is unchanged, except at high rates of strain.     

Structural-phenomenological simulation of the mechanical behavior of rubbers

It is hypothesized that, during deformation of rubbers, polymer chains slip off the layers at filler particles into voids between inclusions and high-strength polymer fibers in the uniaxially oriented state are formed in the voids. As a result, the macroscopic strength of elastomers increases by an order of magnitude and the elongation at break simultaneously increases relative to the unfilled elastomer. Aggregates of carbon black particles that occur close to one another in the initial sample depart to very large distances upon stretching the material. The fibers that tie the aggregates must extend their length by a factor of a few tens in this case. A mathematical model that takes into account these processes is proposed. It was shown that the set of constitutive equations makes it possible to simulate with good accuracy both the viscoelastic behavior of rubbers and the Mullins softening effect under finite strain conditions.     

Dynamic polarized infrared studies of stress relaxation and creep in polypropylene

A new technique was developed to study the molecular mechanics of highly oriented polypropylene during stress relaxation and creep. The polarized infrared spectrum was recorded while the polymer was under load. Stress relaxation effects were investigated during the two-stage process of fast decay followed by a slower “dynamic equilibrium” decay by examining the stress-sensitive 975-cm^?1 band and the orientation-sensitive 899-cm^?1 band. In the fast decay region, the aligned chains became more highly overstressed and the nonaligned chains quickly relieved themselves of their initial overstress. These findings suggest an exchange of stress from nonaligned to aligned chain segments, without much orientation change. Also, a rupture of very highly overstressed aligned chains is though to occur. In the slow decay region, the aligned overstressed chains showed a relief of stress accompanied by some disorientation or helix distortion. Creep, however, appeared to occur via a process which involved all chains regardless of alignment. It was found that the number of highly stressed bonds increased with time at the expense of the intermediately stressed bonds. Very little change in overall orientation was noted, which probably explains the observed crazing and void formation.     

Entropic concepts in electronic structure theory

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations.     

A Universal Reduced Rupture Creep Approach for Prediction of Long Term Failure Behavior of Aged Glass Polymers from the Short Term Test of Rupture Creep Compliance by the Unified Master Curved Extrapolation

The prediction of long term failure behaviors and lifetime of aged glass polymers from the short term tests of reduced rupture creep compliance (or strain) is one of difficult problems in polymer science and engineering. A new “universal reduced rupture creep approach” with exact theoretical analysis and computations is proposed in this work. Failure by creep for polymeric material is an important problem to be addressed in the engineering. A universal equation on reduced extensional failure creep compliance for PMMA has been derived. It is successful in relating the reduced extensional failure creep compliance with aging time, temperature, levels of stress, the average growth dimensional number and the parameter in K-W-W function. Based on the universal equation, a method for the prediction of failure behavior, failure strain criterion, failure time of PMMA has been developed which is named as a universal “reduced rupture creep approach”. The results show that the predicted failure strain and failure time of PMMA at di?erent aging times for different levels of stress are all in agreement with those obtained directly from experiments, and the proposed method is reliable and practical. The dependences of reduced extensional failure creep compliance on the conditions of aging time, failure creep stress, the structure of fluidized-domain constituent chains are discussed. The shifting factor, exponent for time-stress superposition at differentlevels of stress and the shifting factor, exponent for time-time aging superposition at different aging time are theoretically defined respectively.     

Elastic Behaviors of Adsorbed Protein-like Chains

Elastic behaviors of protein-like chains are investigated by Pruned-Enriched-Rosenbluth method and modified orientation-dependent monomer-monomer interactions model. The protein-like chain is pulled away from the attractive surface slowly with elastic force acting on it. Strong adsorption interaction and no adsorption interaction are both considered. We calculate the characteristic ratio and shape factor of protein-like chains in the process of elongation. The conformation change of the protein-like chain is well depicted. The shape of chain changes from “rod” to “sphere” at the beginning of elongation. Then, the shape changes from “sphere” to “rod”. In the end, the shape becomes a “sphere” as the chain leaves away from the surface. In the meantime, we discuss average Helmoholtz free energy per bond, average energy per bond, average adsorbed energy per bond, average α-helical energy per bond, average β-sheet energy per bond and average contact energy per bond.On the other hand, elastic force is also studied. It is found that elastic force has a long plateau during the tensile elongation when there exists adsorption interaction. This result is consistent with SMFS experiment of general polymers. Energy contribution to elastic force and contact energy contribution to elastic force are both discussed. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

Atomic dipole approximation and energies of interactions between purine and pyrimidine bases. I. Electrostatic interactions of adenine with uracil,thymine, thiouracils,dihydrouracil, and 5-fluorouracil

The atomic dipole approximation has been employed to calculate the energies of electrostatic interaction between adenine and various pyrimidine derivatives. Minima of the interaction energy for various planar configurations were determined. Inclusion of the “monopole–dipole” and “dipole–dipole” terms in the multipole expansion improves considerably the agreement with experimental data. The effect of sulfur substitution has been investigated in detail. Formation of N? H…?S hydrogen bonds is less favorable than of N? H…?O bonds, due largely to the lower atomic dipole of the sulfur atom resulting from the shift of the π-electron charge toward the neighboring carbon. The results are relevant to the interactions of thiouracils in nucleic acids.     

Failure Envelope Curves in Polyethylene Solids

The present work demonstrates that the failure envelope analysis can be applied for characterizing the ultimate tensile properties of polyethylene solids in which the inhomogeneous necking process is avoided. As a result, the ultimate properties are essentially identical to those of vulcanized rubbers above the glass transition temperature, suggesting that tie molecules connecting the fragmented lamellar clusters transmit the external led to the fracture site in the same manner as cross-linked rubbers do. Consideration of this crystal-network model may provide information about the molecular processes that lead to rupture. Furthermore, the present analytical method can possibly be developed for predicting rupture times when different types of tests, such as constant drawn, constant stress and constant rate of stress, are conducted.