Simulation study of semi-crystalline polymer interphases

The study of structure and properties of semi-crystalline polymer inter-phases is important to explain and extend polymer applications. In this region, polymer chains exist in three distinct populations: tie chains that bridge the two crystals, chain folds and chain ends. The distribution of these populations influences the properties of the interphase. We have developed off-lattice Monte Carlo simulations of constrained interphases of semi-crystalline polymers which utilize robust off-lattice moves. A united atom model with polyethylene-like interactions and with freely rotating bonds is used to mimic the prototypical flexible chain structure. These simulations capture the limiting distributions of tight and loose chain folds and of tie chains within the metastable phase. The dissipation in order and density between the crystal and amorphous regions has been studied, and results for freely rotating chains indicate that the characteristic decay of anisotropy occurs in a length scale of ca. 10 Å. Simulation results for the effect of system size and molecular weight for freely rotating chains have also been investigated.     

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.     

Fracture behavior in nylon 6 fibers

A reaction rate model of fracture in polymer fibers is described. This model assumes that bond rupture is governed by absolute reaction rate theory with a stress-aided activation energy. It is demonstrated that the key in obtaining good agreement between the model and experiment lies in taking proper account of the variation of stress on the tie-chain molecules. The more taut chains rupture first, and the load is redistributed among the remaining unruptured tie chains. The effect of varying the temperature both in the model and in experiments on fracture in fibers is explored. Good agreement between predictions of the model and experiment is possible only with an undeterstanding of the distribution in stress on the tie chains. The distribution in stress on the chains was experimentally determined by monitoring the kinetics of bond rupture with electron paramagnetic resonance (EPR) spectroscopy. Temperature is found to have two effects on macroscopic strength. (1) The thermal energy aids the atomic stress in breaking the atomic bonds; as a consequence the rate of bond rupture of a family of bonds under a given molecular stress is increased. In this respect temperature might be viewed as decreasing the “strength” of a bond. (2) Temperature also serves to “loosen” the molecular structure and in this way modify the distribution in stress on the tie chains. To explain bond rupture and macroscopic fracture behavior quantitatively, account must be taken of both effects.     

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.     

Crystal stability and mechanical properties of drawn polymers: A statistical-mechanical approach

The partition function is formulated by the generating function method for a stacked lamellar model of alternating crystalline and amorphous layers. The random-walk problem of enumerating statistical weights for conformations of amorphous chains confined by two parallel walls is solved for the body-centered cubic lattice as a generalization of the one-wall model treated by Roe. The mean lengths of loop, tie, and cilia chains and the free energy of the system are calculated for the random-reentry and-bridge model as a function of the distance h of separation between crystal layers and as a function of the number N of loop chains in a crystal block as the basic structural element of the system. The mean length of amorphous chains decreases at a given thickness l of the crystal layers with decreasing h or with increasing N. The free energy of the system exhibits no minimum with respect to N, showing that the folded-chain crystal is thermodynamically stable, especially for relatively small l. Additionally, it is shown that another requirement for stabilizing relatively small crystals (small l) is the formation of an aggregate structure of crystals, whereas a large single-crystal (large l) is relatively stable, irrespective of h and N. Furthermore, a theoretical model is developed to calculate the force and elastic modulus of a highly deformed stacked system, assuming that the only change in the configurations of amorphous chains within the interlamellar regions is due to deformation, except for scission of tie chains having fewer segments than are needed to span the interlamellar distance of the deformed system. It becomes evident that taut tie chains are effective in increasing the modulus of the stacked system.     

The fatigue process in highly oriented nylon 6 fibers

The micromechanism of the fatigue process in highly oriented nylon 6 fibers is discussed on the basis of changes in mechanical and structural properties during fatiguing. Experimental results show that the fatigue process can be divided into two stages. The characteristic features in the initial period are increases in breaking strength, long period, and molecular orientation, and a reduction in dye penetration. In the second period, after about 500 cycles, breaking strength and orientation decrease slightly, and the long period, permanent strain, and dye penetration increase with duration of fatiguing. It is demonstrated that the structural changes mainly occur in the amorphous regions of the fiber structure. The structural and mechanical changes in the initial period lead to the conclusion that the initial cyclic strain causes strain hardening caused by extended tie chains which do not rupture. A combination of load bearing by tie chains and sliding motion of the fibrillar elements can explain the progressive degradation of the fiber during the second stage of fatiguing.     

Relationship between piezoelectricity and superstructure in highly oriented poly(vinylidene fluoride) film prepared by zone drawing

The oriented superstructure of poly(vinylidene fluoride) is controlled by using a forced-quenching type of zone drawing apparatus. Systematic variation of the weight fraction χ(I) of form-I crystals and the orientation function f_a of amorphous chains shows that the piezoelectricity increases with increasing χ(I) and f_a. A change in the state of molecular aggregation during poling is also effective in increasing the piezoelectricity and the orientation of the crystal b axis along the poling direction. Equations relating piezoelectricity to the form-I crystallinity, the orientation of amorphous chains, and the orientation of the crystal b axis along the poling direction are derived. These are based on a mechanical model having regions of taut tie molecules in parallel with composite regions consisting of crystalline and amorphous blocks in series.     

Negative thermal expansion of poly(vinylidene fluoride) and polyethylene tie molecules: A molecular dynamics study

The mechanism of thermal actuation for poly(vinylidene fluoride) (PVDF) and polyethylene (PE) tie molecules has been investigated using molecular dynamics simulations. Tie molecules are found in semicrystalline polymers and are polymer chains that link two (or more) crystalline lamellae, allowing for the transfer of force between these regions. A novel simulation technique has been developed to enable measurement of changes in the tie molecule length upon heating. We investigate the dependence of the percentage actuation observed upon heating, on the external applied force that stretches the tie molecules, the temperature range used for heating as well as the length and the number of tie molecules. Two molecular level mechanisms for actuation are identified. An entropically driven mechanism occurs at low applied forces and is applicable to all flexible polymers. A second mechanism due to conformational changes is observed for PVDF but not for PE at intermediate applied forces. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2223–2232     

The orientation of amorphous chains in spherulites

A theory for amorphous orientation in spherulitic polymers is presented based upon a consideration of conformational changes in the chains, loops, and cilia located between crystalline lamellae within a spherulite which is assumed to undergo an affine deformation. Chain statistics are worked out on the basis of (a) an analytical method involving random walks on a cubic lattice between barriers following a technique proposed by DiMarzio and Rubin and (b) a Monte Carlo computer simulation on a tetrahedral lattice. The latter method is considered more appropriate in view of the chain constraints such that lattice geometry becomes important. Values of the amorphous orientation are calculated as a function of the degree of crystallinity, initial lamellar separation, mole fraction of bonds in amorphous chains of each type, and chain lengths of each type of amorphous chain. It is found that tie chains are the principal contributor to amorphous orientation and the amount increases with increasing fraction and decreasing length of these. Results are compared with measurements of amorphous orientation by the birefringence x-ray and the infrared dichroism technique. It is concluded that the tie chains must be initially quite highly elongated and that the assumed affineness of spherulite deformation is not closely obeyed.     

Solid state extrusion of thermoplastic elastomers 4

A solid state extrusion technique is applied as to produce oriented block copoly(ether ester) under various physical conditions. The morphology of the extruded samples is characterized in relation to the extrusion parameters and hard segment compositions of the polymer, using thermal analysis and X-ray methods. The lateral dimensions of the crystalline domains are found to be approximately 150 Å depending on the extrusion conditions. The statistics of the long range periodicity of the structure along the extrusion direction is in agreement with a one-dimensional two phase model, the crystalline portion of which does not vary much in thickness (35 – 45 Å). The unexpected increase in the long period and the thermal shrinkage suggest the existence of strained interlamellar amorphous chains (tie molecules). The observed variations in tensile properties are interpreted under the assumption that both the number of such tie molecules and their fully extended lengths are determined by the hard segment composition and the extrusion conditions. It is also argued that the increase in the glass transition temperature is not only a function of the composition of hard segments in the amorphous phase but also of the number of strained tie molecules.Herrn Dr. Dr. h. c. H. Hellmann zum 70. Geburtstag gewidmet.Part 3 cf. lit [11]     

Structural developments in synthetic rubbers during uniaxial deformation by in situ synchrotron X‐ray diffraction

The molecular orientation and strain‐induced crystallization of synthetic rubbers—polyisoprene rubber, polybutadiene rubber, and butyl rubber [poly(isobutylene isoprene)]—during uniaxial deformation were studied with in situ synchrotron wide‐angle X‐ray diffraction. The high intensity of the synchrotron X‐rays and the new data analysis method made it possible to estimate the mass fractions of the strain‐induced crystals and amorphous chain segments in both the oriented and unoriented states. Contrary to the conventional concept, the majority of the molecules (50–75%) remained in an unoriented amorphous state at high strains. Each synthetic rubber showed a different behavior of strain‐induced crystallization and molecular orientation during extension and retraction. Our results confirmed the occurence of strain‐induced networks in the synthetic rubbers due to the inhomogeneity of the crosslink distribution. The strain‐induced networks containing microfibrillar crystals and oriented amorphous tie chains were responsible for the ultimate mechanical properties. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 956–964, 2004     

取向态聚对苯二甲酸乙二酯膜热弛豫过程的偏振红外光谱研究

用升温在位偏振红外光谱测量方法，研究了不同取向态的聚对苯二甲酸乙二酯（ＰＥＴ）膜在热弛豫过程中的尺寸变化以及分子链构象和取向的变化．结果说明，ＰＥＴ小尺度取向链段的热弛豫较大尺度取向分子链的热弛豫在较低的温度下发生，取向ＰＥＴ膜的热收缩主要与分子链大尺度取向的弛豫有关，而其后的自发伸长是结晶过程引起的，分子链的取向程度对结晶伸长的幅度有着重要影响．     

Study of stress-induced changes in poly(ethylene terephthalate) through Fourier transform infrared spectroscopy

The molecular level changes resulting from an external stress applied onto a highly uniaxially oriented poly(ethylene terephthalate) film has been studied. For this purpose, a new technique - Fourier Transform Infrared Spectroscopy - has been employed. Stress-induced differences are visible in a number of bands within the IR spectra of stressed PETP films. From the assignments of these IR bands, it is inferred how external stresses applied on the polymer films are actually transmitted to the molecular level. The intermicrofibrillar chains are the first to be stressed followed by stress transmission on the crystalline regions. These stresses are also responsible for stretching the backbone bonds, for transforming gauche conformations (predominantly present in the amorphous regions) of the ethylene glycol linkages to the trans, and for modifying the interchain interactions.     

聚全氟乙丙烯的分子聚集态结构及其对开裂性能的影响

本体结晶的全氟乙丙烯(FEP) 共聚物一般具有球晶形态结构。球晶的发展与完整程度决定于共聚物的分子结构与结晶条件,所研究的球晶尺寸在几微米至一百多微米之间。界面间的联接分子数,在试样的分子量增大和结晶温度降低时增加。它显著地影响其开裂性能。材料中联接链越多,其使用性能越好。FEP在接近其熔点温度退火,能够改善在200℃的使用性能。     

Mechanical relaxations and moduli of oriented nylon 66 and nylon 6

The mechanical relaxations of dry and wet nylon 66 and nylon 6 with draw ratios λ = 1–3 have been studied from ?180 to 160°C and in the frequency range of 1 Hz to 10 MHz. The five independent elastic moduli C_11, C_12, C_13, C_33, and C₄₄ have also been determined by an ultrasonic method at 10 MHz. Wide-angle x-ray diffraction and birefringence measurements reveal that the crystalline orientation rises sharply at low λ and becomes saturated near λ = 3; the amorphous orientation function increases continuously, reaching values of 0.3–0.5 at λ = 3. The alignment of molecular chains and the presence of taut tie molecules in the amorphous regions lead to a lowering of segmental mobility, thereby reducing the magnitude and increasing the peak temperature and activation energy of the α relaxation. Water absorption weakens the interchain bonding and so gives rise to effects opposite to those of drawing. At low temperature, the development of mechanical anisotropy is largely determined by the overall chain orientation, with the c-shear mechanism contributing a small additional effect. However, above the α relaxation, where the amorphous region is rubbery, the stiffening effect of taut tie molecules becomes dominant and leads to increases in all moduli.     

Self-hardening of highly oriented polyethylene

Ultra-oriented polyethylene fibers obtained by drawing to approximately 30 times their original length have a Young's modulus of approximately 800 kbar. Such fibers, if unconstrained, contract on heating to a length near the original. We have studied the forces causing this contractile behavior by monitoring the stress in the fiber while maintaining it at constant length. In the course of this we observed a complex sequence of both reversible and irreversible behavior. In the reversible case we observed first energy and then entropy elastic behavior. The most significant feature observed is that at sufficiently high temperature the fiber stress relaxes to an unmeasurably low value. A fiber allowed to relax in this way possesses a much lower room temperature tensile modulus (ca. 80 kbar) immediately after relaxation but, remarkably, this modulus increases to approach the initial high value over a period of a few hours when the fiber is stored either clamped or unclamped at room temperature. High x-ray orientation is preserved throughout the storage period but the density which dropped during the stress decay rose again in the course of the spontaneous stiffening. None of the stress relaxed fibers displays large-scale contractile behavior on subsequent heating. A phenomenological composite model is proposed which involves stiff microfibrils of short length—surrounded by a matrix present as a minority component. The softening of this matrix on heating and its subsequent stiffening on storage, involving a certain amount of melting and recrystallization, respectively, could then be responsible for the observed variations in the macroscopic tensile properties using simple fiber composite theories. The fibers are likely to be of extended-chain type produced by the initial drawing while the matrix may consist of a combination of oriented amorphous material (tie chains), randomly oriented chains, and transverse lamellar overgrowth present in varying proportions in the different stages of sample treatment. The wider implications, fundamental and practical, of this remarkable self-hardening process are indicated.     

Computer simulation of linkage of two ring chains

We performed off-lattice Monte Carlo simulations of links of two model ring chains with chain length N up to 32,768 in the theta solution or amorphous bulk state by using a random walk model (Model I), and molecular dynamics simulations of two model ring chains in solution with excluded volume interaction (Model II) to investigate topological effects on the geometry of link and ring conformation. In the case of Model I, the mean squared linking number, its distribution, and the size of two chains with fixed linking number are investigated. Our simulation results confirm the previous theoretical prediction that the mean squared linking number decays as pe(-qs(2)) with the distance of centers of chain mass s, where p and q are found to be chain length dependent and q asymptotically approaches to 0.75 as chain length increases. The linking number distribution of two chains has a universal form for long chains, but our simulation results clearly show that the distribution function deviates from the Gaussian distribution, a fact not predicted by any previous theoretical work. A scaling prediction is proposed to predict the link size, and is checked for our simulations for the Model II. The simulation results confirmed the scaling prediction of the blob picture that the link with linking number m occupies a compact volume of m blobs, and the size of the link is asymptotic to R(L) ≈ bN(ν)m(1/3-ν), where N is the chain length, and v is the Flory exponent of polymer in solutions.     

Indirect evidence of supramolecular changes within cellulose microfibrils of chemical pulp fibers upon drying

Dried and never-dried chemical pulps were subjected to strong sulfuric acid hydrolysis and the dimensions of the resulting cellulose nanocrystals (CNCs) were characterized by AFM image analysis. Although the average length of CNCs was fairly similar in all samples (55–65 nm), the length distribution histograms revealed that a higher number of longer crystals and a lower number of shorter crystals were present in the CNC suspensions prepared from never-dried pulps. The distinction was hypothetically ascribed to tensions building in individual cellulose microfibrils upon drying, resulting in irreversible supramolecular changes in the amorphous regions. The amorphous regions shaped by tensions were deemed as more susceptible to acid hydrolysis.     

An analytical technique for measuring relative tie-molecule concentration in polyethylene

While consideration of the crystalline domains have long dominated research in understanding the properties of semicrystalline polymers, a satisfactory understanding of crack growth in these materials can only be realized by developing corresponding analytical tools to characterize the amorphous region. Since slow stable cracks in these materials preferentially form between crystalline lamellae, the role of tie molecules—the amorphous chains that bridge crystalline lamellae—are particularly important in this regard. Unfortunately, there is no method readily available for quantitative assessment of tie molecules. Through deformation and subsequent chlorination of polyethylene films, it is demonstrated that infrared dichroism can be used to determine relative tie-molecule concentration. Using this technique, one can a priori predict which resin in a series having comparable densities but widely varying molecular weights or comonomer distributions exhibits better crack resistance.     

Rheo-optical studies of the nature of the α mechanical loss mechanism of polyethylene

Dynamic x-ray diffraction and dynamic birefringence techniques are employed to determine the nature of the molecular motions associated with the α mechanical loss processes for low-density polyethylene. The results indicate that the low-temperature part of this loss (designated α₁) is associated with an interlammellar “grain boundary” slip process while the higher temperature process (α₂) involves intracrystalline motion and plasticity of the crystal itself. The activation energy for α₁ determined by x-ray response is 25–30 kcal/mole, while that for α₂ is 30–60 kcal/mole. The findings are consistent with dynamic infrared and dynamic light-scattering results which indicate that the motion of amorphous chains is closely correlated with that of the crystals. The relative contributions of amorphous and crystalline regions to the birefringence are dependent on the thermal treatment of the sample. The effect of static strain on the dynamic response indicates that crystal orientability is first increased with strain, probably because of splaying apart of lamellae, is subsequently decreased because of the restrictions of interlamellae tie chains, but then increases again as the spherulites are destroyed at high strain. The static strain reduces the orientability of amorphous regions.