Average Crystal Thickness Research Articles

Effect of ZrC Formation on Graphitization of Carbon Phase in Polymer Derived ZrC-C Ceramics.

Graphitization degree of carbon matrix in ZrC-modified carbon composites is crucial to mechanical and ablation properties of the materials. In order to investigate the effect of ZrC formation on graphitization of the carbon matrix, microstructure of the carbon phase was investigated by X-ray (XRD), Raman, and X-ray photoelectron spectroscopy (XPS) analysis of the ceramic products obtained from zirconium containing polymer precursors at different pyrolysis temperatures. Compared with pure carbon phase, significant increase of average crystal thickness and microcrystalline planar size was observed in the carbon phase of the ZrC–C ceramics, together with the decrease of interlayer spacing and integrated intensity ratio of D peak to the G peak, indicating a significantly increased graphitization degree during the formation of ZrC. With the increasing ZrC content, amorphous (A) carbon was reduced remarkably, while turbostratic (T) component and graphitic (G) carbon components were increased, showing a slight higher graphitization degree. Moreover, the formation of ZrC was the key “ice breaking” step to decrease the defects and improve structure order of the carbon matrix. And the graphitization was dramatically enhanced during carbothermal reduction to create ZrC by breaking the carbon structure. Furthermore, coarsening and aggregation of ZrC particles as a result of high-temperature heat-treatment at 2500 °C and a high content of ZrC exhibit some negative influences on the structure of the carbon phase in ZrC–C ceramics.

Manipulation of Recrystallization and Network Formation of Oil-Dispersed Micronized Fat Crystals.

A detailed investigation was carried out on the modulation of the coupling between network formation and the recrystallization of oil-dispersed micronized fat crystal (MFC) nanoplatelets by varying oil composition, shear, and temperature. Sunflower (SF) and bean (BO) oils were used as dispersing media for MFC nanoplatelets. During MFC dispersion production at high shear, a significant increase in the average crystal thickness (ACT) could be observed, pointing to recrystallization of the MFC nanoplatelets. More rapid recrystallization of MFC occurred in the SF dispersion than in the BO dispersion, which is attributed to higher solubility of MFC in the SF oil. When the dispersions were maintained under low shear in narrow gap Couette geometry, we witnessed two stages of recrystallization (measured via rheo-SAXD) and the development of a local yield stress (measured via rheo-MRI). In the first stage, shear-enabled mass transfer induces rapid recrystallization of randomly distributed MFC nanoplatelets, which is reflected in a rapid increase in ACT (rheo-SAXD). The formation of a space-filling weak-link MFC network explains the increase in yield stress (assessed in real time by rheo-MRI). In this second stage, recrystallization slows down and yield stress decreases as a result of the formation of MFC aggregates in the weak link network, as observed by confocal Raman imaging. The high fractal dimension of the weak-link network indicates that aggregation takes place via a particle-cluster mechanism. The effects of oil type and shear on the recrystallization rate and network strength could be reproduced in a stirred bowl with a heterogeneous shear stress field, which opens perspectives for the rational manipulation of MFC thickness and network strength under industrial processing conditions.

Higher‐order structural analysis of nylon‐66 nanofibers prepared by carbon dioxide laser supersonic drawing and exhibiting near‐equilibrium melting temperature

ABSTRACTExtended chains and/or extended chain crystals (ECC) are important structures for improving the mechanical properties of polymer fibers. ECC have so far been produced using specially prepared materials or manufacturing methods. In our study on the production of nanofibers by carbon dioxide (CO2) laser supersonic drawing, we succeeded in producing nylon‐66 nanofibers having a high melting point near the equilibrium melting point (Tm0). Two melting points (Tm) of 260 and 276°C were observed for the nanofibers, with the latter temperature being close to the Tm0 (280°C) of nylon‐66. A nanofiber that was heat treated at 279°C for 10 min displayed a large stacked lamellar structure with an average crystal thickness of 140 nm. That value was close to the average molecular chain length of 212 nm, which was calculated from the average molecular weight of the nanofibers. It was inferred from these results that ECC corresponding to the average molecular chain length were present in the nanofibers. The CO2 laser supersonic drawing process is applicable to general purpose thermoplastic polymers and uses a simple drawing system. It is expected that this drawing method will help to improve the fundamental performance of general purpose polymers. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40361.

Model prediction of the ESCR of semicrystalline polyethylene: Effects of melt cooling rate

AbstractThe effects of melt cooling rate on the morphology and environmental stress cracking resistance (ESCR) of a commercial‐grade high‐density polyethylene (HDPE) were investigated by DSC, WAXS, Raman spectroscopy, DMTA, microhardness, and standard Bell test. The results showed exclusion of short chain branches from the crystallites leading to their perfection by decrease in the melt cooling rate. Accordingly, samples' ESCR increased because of the aforementioned crystal thickening. In addition, quantitative evaluation of crystal strength was performed for the first time by microhardness technique. Crystal strength or the required energy for plastic deformation of unit area of the crystals, Δh·ℓc, complemented crystal thickening hypothesis. The product of Δh and average crystal thickness, ℓc, was also proportional with storage modulus of the samples at ESCR test temperature. The evaluation of the results using the recently proposed model based on the analogy of crack growth through amorphous phase of semicrystalline polymers in harsh environments with crack growth at adhesive polymer–substrate interfaces showed reasonably good correlation. Finally, the comparison of literature and current research data based on the new model delineated new directions for phenomenon generalization. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Electron crystallography without limits? Crystal structure of Ti45Se16 redetermined by electron diffraction structure analysis.

The crystal structure of the metal-rich compound Ti(45)Se(16) was redetermined from selected-area electron diffraction film data. The structure was solved by quasi-automatic direct methods using a data set of quantified h0l electron diffraction intensities. Improved atomic coordinates were obtained from a subsequent least-squares refinement on the basis of the kinematical approximation. The compound crystallizes in the monoclinic space group C2/m with lattice parameters a = 36.534, b = 3.453, c = 16.984 A, beta = 91.73 degrees. The structure contains 23 titanium and 8 selenium atoms per asymmetric part of the unit cell. The refined atomic coordinates agree on average within 0.18 A with the previously determined structure from high-resolution electron-microscopy images. The precision of the determined atomic coordinates obtained in this study is better than 0.05 A. The structure of Ti(45)Se(16) is the eighth metal-rich structure that has been solved by direct methods from two-dimensional selected-area electron diffraction data using the quasi-kinematical approximation. The present investigation proves again that direct methods with electron diffraction data work extremely reliably provided that the structure in question is composed of elements of nearly equal scattering power and that data covering the most significant parts of the unit-cell transform up to atomic resolution are available. Moreover, a method was developed that allows the estimation of the average crystal thickness from the effective atomic potential in the refined structure.

Real-time small angle X-ray scattering study of two-stage melt crystallization of PEEK

We report a study of dual stage crystallization and subsequent melting of Poly(etherether ketone) (PEEK) and an 80/20 blend with Poly(etherimide) (PEI) using differential scanning calorimetry (DSC) and real-time small angle X-ray scattering (SAXS). The treatment scheme involves annealing/crystallization at T1 followed by annealing/crystallization at T2, where either T1 T2. The holding time during isothermal melt treatment was varied. DSC studies show there exist two endotherms when T1 T2, for both PEEK and PEEK/PEI blend. Dual populations of crystals form during the first stage regardless whether T1 T2. In the high-to-low temperature sequence, holding at the second stage causes an additional third population of crystals to grow, creating a third endotherm. As the first stage holding time increases, space available for the growth of additional crystals decreases, and the amount of crystals formed during the second stage decreases. During melting, the average long period increases while the linear stack crystallinity decreases continuously. The average crystal thickness also first increases, as the least perfect, thinnest crystals melt. Eventually, the crystal thickness levels off and begins to decline with increasing temperature. Melting of the thickest, most perfect crystals occurs most probably from the surfaces accounting for the roll-off and decrease in crystal thickness during the final stages of melting.

Analysis of Small-Angle X-Ray Scattering Patterns

Small-angle X-ray scattering (SAXS) patterns are used to identify features of semicrystalline polymers composed of alternating lamellar crystals and amorphous regions. Provided that lamellae are wide and flat, the structure is a one-dimensional stack with an average period L established by distributions of crystal thickness H(y) and amorphous thickness h(z) and with crystallinity α = [ybar]/[xbar], where average crystal thickness is [ybar], and average long period is [xbar]. The one-dimensional intensity I 1(s 1) gives LB , while the one-dimensional correlation function γ1(r) and the one-dimensional interface distribution function g 1(r) also provide measures of periodicity r * and r 3, respectively. Obvious features of γ1(r) and g 1(r) also permit estimation of crystallinity, designated αγ and α g respectively. I 1(s 1), γ1(r) and g 1(r) are calculated for models having symmetric and positively skewed distributions H(y) and h(z) and for stacks of finite height N[xbar]. For all conditions, it is found that LB ≥r * ≥ r 3, and that α g ≥ α ≥ αγ. With symmetric distributions and infinite N, LB nearly equals the weight-average period [xbar]w, and r 3 = [xbar]. These equalities do not hold when thickness distributions are skewed. Small stack height N[xbar] distorts I 1(s 1) and γ1(r), but the interface distribution function g 1(r) is scarcely affected, returning r 3 = [xbar] and α g = α. It is recommended that all three functions be analyzed to obtain the most complete picture of the semicrystalline microstructure.

Effect of polydispersity on the evolution of density fluctuations to lamellar crystals in linear polyethylene

The effect of polydispersity on structure development in linear polyethylenes is studied by simultaneous real time small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS). Our measurements show that below 128 °C, changes in the SAXS and WAXS intensity profiles for a broad molecular-weight distribution sample occur simultaneously as previously reported for a narrow molecular-weight distribution sample. We demonstrate that variations in the SAXS profile can be correlated with the morphological changes associated with the evolution of single chain folded crystal lamellae to lamellar aggregates. At 128 °C and higher temperatures, changes in the SAXS intensity profile for the broad molecular weight distribution sample occur much earlier than the onset of lamellar crystal growth evidenced in the WAXS profile. For the period before crystal growth is manifest in the WAXS scattering, the SAXS intensity at low angles increases while the domain size remains constant. The low-angle intensity uptake in SAXS can be best described by the Guinier approximation. On the other hand, the temperature dependence of the variation in the average crystal thickness during isothermal crystal growth is a function of the relative rates of primary crystallization and thickening at a given temperature. We discuss the effect of a broad distribution in chain length on the various stages in the development of the morphology.

PD resistance of thermally aged polyethylene and carbonyl-containing model polymers

Films of polyethylene (PE) with different degrees of crystallinity, including a crosslinked cable grade and a crosslinked grade containing 2-vinylnaphthalene, were aged in air at 373, 388 and 403 K for periods to 19000 h and subsequently exposed to external partial discharge (PD) in dry air at 298 K. Stress-strain measurements in a tensile testing machine, differential scanning calorimetry to assess the antioxidant concentration, crystallinity and crystal thickness, infrared spectroscopy to determine the concentrations of oxidation products, and size exclusion chromatography (sec) were used to characterize the samples before and after the oven aging. The thermal oxidation led to a combination of chain scission, as revealed by sec on the soluble fraction of aged samples, and crosslinking which was evident from the gel formation. Oxidation-induced chain scission increased the crystallinity of the crystal lamella stacks stable at the aging temperature, and lead to a pronounced brittleness of these materials. The fraction that was molten at the aging temperature and crystallized during the subsequent cooling phase dropped substantially in crystallinity after oxidation. Mere oxidation was not sufficient to cause a decrease in PD life, unless the carbonyl content was above a certain threshold value above which the PD life decreased rapidly with increasing concentration of carbonyl groups. It is suggested that the carbonyl groups enhance radical formation and thereby accelerate surface erosion, causing early PD breakdown. The PD life was not influenced by the degree of crystallinity, the average crystal thickness, the concentration of antioxidant or by the fracture toughness. Vinylnaphthalene acted in crosslinked PE as a stabilizer and prolonged the incubation period for oxidation.

Surface free energy of the chain-folding crystal faces of ethylene-butene random copolymers

The determination of the surface free energy of the chain-folding faces of crystals of ethylene-butene random copolymer is performed by fitting the most probable value of the crystal thickness distribution with the average crystal thickness assessed from small-angle X-ray scattering. The surface free energy is the adjustable parameter in the equation of the crystal thickness distribution derived from the Thomson-Gibbs relation for the melting of lamellar crystals of finite thickness. On the one hand, the steady increase of the surface free energy of bulk-crystallized copolymers with increasing co-unit concentration is relevant to a growing disorder in the amorphous overlayer of the lamellar crystals. On the other hand, the decrease of the surface free energy with increasing dilution for a given copolymer crystallized from decalin solutions is an indication of an improved regular chain folding. Both conclusions support previous studies dealing with the mechanical behaviour of ethylene-butene copolymers in relation to co-unit concentration and crystallization conditions.

A novel concept in describing elastic and plastic properties of semicrystalline polymers: polyethylene

An analysis of micro-hardness and elastic modulus data for different lamellar systems in the light of both eutectoid copolymer and chain folded lamellar microphases is presented. A novel thermodynamically derived expression offering a fair description of hardness (stress required to plastically deform a crystal) of autonomous non-homogeneous microphases in terms of the average crystal thickness, including a defective surface boundary is developed. The present results characterize the mechansim of plastic deformation as primarily governed by the initial mosaic-block structure controlling the “solid state” mechanism underlined. The average dimensions of the remaining blocks after crystal destruction are thus related to the original block dimensions before plastic deformation. Within this context it is shown that the dissipated energy for crystal destruction increases very rapidly with the molar mass-function of crystalline material.The elastic deformation of these lamellar systems at small strains is correlated to the rubber-like behaviour of the cluster-network. Finally, the role of the average thickness of the non-homogeneous microcrystallites is stressed as describing concurrently the elastic and plastics properties of the polymer allowing a quantitative description of the correlation found between micro-hardness and elastic modulus.

Structural disorder in microcrystalline MgCl2

Structural disorder in severely ground MgCl2 is interpreted on the basis of a Bernoullian model with four parameters, specifying both the size and the statistical sequence of the layers; their choice completely dictates the intrinsic shape of all the X-ray diffraction lines. The X-ray powder spectra are reasonably well reproduced over a wide range of Bragg distances (~1.7 < d < ~9 Å) for samples with various degrees of disorder. Practical criteria are given to derive the statistical parameters from the X-ray spectra. Average crystal thickness as small as 20 Å across the layers is observed. From the usual structure with cubic packing in the Cl atoms, with increasing disorder at first the probabilities of cubic and hexagonal-like interlayer shifts (Pcub and Phex) tend to become equal; the ultimate degree of disorder also involves ± 60° rotations between adjacent layers, with about the same probability as Pcub and Phex.

Structural Studies of Hydrostatically Extruded Polypropylene

A study was made on the X-ray long period and melting behavior of isotactic polypropylene extrudates with smooth surfaces. The extrusion was effected hydrostatically in the range of extrusion ratio Re from 2.0 to 6.5 at temperatures of 90—150°C. It was found that the long period of the extrudates increased with increasing temperature and also at higher extrusion ratios. The crystalline and amorphous layer thicknesses of the products extruded with Re=5.2 and 6.5 at 150°C were studied by nitric acid etching followed by a GPC measurement. We found that the extrudate for Re=6.5 had a larger average crystal thickness with narrower crystal size distribution than the extrudate for Re=5.2, but the ratio in thickness of amorphous to crystalline layers was almost the same for the two extrudates. Thickening of crystalline and amorphous layers at high extrusion ratios suggest that heat is generated in the sample near the die during hydrostatic extrusion and influences strongly the fine structure of the extrudates at high extrusion ratio and high temperature.

Crystallite Size Analysis of Pressure-Crystallized Polyethylene by Nitric Acid Etching and Gel-Permeation Chromatography. II. Folded-Chain Crystals and Ordinary Extended-Chain Crystals

Statistical analysis of average lamellar thickness and its size distribution in the molecular chain direction has been made on a variety of folded-chain crystals and ordinary extended-chain crystals of linear polyethylene which were crystallized under high pressures of 106 MPa and 305 MPa. This was done by fuming nitric acid degradation followed by gel-permeation chromatography (GPC) measurement of molecular weight distribution of the degraded samples. The observed GPC curves were corrected for instrumental spreading using the Chang–Huang’s method of correction. Several new experimental facts became clear. First, the existence of folds was confirmed in the ordinary extended-chain crystals formed at 305 MPa. Second, the average lamellar thickness of the defect-free crystalline core of folded-chain crystals was often found to be approximately one tenth the average thickness of ordinary extended-chain crystals in the same sample. Third, in ordinary extended-chain crystals with average lamellar thicknesses of several hundred nanometers, it was observed that the average crystal thickness decreased markedly with increasing degradation time, compared with the folded-chain crystals and that the chain-thinning effect tended to be become greater with an increase in average crystal thickness. This suggests strongly that ordinary extended-chain crystals have surface structures easily accessible to nitric acid etching. Since the crystal thickness of ordinary extended-chain crystals is comparable to the number-average molecular weight of the original material, crystalline lamellae will be terminated predominantly in the form of extended-chains. It may be reasonable to assume extended-chain crystals with gradually disordered, long surface layers from about 20 to 50 nanometers as a possible model for ordinary extended-chain crystals.

Crystallite Size Analysis of Pressure-Crystallized Polyethylene by Nitric Acid Etching and Gel-Permeation Chromatography. I. Extended-Chain Crystals

Average crystal thickness and its size distribution in the molecular chain direction of polyethylenes crystallized under a high pressure of about 500 MPa were determined statistically by fuming nitric acid degradation followed by gel-permeation chromatography (GPC) measurement for molecular weight distribution of the degraded samples. The observed GPC curves were corrected for instrumental spreading by Chang–Huang’s method in order to estimate precisely the crystal size distributions. Several important facts were found. First, the so-called extended-chain crystals which show a main melting peak at ca. 415 K on the DSC curve consisted of two constituents having lamellar thicknesses of highly extended-chain crystals and ordinary extended-chain crystals, which corresponded to the thermal behavior observed before by DSC and high-pressure dilatometry. Second, it was found that the average crystal thickness of ordinary extended-chain crystals is between one half and one third the average thickness of highly extended-chain crystals. Third, it seems that folded-chain structure exists in the ordinary extended-chain crystals having an average thickness of several hundred nanometers.

Structural studies of ultrahigh‐modulus linear polyethylene using nitric acid etching and gel permeation chromatography. I. Determination of the crystal size distribution

AbstractThe technique of nitric acid etching followed by gel permeation chromatography (GPC) has been used to study the structure of ultrahigh‐modulus linear polyethylene (LPE) tapes drawn to draw ratio λ of 20. For comparison, lower draw ratio (λ = 11) samples were also examined. The etching was carried out in fuming nitric acid at 60°C and the progress of the reaction was monitored by measuring weight loss and molecular weight distributions as a function of time over a period up to 25 days. Consistent with previous work by us and other workers, notably Porter and Peterlin and co‐workers, the ultrahigh‐modulus products exhibit an exceptional resistance to the acid attack, i.e., after 3 days their weight loss is still negligible while at lower draw ratios it could be as high as 30%. At longer times, however, the rate of weight loss becomes comparable for the two sets of samples, even if the absolute values are much smaller for the products of λ = 20. During the early stages of the etching treatment a rapid decrease in molecular weight and narrowing of the molecular weight distribution is observed in all cases. Eventually the molecular weight distribution becomes time independent, while the weight loss continues to increase. This stage coincides with the attack of the lateral surfaces of the crystals becoming the dominant process and it is considered that the observed molecular length distribution then reflects the distribution of crystal thicknesses. The values of the weight average crystal thickness derived from the GPC experiments (L̄w) are in very good agreement with those obtained from wide‐angle x‐ray determinations. Furthermore the ratio of weight‐average to number‐average crystal thickness (L̄w/L̄n) is about 2 for the high draw (λ = 20) samples, i.e., the value predicted by the simple statistical model proposed by Gibson, Davies, and Ward for the structure of ultrahigh‐modulus LPE. It is therefore concluded that the nitric acid etching/GPC technique can be used for reliable measurements of crystal size and crystal size distribution in ultraoriented LPE.

The structure-properties relationship in ultra-high modulus polymers

The most recent studies on the structure of ultra-high modulus polyethylene and polypropylene have been reviewed with the specific purpose of interpreting the mechanical and thermal properties of these materials. In particular, results from X-ray diffraction measurements, nitric acid etching/GPC experiments, and Raman spectroscopy have been compared for a variety of LPE samples. The X-ray evidence has been that the average crystal thickness increases as a function of draw ratio, up to values of 500–600 Å. This finding has been confirmed by the GPC analysis on etched samples. In addition, the GPC experiments have provided a full characterization of the crystal-size distribution of samples of different draw ratio. The disappearance of the LAM lines in the Raman spectra of ultra-drawn LPE has also been found consistent with a shift of the distribution of crystal thicknesses. It has been concluded that the structure of ultra-high modulus LPE products is characterized by crystalline continuity over distances much larger than the size of the lamellar crystals. This is achieved by the formation, during the deformation process, of crystalline bridges linking adjacent lamellae. The concentration of these bridges increases with draw ratio and explains quantitatively the increase in Young's modulus. The great chemical interness and thermal stability of these materials have also been interpreted in the light of this structure.

Single crystals of a random copolypeptide composed of γ-benzyl l-glutamate and l-phenylalanine

Lamellar single crystals were formed from a random copolypeptide composed of γ-benzyl l-glutamate and l-phenylalanine at the ratio of 4 to 1. The copolypeptide takes the αhelical structure. The crystals were formed by casting dilute solutions at room temperature from a solvent consisting of a 1 to 1 mixture of chloroform and trifluoroacetic acid and were observed by electron microscopy. The average crystal thickness was 670 a in the as-polymerized sample, and 580 a in a fractionated sample. The thickness was decreased by annealing at temperatures above 110 C. A hexagonal form, a group of three orthorhombic forms (group 1), and a group of an orthorhombic form and two monoclinic forms (group II) were observed by electron diffraction. The diversity of the crystal structures is suggested to be caused by a variation in crystallization conditions during evaporation of the solvent. The hexagonal form and the structures of group I are changed into the structures of group II by annealing. The crystal structures other than the hexagonal form indicate on ordered arrangements of side chains in the crystals.

Morphology of isotropic and oriented linear polyethylene. Study by small-angle X-ray scattering, Raman spectroscopy and nitric acid etching

In the first instance, measurements of the Raman longitudinal acoustic mode (l.a.m.) were combined with small-angle X-ray scattering (SAXS) and nitric acid etching, followed by gel-permeation chromatography (g.p.c.) to examine the morphology of bulk-crystallized linear polyethylene (LPE). It was concluded that there were unambiguous differences between the SAXS and the Raman data, provided that the Raman length is compared with the layer thickness deduced from the SAXS long spacing taking into account chain tilt. The nitric acid/g.p.c. results strongly support the conclusion that the l.a.m. relates to the all-trans molecular length, i.e., to the direct determination of the crystal single traverse. For isotropic samples there is a direct correspondence between the Raman length and the crystal thickness deduced from the SAXS measurements. The combined results from the Raman, SAXS and g.p.c. experiments therefore suggest a uniform morphology with regular lamellar stacks separated by amorphous material.Further measurements were then carried out on drawn samples, including ultra high modulus materials, which were prepared by drawing both slow cooled and quenched sheets to draw ratios up to 30. It was found that the Raman line due to the l.a.m. which is present in the isotropic polymer gradually reduces in intensity on drawing so that by a draw ration of ≈ 5 it is not detectable. By draw ratio ≈ 10 an l.a.m. line can again be identified at a frequency which depends on the draw temperature.There is an apparent decrease in the intensity of the l.a.m. line at high draw ratio. This can be attributed to an increase in the average crystal thickness, consistent with X-ray diffraction and g.p.c. data.A remarkable finding is that the morphology of the isotropic sheet can have a considerable effect on the Raman spectrum of the drawn material. For the same drawing conditions significant differences were observed between drawn samples prepared from slow-cooled and quenched sheets.

Oriented chain-extended polyethylene

Abstract Simple observations have been made of the fracture behaviour and Young's modulus parallel to c, for drawn polyethylene after annealing at 5·34 kbar between 220 and 260°C. The modulus shows three regions of behaviour, corresponding to the textural changes described in the preceding paper. At first the polymer has extra stiffness associated with drawing, but this has disappeared by 236°C when the average crystal thickness is only of order 500 A. There follows a region of series behaviour, to 1000 A thickness, in which the modulus increases according to the proportion of crystalline and interlamellar regions, both of which have constant properties. Beyond this the polymer softens abruptly as chain-extended lamellae replace chainfolded and then stiffens again with further increase of crystal thickness. The maximum overall chain modulus produced is about 40 kbar, essentially determined by the proportion of interlamellar regions, which have a modulus of 3 kbar. Attainment of the theoretical modulus req...