Micromechanical modeling of the elastic properties of semicrystalline polymers: A three‐phase approach

The mechanical performance of semicrystalline polymers is strongly dependent on their underlying microstructure, consisting of crystallographic lamellae and amorphous layers. In line with that, semicrystalline polymers have previously been modeled as two and three‐phase composites, consisting of a crystalline and an amorphous phase and, in case of the three‐phase composite, a rigid‐amorphous phase between the other two, having a somewhat ordered structure and a constant thickness. In this work, the ability of two‐phase and three‐phase composite models to predict the elastic modulus of semicrystalline polymers is investigated. The three‐phase model incorporates an internal length scale through crystalline lamellar and interphase thicknesses, whereas no length scales are included in the two‐phase model. Using linear elastic behavior for the constituent phases, a closed form solution for the average stiffness of the inclusion is obtained. A hybrid inclusion interaction model has been used to compute the effective elastic properties of polyethylene. The model results are compared with experimental data to assess the capabilities of the two‐ or three‐phase composite inclusion model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Hyperelastic characterization of the interlamellar domain and interphase layer in semicrystalline polyethylene

The interphase layer in semicrystalline polyethylene (PE) serves as the transition between the crystalline lamellae and the amorphous domains and is recognized as the third constituent of PE. When PE undergoes large deformations, this interphase layer together with the amorphous phase behaves hyperelastically. Because of the metastable nature and nanometric size of the interphase and its intimate mechanical coupling to the neighboring crystal and amorphous domains, detailed characterization of its hyperelastic properties have eluded detailed experimental evaluation. To extract these properties, a combined algorithm is proposed based on applying the constitutive relations of an isotropic, compressible, hyperelastic continuum to the molecular dynamics simulation results of a PE stack from Lee and Rutledge (Macromolecules 2011, 3096–3108). The simulation element is incrementally deformed to a large strain, during which the stress–strain information is recorded. Assuming a neo‐Hookean model, the tensorial constitutive equation is derived. The hyperelastic parameters for the central amorphous phase, the interphase layer, and the interlamellar domain are identified with the help of the optimization notion and a set of nonnegative objective functions. The identified hyperelastic parameters for the interlamellar domain are in good agreement with the ones estimated experimentally and frequently used in the literature for the noncrystalline phase. The specifically developed sensitivity analysis indicates that the shear modulus is identified with a higher degree of certainty, in contrast to the bulk modulus. It is also revealed that the presented continuum mechanics analysis is able to capture the melting/recrystallization and rotation of crystalline chains that take place during the deformation. The evolutions of the boundaries of the hyperelastic elements are also identified concurrently with the hyperelastic parameters as the by‐product of the presented methodology. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1692–1704     

The mechanism and a slip model for the initial plastic deformation of amorphous polyethylene under uniaxial tension

The mechanical behaviors of a polyethylene (PE) bulk consisting of amorphous molecular chains under uniaxial tension have been explored using molecular simulations. The stress–strain relationship and the plastic deformations of the PE bulk have been analyzed. Two deformation stages were found in the stress–strain curve, the elastic stage with a straight linear part of the curve and the plastic stage with a flat sawtooth‐like part. The Young's modulus calculated from the elastic part is in good agreement with experimental results. Some key parameters such as the energy variations in different terms reveal that the interchain slip should be chiefly responsible for the initial plastic deformations of amorphous PE under uniaxial tension. In order to address how this slip influences the plastic deformations, the mechanical details of a single chain have been elucidated when it was pulled out from two PE clusters consisting of regular and amorphous chains, respectively. The interchain slip, found as the basic movement style, is responsible for the movement of the stretched chain. Both the critical slip force and the critical slip length have been found in these two cases. For the straight chain pulled out from the cluster with regular chains, the critical slip force is about 1.81 nN and the critical slip length is about 40 polymerization degrees. While for the chain in the amorphous cluster, the critical force is about 0.86 nN and the critical length is almost the same. Based on the simulation results, a meso slip model has been deduced to explain the behaviors of the amorphous PE bulk under uniaxial tension. With reference to the slip model of single crystals and polycrystals a constitutive relation was obtained by considering the Young's modulus, the equivalent slip stress and the average orientation parameters of each chain. The comparison of the results from the constitutive relation and the simulations proves that this model does well in predicting the mechanical behaviors of amorphous PE under uniaxial tension in general. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 986–998     

Micromechanical modeling of anisotropic behavior of oriented semicrystalline polymers

Some manufacturing processes of polymeric materials, such as injection molding or film blowing, cause the final product to be highly anisotropic. In this study, the mechanical behavior of drawn polyethylene (PE) tapes is investigated via micromechanical modeling. An elasto‐viscoplastic micromechanical model, developed within the framework of the so‐called composite inclusion model, is presented to capture the anisotropic behavior of oriented semicrystalline PE. Two different phases, namely amorphous and crystalline (both described by elasto‐viscoplastic constitutive models), are considered at the microstructural level. The initial oriented crystallographic structure of the drawn tapes is taken into account. It was previously shown by Sedighiamiri et al. (Comp. Mater. Sci. 2014, 82, 415) that by only considering the oriented crystallographic structure, it is not possible to capture the macroscopic anisotropic behavior of drawn tapes. The main contribution of this study is the development of an anisotropic model for the amorphous phase within the micromechanical framework. An Eindhoven glassy polymer (EGP)‐based model including different sources of anisotropy, namely anisotropic elasticity, internal stress in the elastic network and anisotropic viscoplasticity, is developed for the amorphous phase and incorporated into the micromechanical model. Comparisons against experimental results reveal remarkable improvements of the model predictions (compared to micromechanical model predictions including isotropic amorphous domains) and thus the significance of the amorphous phase anisotropy on the overall behavior of drawn PE tapes. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 378–391     

The mechanical moduli of lamellar semicrystalline polymers

Bounds on the elastic constants are derived for semicrystalline polymers whose local morphology is lamellar. Local response matrices (stiffness and compliance) are formulated in three dimensions that simultaneously incorporate uniform in-plane strain and additive forces from layer to layer of crystalline and amorphous phases and uniform stress and additive displacements normal to the lamellar surfaces. Spatial averaging of the stiffness and compliance matrices under the assumption of axially symmetric orientation gives the upper and lower bounds on the longitudinal and transverse tensile moduli and the axial and transverse shear moduli as functions of the separate phase elastic constants, the volume percent crystallinity, and the moments of the orientation 〈cos²θ〉 and 〈cos⁴θ〉. The bounds are much tighter than the Voight upper and Reuss lower bounds that do not recognize phase geometry. Using the known crystal elastic constants of polyethylene, sample calculations on isotropic unoriented materials show that the divergence of bounds at high crystallinity necessitated by the extreme crystal anisotropy shows up only at very high crystallinity. At low temperature the bounds are tight enough to specify G₁, the amorphous modulus, from the measured G and the known crystal elastic constants. At higher temperatures and lower G, the bounds are not tight enough for this purpose but the shear modulus versus crystallinity and temperature data are well fitted by the lamellar lower bound using a temperature-dependent, crystallinity-independent G₁.     

Stretched polymer surfaces: Atomic force microscopy measurement of the surface deformation and surface elastic properties of stretched polyethylene

The surface structure and surface mechanical properties of low‐ and high‐density polyethylene were characterized by atomic force microscopy (AFM) as the polymers were stretched. The surfaces of both materials roughened as they were stretched. The roughening effect is attributed to deformation of nodular structures, related to bulk spherulites, at the surface. The surface‐roughening effect is completely reversible at tensile strains in the elastic regime and partially reversible at tensile strains in the plastic regime until the polymers are irreversibly drawn into fibers. AFM force versus distance interaction curves, used to measure changes in the stiffness of the surface and the surface elastic modulus as a function of elongation, show that the surfaces become softer as the polymers are drawn into fibers at high strains. At low elastic strains, however, the surface elastic modulus of HDPE increases—attributed to elastic energy stored by the amorphous regions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2263–2274, 2001     

Poly(4-methylpentene-1)/hydrogenated oligo (cyclopentadiene) blends: Miscibility,tensile stress–strain,and dynamic mechanical behaviors

This article discusses the influence of the oligomeric resin, hydrogenated oligo(cyclopentadiene) (HOCP), on the morphology, and thermal and tensile mechanical properties of its blends with isotactic poly(4-methylpentene-1) (P4MP1). The P4MP1 and HOCP are found not miscible in the melt state. P4MP1/HOCP blends after solidification contain three phases: the crystalline phase of P4MP1, an amorphous phase of P4MP1, and an amorphous phase of HOCP. From optical micrographs obtained at 150°C, it is found that the solidified blends show a morphology constituted by P4MP1 microspherulites and small HOCP domains homogeneously distributed in intraspherulitic regions. DSC and DMTA results show that the blends present two glass transition temperatures (T_g) equal to the T_gs of the pure components. The tensile mechanical properties have been investigated at 20, 60, and 120°C. At 20°C both the HOCP oligomer and the amorphous P4MP1 are glassy, and it is found that all the blends are brittle and the stress–strain curves have equal trends. At 60°C the HOCP oligomer is glassy, whereas the amorphous P4MP1 is rubbery. The tensile mechanical properties at 60°C are found to depend on blend composition. It is found that the Young's modulus, the stresses at yielding and break points slightly decrease with HOCP content in the blends and these results are related to the decrease of blend crystallinity. The decrease of the elongation at break is accounted for by the presence of glassy HOCP domains that act as defects in the P4MP1 matrix, hampering the drawing. At 120°C both the amorphous phases are rubbery. It is found decreases of Young's modulus, stresses at yielding and break points. These results have been related to the decrease of blend crystallinity and to the increase of the total rubbery amorphous phase. Moreover, it is found that the blends present elongations at break equal to that of pure P4MP1. This constancy is attributed to: (a) at 120°C the HOCP domains are rubbery and their presence seems not to disturb the drawing of the samples; (b) a sufficient number of the tie-molecules and entanglements of P4MP1 present in the blends. In fact, although the numbers of tie-molecules and entanglements decrease in the blends, increasing the HOCP oligomer, they seem to be enough to keep the material interlaced and avoid earlier rupture. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1269–1277, 1997     

Morphology and mechanical properties of a novel amorphous polyamide/nanoclay nanocomposite

A novel amorphous polyamide/montmorillonite nanocomposite based on poly(hexamethylene isophthalamide) was successfully prepared by melt intercalation. Wide angle X-ray diffraction and transmission electron microscopy showed that organoclay containing quaternary amine surfactants with phenyl and hydroxyl groups was delaminated in the polymer matrix resulting in well-exfoliated morphologies even at high montmorillonite content. Differential scanning calorimetry results indicated that clay platelets did not induce the formation of a crystalline phase in this amorphous polymer. Tensile tests demonstrated that the addition of nanoclay caused a dramatic increase in Young's modulus (almost twofold) and yield strength of the nanocomposites compared with the homopolymer. The nanocomposites exhibited ductile behavior up to 5 wt % of nanoclay. The improvement in Young's modulus is comparable with semicrystalline aliphatic nylon 6 nanocomposites. Both the main chain amide groups and the amorphous nature of the polyamide are responsible for enhancing the dispersion of the nanofillers, thereby, leading to improved properties of the nanocomposites. The structure-property relationship for these nanocomposites was also explored. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2605–2617, 2008     

Correlation between local mobility and mechanical properties of high‐speed melt‐spun nylon‐6 fibers

This article establishes the processing–microstructure–motion–property relationship of high‐speed melt‐spun nylon‐6 fibers. From solid‐state ¹H NMR T_1ρ (spin–lattice relaxation time in the rotating frame) relaxation studies, all nylon‐6 fibers spun at 4500–6100 m/min showed three‐component exponential decay with the time constants T_1ρ,I, T_1ρ,II, and T_1ρ,III, indicating that there existed three different motional phases. These phases were assigned to immobile crystalline, intermediate rigid amorphous, and mobile amorphous regions. The determination of the correlation time (τ_c) of the respective phases provided information about the local molecular mobility of each phase with respect to the spinning speed. As the spinning speed increased, τ_c of the crystalline region increased (4500–5200 m/min) and then reached a plateau. However, τ_c for the rigid amorphous region increased from 5200 m/min onward, indicating that the rigid amorphous chains were more oriented and constrained in the spinning speed range of 5500–6100 m/min. The drastic increase of the maximum thermal stress for all fibers from 5500 to 6100 m/min was coincident with the τ_c characteristics of the rigid amorphous region. The significant increase in tenacity and Young's modulus and the large decrease in elongation at break at 5500–6100 m/min were also in good agreement with the local molecular motion of the intermediate rigid amorphous phase in the nylon‐6 fibers. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 993–1000, 2001     

Elastic modulus and thermal conductivity of ultradrawn polyethylene

The axial and transverse Young's modulus and thermal conductivity of gel and single crystal mat polyethylene with draw ratios λ = 1–350 have been measured from 160 to 360 K. The axial Young's modulus increases sharply with increasing λ, whereas the transverse modulus shows a slight decrease. The thermal conductivity exhibits a similar behavior. At λ = 350, the axial Young's modulus and thermal conductivity are, respectively, 20% and three times higher than those of steel. For this ultradrawn material both the magnitude and the temperature dependence of the axial Young's modulus are close to those of polyethylene crystal. The high values of the axial Young's modulus and thermal conductivity arise from the presence of a large percentage (∼85%) of long needle crystals. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3359–3367, 1999     

Optical,mechanical, and photoelastic anisotropy of biaxially stretched polyethylene terephthalate films studied using transmission ellipsometer equipped with strain camera and stress gauge

The anisotropic properties of polyethylene terephthalate film resulting from its manufacturing process are quantitatively investigated in terms of its optical, mechanical, and photoelastic aspects. Transmission ellipsometers and a Jones‐matrix‐based analysis software together with a 4 × 4 Berreman‐matrix‐based analysis software are adopted to determine the wavelength‐dependent in‐plane birefringence, the principal refractive indices, and the orientation of the optical axis. Mechanical anisotropy is characterized in terms of the elastic compliance tensor components using the measured azimuthal angle‐dependent Young's modulus and Poisson's ratio. From the measured variation of the wavelength‐dependent in‐plane birefringence as a function of tensile stress, the dispersive photoelastic coefficients are obtained for a few sample azimuthal angles, and the components of the photoelastic tensor are determined. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 152–160     

Theoretical modeling of the relationship between Young's modulus and formulation variables for segmented polyurethanes

We describe a new modeling approach to prediction of Young's modulus of segmented polyurethanes. This approach combines micromechanical models with thermodynamic considerations based on the theory of block copolymers. The resulting model predicts both the equilibrium morphology and the “ideal” Young's modulus of a segmented polyurethane polymer as a function of its formulation (hard segment chemical structure, hard segment weight fraction, soft segment equivalent weight) and temperature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2123–2135, 2007     

Effect of surface modification of colloidal silica nanoparticles on the rigid amorphous fraction and mechanical properties of amorphous polyurethane–urea–silica nanocomposites

Colloidal silica nanoparticles (NPs) modified with eight different silane coupling agents were incorporated into an amorphous poly(tetramethylene oxide)‐based polyurethane–urea copolymer matrix at a concentration of 10 wt % (4.4 vol %) in order to investigate the effect of their surface chemistry on the structure–property behavior of the resulting nanocomposites. The rigid amorphous fraction (RAF) of the nanocomposite matrix as determined by differential scanning calorimetry and dynamic mechanical analysis was confirmed to vary significantly with the surface chemistry of the NPs and to be strongly correlated with the bulk mechanical properties in simple tension. Hence, nanocomposites with an RAF of about 30 wt % showed a 120% increase in Young's modulus, a 25% increase in tensile strength, a 15% decrease in elongation at break with respect to the neat matrix, which had no detectable RAF, whereas nanocomposites with an RAF of less than 5% showed a 60% increase in Young's modulus, a 10% increase in tensile strength and a 5% decrease in the elongation at break. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2543–2556     

Boehmite nanorod‐reinforced‐polyethylenes and ethylene/1‐octene thermoplastic elastomer nanocomposites prepared by in situ olefin polymerization and melt compounding

Nanocomposites of polyethylene (HDPE) and poly(ethylene‐co‐1‐octene) thermoplastic elastomers, both containing boehmites with variable sizes, shapes, and aspect ratios (1–20), were prepared by means of in situ olefin polymerization and melt compounding. The in situ olefin polymerization in the presence of boehmite nanorods afforded nanocomposites containing 4–8 wt % of boehmite. In an alternative process, the in situ olefin polymerization was used to produce polyolefins with high boehmite content of 50 wt % as masterbatches for polyolefin melt compounding with ethylene homo‐ and copolymers. The addition of the boehmite nanofillers improved the stiffness without sacrificing high elongation at break. The stiffness, as expressed by Young's modulus, increased with increasing boehmite aspect ratio. In case of thermoplastic elastomer nanocomposites the increase of stiffness was accompanied by a simultaneous increase of elongation at break. According to transmission electron microscopy (TEM), fine dispersion of the polar boehmite nanorods and nanoplatelets within the nonpolar hydrocarbon polymer matrix was obtained without requiring the addition of special dispersing agents or functionalized polyolefin compatibilizers. The comparison of melt compounding of polyethylene with boehmites or polyethylene/boehmite masterbatches revealed that compounding of masterbatches prepared by in situ polymerization filling afforded much finer and more uniform nanoboehmite dispersions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2755–2765, 2008     

Ultrasonic measurements of the elastic moduli of ultradrawn polyoxymethylene

We have employed an ultrasonic method to measure from ?40 to 60°C the five independent elastic moduli C₁₁, C₁₃, C₃₃, C₄₄, and C₆₆ of polyoxymethylene with draw ratio λ from 1 to 26 prepared by continuous drawing under microwave heating. The elastic moduli are controlled by three major factors: molecular orientation in the crystalline regions, fraction of noncrystalline taut tie molecules, and void content. The steep rise in the axial extensional modulus C₃₃ and axial Young's modulus E₀ with increasing draw ratio results from the alignment of chains in the crystalline blocks and an increase in the number of disordered taut tie molecules. Below the γ relaxation (located at 0°C at our measurement frequency of 10 MHz), these two factors also give rise to a slight decrease in the transverse extensional modulus C₁₁, Young's modulus E₉₀ and shear modulus C₆₆. At high temperature where the amorphous regions have very low modulus, the stiffening effect of taut tie molecules becomes dominant, leading to an increase in all moduli as λ increases from 1 to 10. At higher λ the void fraction increases appreciably, causing small decreases in E₉₀, C₁₁, and C₆₆ at all temperatures.     

Structural arrangement of crystalline/amorphous phases of polyethylene‐block‐polystyrene copolymer as induced by orientation techniques

A polyethylene‐block‐polystyrene copolymer film having a bicontinuous crystalline/amorphous phases was tensile‐drawn under various conditions for the structural arrangement of these phases. The prepared film could be drawn below the melting temperature of the polyethylene component, with the highest drawability obtained at 60°C. However, the initial bicontinuous structure was gradually destroyed with increasing strain because the drawing temperature was lower than the glass‐transition temperature of the polystyrene component. Correspondingly, a necking phenomenon was clearly recognizable when samples were drawn. In contrast, drawing near the melting temperature of the polyethylene component produced less orientation of both the crystalline and amorphous phases, resulting in homogeneous deformation with lower drawing stress. These results indicated that the modification of the lower ductility of the polystyrene component was key to the effective structural arrangement of both phases by tensile drawing. Here, a solvent‐swelling technique was applied to improve polystyrene deformability even below its glass‐transition temperature. Tensile drawing after such a treatment successfully induced the orientation of both the crystalline and amorphous phases while retaining their initial continuities. A change in the deformation type from necking to homogeneous deformation was also confirmed for the stress–strain behavior. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1731–1737, 2006     

Multiaxial deformation of polyethylene and polyethylene/clay nanocomposites: in situ synchrotron small angle and wide angle X‐ray scattering study

A unique in situ multiaxial deformation device has been designed and built specifically for simultaneous synchrotron small angle X‐ray scattering (SAXS) and wide angle X‐ray scattering (WAXS) measurements. SAXS and WAXS patterns of high‐density polyethylene (HDPE) and HDPE/clay nanocomposites were measured in real time during in situ multiaxial deformation at room temperature and at 55 °C. It was observed that the morphological evolution of polyethylene is affected by the existence of clay platelets as well as the deformation temperature and strain rate. Martensitic transformation of orthorhombic into monoclinic crystal phases was observed under strain in HDPE, which is delayed and hindered in the presence of clay nanoplatelets. From the SAXS measurements, it was observed that the thickness of the interlamellar amorphous region increased with increasing strain, which is due to elongation of the amorphous chains. The increase in amorphous layer thickness is slightly higher for the nanocomposites compared to the neat polymer. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Effect of a post‐annealing process on microstructure and mechanical properties of high‐density polyethylene/silica nanocomposites

High‐density polyethylene (HDPE) and nanosilica nanocomposites were prepared for SiO₂ content up to 15 wt%. Microstructural characterization evidenced a homogenous distribution of silica aggregates with a mean size increasing with the filler content finally resulting in a rheological percolation between 7.5 and 10 wt%. Nanoparticles did not induce any significant impact on the matrix crystallinity but led to a real improvement on elastic properties accompanied with a large embrittlement above the percolation threshold. The effect of annealing near HDPE melting temperature was studied. Differential scanning calorimetry, X‐ray diffraction, and small‐angle X‐ray scattering analyses showed a significant change in the HDPE microstructure after annealing at 125°C. A large increase in the crystallinity (from 68 to 76%) and a clear improvement of Young's modulus (by 55%) were observed prior to polymer degradation. A valuable impact of silica particles on thermal stability was also obvious regarding the evolution of elastic properties for extended exposure times (850–1,200 h). © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 535–546     

Influence of the crosslink network structure on stress‐relaxation behavior: Viscoelastic modeling of the compression set experiment

A viscoelastic approach of the compression set test is addressed in this work. This test measures the ability of rubber compounds to retain elastic properties after prolonged action of compressive stresses. Elastic properties were tested by recording the normal stress under a constant deformation of 25% with a laboratory rheometer. Considering the Boltzmann superposition principle, compression set data were modeled from the relaxation of Young's modulus, described by a Maxwell spectrum plus a constant E_∞ defining the elastic properties at the long times. This approach was developed with the copolymer of ethylene and vinyl acetate (EVA) networks crosslinked by radical chemistry and by an exchange reaction between acetate groups and silane compounds as crosslinking agents. Regarding the recovery of the elastic properties, radical chemistry provided better results than the exchange reaction for the identical crosslinking density of the network. Then, the Curro–Pincus molecular approach was developed to understand the influence of the microstructure of the EVA network on the elastic properties. The difference of the elastic properties between the two networks crosslinked by two different chemistry means was accounted for by considering the probability of having a dangling end of n units for a random crosslinking process. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1779–1790, 2003     

A raman spectroscopic determination of the interlamellar forces in crystalline n-alkanes and of the limiting elastic modulus Ec of polyethylene

A simple treatment based on continuum mechanics shows that weak interlamellar forces in crystalline n-alkanes should result in a characteristic upward shift of the frequencies of the longitudinal acoustical (LA) modes, which is independent of the chain length and decreases inversely with the mode order. A raman spectroscopic determination of the LA mode frequencies of a series of different n-alkanes confirms the theoretical conclusion and permits a derivation of a force constant characteristic of the interlamellar forces. The discussion results in a new formula valid for the LA mode frequencies of the orthorhombic n-alkanes in the acoustical limit and yields a new determination of the limiting elastic modulus E_c of crystalline polyethylene. The value obtained, E_c = 2.9 × 10¹² dyne/cm², is markedly smaller than the value derived by Schaufele and Shimanouchi neglecting the influence of the interlamellar forces on the LA mode frequencies.