Articles in Refereed Journals

Lawrence F. Drummy, Christian Kuebel, Aleksander White, Daniel Lee, and David C. Martin, “Direct Imaging of Defects Structures in Pentacene Nanocrystals by HREM”, Advanced Materials, in press, (2001).

Lawrence F. Drummy, Ingrid Voigt-Martin, and David C. Martin, “Analysis of the Displacement Fields Near Dislocation Cores in Ordered Polymers”, Macromolecules, 34(21), 7416-7426, (2001).

Xinyan Cui, Valerie Lee, Yehoash Raphael, James Wiler, Jamie Hetke, David J. Anderson, and David C. Martin, “Surface Modification of Neural Recording Electrodes with Conducting Polymer / Biomolecule Blends”, Journal of Biomedical Materials Research, 56(2), 261-272, (2001).

Xinyan Cui, Jamille Hetke, James Wiler, David Anderson and David C. Martin, ‘Electrochemical Deposition and Characterization of Conducting Polymer Polypyrrole / PSS on Multichannel Neural Probes”, Sensors and Actuators A: Physical, 93, 8-18, (2000).

Christian Kübel and David C. Martin, “Influence of Structural Variations on High-Resolution Electron Microscopy Images of Poly[1,6-di(N-carbazolyl)2,4-hexadiyne] Nanocrystals”, Philosophical Magazine A, 81(7), 1651-1673, (2001).

Houxiang Tang, Brendan Foran, and David C. Martin, “Characterization of the Adhesion of Painted Layers on Thermoplastic Polyolefin (TPO) Substrates”, Polymer Engineering and Science, 41(3), 440-448, (2001).

Christopher J. Buchko, Kenneth M. Kozloff, and David C. Martin, “Surface Characterization of Porous, Biocompatible Protein Polymer Thin Films”, Biomaterials, 22, 1289-1300, (2001).

J. K. Politis, M. D. Curtis, L. Gonzalez-Ronda, and D. C. Martin, “Poly(nonylbisoxazole): A Member of a New Class of Conjugated Polymers”, Chemistry of Materials, 12(9), 2798-2804, (2000).

Christian Kübel, Lawrence Drummy, Lebzylisbeth Gonzalez, and David C. Martin, Defect-Mediated Twisting and Curvature in Polymer Crystals”, Journal of Physical Organic Chemistry, 13: 1-13, (2000).

Crystalline polymer solids almost inevitably exhibit defects due to chain ends, chain folding and the limited molecular mobility. The defects result in local (dislocations, grain boundaries) or global (bending, twisting) distortions of the molecular symmetry with prounounced implications on materials properties. Depending on the localization of the deformation, continuous molecular distortions or chain scission are expected, resulting in distinct differences for the mechanical (crack formation) and optoelectronic properties (charge transport and delocalization), which becomes especially important in the light of the recent extraordinary developments in molecular electronics. Further studies of defect structure and properties in polymers are expected to result in an increasingly sophisticated understanding of the microstructure and microstructural evolution during processing necessary to control and optimize the nano- and micrometer scale structure of organic materials.

Allen F. Mensinger, David J. Anderson, Christopher J. Buchko, Michael A. Johnson, David C. Martin, Patrick A. Tresco, Robert B. Silver, and Stephen M. Highstein, “Chronic Recording of Regenerating VIIIth Nerve Axons With a Sieve Electrode”, The Journal of Neurophysiology, 83(1), 611-615, (2000).

A micromachined silicon substrate sieve electrode was implanted within transected toadfish (Opsanus tau) otolith nerves. High fidelity, single unit neural activity was recorded from seven alert and unrestrained fish 30 to 60 days after implantation. Fibrous coatings of genetically engineered bioactive protein polymers and nerve guide tubes increased the number of axone regenerating through the electrode pores when compared with controls. Sieve electrodes have potential as permanent interfaces to the nervous system and to bridge missing connections between severed or damaged nerves and muscles. Recorded impulses might also be amplified and used to control prosthetic devices.

Christopher J. Buchko, Loui C. Chen, Yu Shen, and David C. Martin, “Processing and Microstructural Characterization of Porous Biocompatible Protein Polymer Thin Films”, Polymer, 40, 7397-7407, (1999).

The process of electrostatic fiber formation, or electrospinning, was used to create biocompatible thin films for use in implantable devices. The morphology of the thin films was found to depend on process parameters including solution concentration, applied electric field strength, deposition distance, and deposition time. The microstructure of the coatings was examined by Transmission Electron Microscopy (TEM) and Wide-Angle X-ray Scattering (WAXS), with electrospun filaments being weakly oriented along the fiber axis. A shish kebab model for the filament morphology was proposed. The electrospinning process was shown to be a means of creating porous thin films with structural gradients and controlled morphology that could enhance biocompatibility.

Christopher J. Buchko, Margaret J. Slattery, Kenneth M. Kozloff, and David C. Martin, “Mechanical Properties of Biocompatible Protein Polymer Thin Films”, Journal of Materials Research, 15(1), 231-242, (2000).

A silklike protein with fibronectin functionality (SLPF) (ProNectin F©, Protein Polymer Technologies, Inc.) is a genetically engineered protein polymer containing structural and biofunctional segments. The mechanical properties and deformation mechanisms of electrostatically deposited SLPF thin films were examined by scratch testing, tensile testing, and nanoindentation. Scanning electron microscopy and scanned probe microscopy revealed that the macroscopic properties were a sensitive function of microstructure. The SLPF films were relatively brittle in tension, with typical elongation-to-break values of 3%. Nanoindentation date were fit to a power law relationship.

L. Gonzalez-Ronda, D. C. Martin, J. I. Nanos, J. K. Politis, and M. D. Curtis, “Structural Characterization of Electrooptically Active Poly(nonylbithiazole)”, Macromolecules, (1999).

We have examined the microstructure, solution processing, thermal transitions, and mechanical properties of regioregular poly(nonylbithiazole) (PNBT). PNBT can adopt three distinct colors in the solid state—yellow, red, and metallic green—depending on processing conditions such as polymer concentration, solvent evaporation rate, temperature, and pressure. Microstructural variations were observed between samples of different colors, including the intensification of optical absorption with the degree of crystalline order and/or crystal size. Yellow samples lacked well-developed three-dimensional order, whereas the red and green samples were semicrystalline. The development of a lyotropic mesophase was observed at intermediate concentrations in a “diffusion couple” geometry. A crystal model with two planar, pi-stacked chains per unit cell was shown to be consistent with the experimental diffraction data. The simulated orthorhombic unit cell parameters are a=2.38 nm, b=0.72 nm, and c=0.79 nm.

Shankarram A. Athreya and David C. Martin, “Impedance Spectroscopy of Protein Polymer Modified Silicon Micromachined Probes”, Sensors and Actuators A, 72, 203-216, (1999).

The electrical properties of thin films of a biologically active protein polymer (SLPF) deposited onto micromachined neural prosthetic devices were examined by impedance spectroscopy (IS) over a broad range of temporal frequencies (10 Hz to 1 MHz). The properties of the protein polymer films were examined as a function of morphology as characterized by scanning electron microscopy (SEM) and atomic force microscopy (AFM), and the differences between continuous and discontinuous films were determined and compared. There was an increase in the capacitive component of the impedance as the coverage increased. The total increase in impedance of a coated probe at the biologically-relevant frequency of 1 kHz was less than the decrease in impedance seen during probe activation. For a given thickness, solution cast continuous films were of higher impedance than discontinuous electrospun films. The magnitude of the impedance of the coated probes a function of temporal frequency showed a power law dependence which was correlated with the roughness of the surface. By combining information from IS and quantitative measurements of surface roughness from the AFM, it was possible to estimate the dynamics of carrier transport at the interface between the electronically conductive device and the ionically conductive solution.

Elizabeth Pingel, Larry J. Markoski, Gary E. Spilman, Brendan J. Foran, Tao Jiang, and David C. Martin, “Thermally Crosslinkable Thermoplastic PET-co-XTA Copolyesters”, Polymer, 40, 53-64, (1998).

A series of thermally crosslinkable polyester copolymers were synthesized by incorporation of a benzocyclobutene-containing terephthalic acid derivative (XTA) into polyethylene terephthalate (PET). The cyclobutene moiety on the XTA monomer allows for reactive crosslinking at temperatures ~350 C requiring no catalyst and causing no change in mass. Copolymers were synthesized containing 1, 5, 10, 20, 50, and 100 mol% XTA. Crosslinking occurred above the melting temperature (~250 C) yet below the degradation temperature (~400 C), providing a window for melt processing of the copolymer. To demonstrate this point fibres were melt spun. The PET-co-XTA copolymers show systematic variations in the glass transition, recrystallization, melting and degradation temperatures as a function of benzocyclobutene content. The degradation and melting temperature both decrease slightly with increased XTA, while the recrystallization and glass transition temperature were relatively insensitive to XTA content. Thermal gravimetric analysis (TGA) indicated a decrease in the degradation temperature as higher amounts of XTA were incorporated, although an increase in the %char at 800 C was seen. This decrease in degradation temperature may be due to the generation of free radicals. Limiting Oxygen Index (LOI) measurements showed an increase in the oxygeny content required to maintain a stable flame in the copolymers with increasing amounts of XTA. LOI values ranged from 18 for neat PET to 35 for the copolymer containing 20 mol% XTA. Wide-angle X-ray Scattering data showed little change in the crystalline structure, but decreasing crystallinity for PET for blends containing up to 20 mol% XTA. The 50 mol% XTA copolymer was amorphous, while the 100% XTA homopoymer (PEXTA) showed evidence of a new crystalline structure. Crystalline diffraction peaks showed reduced intensities in data recorded for heat treated samples, and there was evidence for new peaks in the copolymer containing 20 mol% XTA when heated near 300 C. Transmission electron microscopy of cross-sections through the burned samples shoed a highly crystalline char at the surface of XTA copolyesters. This crystalline char appeared to protect the underlying copolymer from further flame-induced degradation. Evidence for significantly increased adhesion of the copolymers to polyimide films was also obtained.

Yu Shen, Michael Johnson, and David C. Martin, “Microstructure of B. Mori Silk Fiber”, Macromolecules, (1998).

The microstructure of Bombyx mori silk fibers before and after degumming was examined by transmission electron microscopy (TEM), selected area electron diffraction (SAED), wide-angle X-ray scattering (WAXS), and low-voltage high-resolution scanning electron microscopy (LVHRSEM). LVHRSEM micrographs of the neat cocoon revealed a network of pairs of twisting filaments. After degumming, there were only individual filaments showing a surface texture consistent with an oriented fibrillar structure in the fiber interior. WAXS patterns confirmed the oriented beta-sheet crystal structure common to silkworm and spider (dragline) silks. Low-dose SAED results were consistent with the WAXS data and revealed that the crystallographic texture did not vary significantly across the fiber diameter. TEM observations of individual microtomed fibers indicated a nominally triangular cross section and a 0.5-2 pm sericin coating. After degumming to remove the sericin, a banded feature was revealed with a characteristic spacing of nominally 600 nm along the fiber axis. These bands were oriented in a roughly parabolic or V-shape pointing along one axis within a given fiber. We hypothesize that this orientation was induced by the extrusion and drawing during the spinning process. Equatorial dark field (DF) images revealed that axial and lateral sizes of the beta-sheet crystallites in silk fibroin ranged from 20 to 170 nm and from 1 to 24 nm, respectively. Crazes developed in the degummed silk fiber parallel to the fiber direction. The formation of these crazes suggests that there are significant lateral interactions between microfibrils in silk fibers.

J. K. Politis, M. D. Curtis, L. Gonzalez, D. C. Martin, Y. He, and J. Kanicki, “Synthesis and Characterization of Conjugated, n-Dopable, Bithiazole-Containing Polymers”, Chemistry of Materials, 10(6), 1713-1719, (1998).

Three polymers, poly(4,4'-dinonyl-5,5'-bithiazole-2,2'-diyl-co-5-tert- butylphenylene-1,3-diyl) (PBBNBT), poly(4,4'-bis(p-dodecylphenyl)-2,2'-bithiazole-5,5'-diyl) (PDPBT), and poly(4,4'dinonyl-2,2'-bithiazole-5,5'-diyl-co-ethylene) (PENBT), have been synthesized. These polymers illustrate the ability to tune polymer properties around a specific chromophore, in this case the bithiazole ring system. Alterations of optical properties and solid-state morphology have been made while lie electrochemical behavior characteristic of the bithiazoles, i.e., reversible reduction near -2.0 V and n-dopability resulting in conductivities around 10(2) S/cm, has been maintained. All three polymers have also been used as the emitting layer in polymer-based LEDs.

Patrick T. Mather, Kevin P. Chaffee, Angel Romo-Uribe, Gary E. Spilman, Tao Jiang, and David C. Martin, “Thermally Crosslinkable Thermotropic Copolyesters: Synthesis, Characterization, and Processing”, Polymer, 38(24), 6009-6022, (1997).

The synthesis, characterization, and processing of thermotropic copolymers composed of hydroxybenzoic acid (HBA), hydroxynaphthoic acid (HNA), and systematically varying amounts of hydroquinone (HQ) and crosslinkable terephthalic acid (XTA) are described. The XTA monomer contains a benzocyclobutene (BCB) group that lies dormant during synthesis and initial steps of processing, but that can be thermally activated to introduce covalent crosslinking between laterally adjacent macromolecules. The XTA-containing HBA/HNA copolymers all remain thermotropically liquid crystalline, and can be processed into oriented fibres by melt spinning. Rheological characterization reveals an increase in the viscosity and transition from liquid-like to solid-like behavior as the crosslinking proceeds. X-ray diffraction reveals the changes in local organization with increasing XTA content. The microstructures of the XTA-containing copolymers (up to 20% XTA) in the condensed state are similar to those seen in HBA/HNA copolymers.

Marie-Christine G. Jones, Edgar Lara-Curzio, Adam Kopper, and David C. Martin, “The Lateral Deformation of Cross-linkable PPXTA Fibres”, Journal of Materials Science, 32, (1997).

The lateral deformation properties of oriented polymer fibres were examined by transverse compressive and torsional experiments. A modified interfacial test system machine was used to study the transverse compressive deformation behaviour of thermally cross-linkable poly(p-1,2-dihydrocyclobutaphenylene terphthalamide) (PPXTA) fibres and a number of commercially available polymer (Nomex, nylon, Kevlar, Dacron) and ceramic (Nicalon and FP) fibres. The torsional (shear) modulus G of PPXTA and Kevlar poly(p-phenylene terephthalamide) (PPTA) fibres was measured by pendulum experiments. During both fibre torsion and transverse compression, the deformation involves materials slip on (hk0) planes, in the [001] direction for the torsion and the [hk0] directions for transverse compression. The intermolecular crosslinks in PPXTA did not significantly modify the elastic transverse modulus Et and caused only slight (13%) increase in shear modulus G. However, the plastic transverse properties of crosslinked PPXTA were significantly different than those of uncrosslinked PPXTA. The stress at the proportional limit, sp, determined from the transverse load-displacement curves, was substantially higher for the cross-linked fibres than for the uncross-linked fibres. In addition, the cross-linked PPXTA fibres exhibited a large strain recoverable response reminiscent of elastomers, whereas the PPTA and uncross-linked PPXTA fibres exhibited a large strain irreversible response.

Lebzylisbeth Gonzalez-Ronda and David C. Martin, “Lattice Imaging of Electro-Optically Active Poly(nonylbithiazole) (PNBT)”, Macromolecules, 30(5), 1524-1526, (1997).

No abstract.

Marie–Christine G. Jones and David C. Martin, “The Compressive Deformation of Cross-linkable PPXTA Fibres”, Journal of Materials Science, 32, (1997).

A study has been conducted on the compressive deformation behaviour of thermally cross-linkable poly(p-1,2-dihydrocyclobutaphenylene terephthalamide) (PPXTA) fibres. The morphology of the failure zones was examined by scanning electron microscopy and dark-field transmission electron microscopy. On increasing the heat-treatment temperature from 260-400 C, and therefore increasing cross-link density, fewer kinks per unit length were displayed after compressive deformation. The kink specific energy was estimated to increase by a factor of 30, as determined by quantitative measurements of kink density at a given strain and of the critical strain to kink formation. Thus, the intermolecular cross-links still allowed deformation to proceed by kinking, but significantly raised the energy of kink formation. Finally rupture zones were predominantly observed in axially compressed PPXTA fibres heat-treated at 440 C. Compressive failure of the fibres changed from kink-dominated failure to brittle rupture with increased heat-treatment temperature, evidently as the result of cross-linking or of chain degradation. A dislocation model of the kink boundary developed by Vladimirov et al. was analysed and critically compared with our data. The analysis of this theory with our experimental results suggested that the dramatic change in compressive behaviour with cross-linking was due to a transition from fine intermolecular shear to block interfibrillar shear.

Jun Liao and David C. Martin, “Crystal Growth and Textured of 1,6-di(N-carbazolyl)-2,4 hexadiyne diacetylene”, Journal of Materials Research, 11(11), 2921, (1996).

We are developing techniques to isolate and characterize grain boundary defects with controlled geometries in 1,6-di(N-carbazolyl)-2,4 hexadiyne (DCHD) diacetylene polymer bicrystals. To be successful in this endeavor, it is important to determine the influence of processing variables such as evaporation rate, solution concentration, and environment on DCHD diacetylene crystal morphology. We have found that large, high quality DCHD diacetylene single crystals can be grown from solution under a controlled atmosphere. The quality of the DCHD crystals can be evalued by optical microscopy and quantitative digital image analysis. Defect structures in DCHD diacetylene crystals have been studied by Transmission Electron Microscopy (TEM). Two single-crystal textured structures have been found in porous DCHD crystals precipitated from solution: (1) a microfibrillar structure and (2) a “cross-hatched” structure. The porous DCHD crystals show localized shear deformation zones (twins and kinks), but only in those regions where the density is greater than 95% that of the perfect crystal. Lateral chain invariant (LCI) small-angle grain boundaries have been identified in DCHD by HREM.

Jun Liao and David C. Martin, "Dynamic Transmission Electron Microscopy of the (1,6-di(N-carbazolyl)-2,4-hexadiyne) Diacetylene Monomer-Polymer Phase Transformation", Philosophical Magazine A, 74, 1-19, 1996.

The monomer-polymer phase transformation has been directly imaged in (1,6-di(N-carbazolyl)-2-4-haxadiyne) diacetylene crystals by low-dose dynamic transmission electron microscopy. The crystallography of the phase transition has been studied by dynamic selected-area electron diffraction. The polymerization was found to be quasihomogeneous, with the lattice parameters changing continuously through a series of crystalline intermediate states. The solid-state reaction was found to be analogous to a martensitic phase transition with three invariant planes: (001),(220), and (220). The transformation matrix Tmp relating the monomer and polymer crystal reciprocal lattices was determined. Diffraction streaks developed along directions normal to (220) and (220) planes during the phase transformation. These streaks fade away at the end of the polymerization reaction was also examined by dynamic dark-field and high-resolution electron microscopy.

Patricia M. Wilson and David C. Martin, "High Resolution Electron Microsropy of

Crystalline Polymer Wedges", Ultramicroscopy, 62, 215-228, 1996.

High resolution electron microgaphs (HREM) of wedge-shaped crystalline samples of the polydiacetylene 1,6-di(N-carbazolyl)-2,4-hexadiyne (DCHD) are compared to quantitative predictions of image contrast obtained from dynamical electron scattering theory. Multislice calculations using experimentally determined instrument operating parameters make it possible to interpret the variation in HREM image contrast as a function of crystal thickness. Pendellosung plots of the intensity of the main beam and the scattered beams as a function of thickness corroborate characteristic features in the lattice images includeing extinctions and half-spacings. The position of these contrast features with respect to the edge of the polymer crystal wedge are compared to the theoretical calculations and used to estimate the height profile. This profile is then compared to the wedge height profiles measured with scanning probe microscopy (SPM). The two approaches give similar results for DCHD crystal thicknesses below 50 nm.

Robert S. Kody and David C. Martin, "Quantitative Characterization of Surface

Deformation in Polymer Composites Using Digital Image Analysis", Polymer

Engineering and Science, 36, 298-304, 1996.

The stress whitening of polymers and polymer composites during surface deformation (scratching) can represent a severe technological problem in certain applications. For example, scratch resistance is particularly important for poly(propylene) automobile interior components. Unfortunately, the addition of reinforcing agents such as talc or mica for improved dimensional stability and rigidity often results in an increased sensitivity to scratching. The ability to design new materials with reduced visible surface deformation requires more sophisticated information about the deformation mechanisms of polymers and polymer composites near surfaces and their relationship to the scattering of incident light. We have developed a technique to quantify the light scattered from polymer composite surfaces due to surface deformation. We first deform the material in a controlled manner using a scratch testing apparatus. We then analyze the region near the scratch with reflected polarized light in an optical microscope coupled to a digital image analysis system. By measuring the light scattering from the sample as a function of incident light polarization and sample orientation, it is possible to obtain information about the nature and extent of deformation at the sample surface. In this report, we desribe out technique and demonstrate how it can be used to quantify the surfacedeformation of poly(propylene)-talc composites. By examining a series of materials as a function of talc content, we have been able to obtain information that can be related to specific micromechanisms of deformation near the scratch, such as the orientation of the polymer and the voiding near the talc particles. The technique should assist in the improved development of similar materials for applications in which surface appearance is a primary concern.

John I. Nanos, Jeff W. Kampf, M. David Curtis, Lebzylisbeth Gonzalez, and David C.

Martin, "Poly(alkylbithiazoles): A New Class of Variable-Bandgap, Conjugated Polymer", Chemistry of Materials, 7, 2232-2234, 1995.

No Abstract.

Jun Liao and David C. Martin, "Construction and Characterization of (1,6-di(N-

carbazolyl)-2,4-hexadiyne) Diacetylene Polymer Bicrystals", Macromolecules, 29, 568-580, 1996.

We have developed schemes to construct and characterize the microstructure and macroscopic properties of individual grain boundary defects in extended-chain, conjugated polymers. Our approach has been to take [1,6-di(N-carbazolyl)-2,4-hexadiyne] (DCHD) diacetylene monomer crystalsand introduce a single defect under specified boundary conditions. Two monomer seed crystals are cut from a precursor single crystal and then brought into close proximity with one another. Monomer bicrystals are created by a recrystallization step involving slow evaporation of a DCHD solution. The monomer bicrystals are then converted into polymer bicrystals through thermal energy or by exposure to high-energy radiation. We have found that the ability to retain a cohesive interface between the crystals after the solid-state reaction in a sensitive function of their relative misorientation and the method of polymerization. In general, small-angle grain boundaries remain intact, while large-angle grain boundaries are broken after polymerization. The geometrical conditions required to obtain a coherent interface are more stringent for radiation than thermal polymerization. The macroscopic properties of the polymer bicrystals are particularly sensitive to the geometry of the interface. The efficiency of photoconductive charge carrier transport across the grain boundary decreases systematically with increasing misorientation. The mechanical strength of the polymer bicrystals also decreases with increaseing misorientation between crystals, with the fracture localized to the engineering interface. Our results are consistent with decreasing covalent bond connectivity of the polymer chains across the interface with increasing misorientation angle.

Patricia M. Wilson and David C. Martin, "Quantitative Measurements of Polymer Chain-End Edge Dislocation Strain Fields by High Resolution Electron Microscopy",

Macromolecules, 29, 842-851, 1996.

The strain fields around chain-end edge dislocations in poly(diacetylene) crystals were analyzed by high resolution electron microscopy (HREM). Experimental measurements of the tilt of the polymer chain axis as a function of azimuthal angle À at a constant radius r fro the dislocation core were compared to theoretical predictions. The shear deformation was localized in parabolic regions parallel to the Burger's vector b near the chain end. For an edge dislocation in the poly(diacetylene) 1,6-di(N-carbazolyl)-2,4-hexadiyne (DCHD) with a Burger's vector of b = 3a/2 (100) (2.4nm), we found a tilt distortion of +/- 6 degrees at 12 nm from the core. A parameter W was introduced to describe the anisotropy of the compliance matrix with respect to the chain direction. A parameter of W = 3.5 was needed to fit the measured tilt deformation with anisotropic linear elastic dislocation theory. We also found that the theory of distortions near the dislocations in columnar liquid crystals could closely predict our experimental observations. A value of 0.8 nm (the interchain spacing) for the characteristic length was the best fit for the columnar liquid crystal solution. This analysis reveals similarities between the elasticity of anisotropic crystals and liquid crystals.

David C. Martin, Patricia M. Wilson, Jun Liao, and Marie-Christine G. Jones, "Chain-End Defects in Extended-Chain Polymer Solids", MRS Bulletin, 9, 47-50, 1995.

No Abstract.

M.C.G. Jones and David C. Martin, "Molecular Stress and Strain in an Oriented Extended-Chain Polymer of Finite Molecular Length", Macromolecules, 28, 61616174, 1995.

We have developed constitutive and moleular mechanics models to investigate the influence of chain-end defects on the macroscopic tensile properties of extended-chain polymers of finite molecular weight. Molecular mechanics simulations have been performed on the rigid-rod polymer PBZO, poly(p-phenylene benzobisoxazole), using the Dreiding II force field. The distance between chain ends (i.e., the chain length) can be varied systematically by increasing the size of the simulation unit cell in the chain direction. From the analysis it is possible to analyze the micromechanics of stress transfer between chains in detail. At chain ends, the applied tensile stress is transferred to the nearby chains throuth a shear lag region via secondary bonds. A constitutive model is developed for a geometry similar to the PBZO molecular simulations. The calculated strain distribution along individual chains describes well the strain distribution along the PBZO molecules. The model predicts a nonlinear response of the material and a transition in tensile failure mode from chain slip to chain scission, which depend on the interchain shear strength and the length of the polymer molecules. The influence of intermolecular shear modulus, shear strength, and molecular chain length on macroscopic properties such as tensile modulus, tensile strength, and elongation to break is examined. It is found that in the molecular engineering of strong, tough polymer fibers, an optimum combination of shear strength and chain length must be chosen.

Tao Jiang, Jennifer Rigney, Marie-Christine G. Jones, Larry J. Markoski, Gary E.

Splman, Deborah F. Mielewski, and David C. Martin, "Processing and Characterization of Thermally Crosslinkable PPTA-co-XTA Copolymer Fibers", Macromolecules, 28,

3301-3312, 1995.

A scheme was developed to cross-link poly(p-phenyleneterephthalamide) (PPTA

or Kevlar) in order to modify its macroscopic properties. The method is based on incorporating XTA , a benzocyclobutene-modified derivative of terephthalic acid, into the polymer backbone and then inducing crosslinking by heat treatment after the fiber is formed. PPTA-co-XTA copolymers with various XTA contents exhibited lyotropic nematic liquid crystalline behavior and could be spun into fibers by jet-dry wet spinning techniques. As-spun fibers were heat-treated at intermediate temperatures (200-300 oC) to increase crystallinity and orientation and at higher temperatures (aove 320 oC) to trigger cross-linking. Wide angle X-ray diffraction conformed high molecular orientation in the fibers before and after cross-linking. The mechanical properties of these fibers were studied as a function of XTA content and conditions of heat treatment. Cross-linked copolymer fibers generally showed an improvement in tensile modulusover as-spun fibers. For the PPXTA homopolymer, however, the tensile strength and toughness tended to decrease with increasing length and temperature of the heat treatment. FTIR and ESR spectroscopic studies suggested this resulted from a degradative chain scission process. Compressive properties of these fibers were investigate through elastica and recoil tests, and through measurement of the fiber critical strain to kinking in a beam bending geometry. The strain to induce kinking in cross-linked PPXTA fibers is approximately twice that of the un-cross-linked material. The copolymer fibers also exhibited increased resistance to creep and lateral deformation after heat treatment.

David C. Martin and Edwin L. Thomas,"Experimental High Resolution Electron

Microscopy of Polymers", Polymer, 36(9), 1743-1759, 1995.

High-resolution imaging of ordered polymers is described both theoretically and experimentally. The relationship between the actual three-dimensional specimen structure and the resultant two-dimensional image intensity distribution is developed using the multislice formalism. The influence of the electron optical conditions on the image is demonstrated with experimental data, as well as with image simulations. Practical details of specimen preparation, as well as the effects of specimen structural defects on the image, are presented. A significant challenge for polymer microscopists is to minimize the deleterious effects of electron beam damage and to identify image artifacts resulting from damage. Future applications of ultrahigh-resolution capabilities are illustrated with respect to direct imaging of the anisotropic potentials present in covalently bonded materials.

Christopher J. Buchko, Patricia M. Wilson, Zheng Xu, Jin Zhang, Stephen Lee, Jeffrey S. Moore, and David C. Martin,"Electron Microscopy and Diffraction of Crystalline Dendrimers and Macrocycles", Polymer, 36(9), 1817-1825, 1995.

The precisely defined geometry of phenylacetylene dendrimers and macrocycles makes it possible to investigate systematic variations in chemical architecture on the nature of microstrucural organization. Here we report on transmission electron microscopy, selected-area electron diffraction and high-resolution electron microscopy studies of crystalline phases of these synthetic materials. Since the molecules are sensitive to electron beam damage, low-dose techniques were used to capture images and diffraction patterns dynamically. The data show increased crystal misorientation with increased side-group length and molecular complexity. As the size increases, the number of conformations available to the molecule also increases, making it difficult to pack the molecules with fewer defects.

Jaime Ojeda, Juliana Mobley, and David C. Martin,"Physical and Chemical Evolution of PMDA-ODA During Thermal Iminization", Journal of Polymer Science, B:

Polymer Physics Edition, 32, 559-569, 1995.

The processing of poly(imide) films from poly(amic acid) solutions involves the simultaneous loss of solvent and chemical conversion, and may involve structural reorganization such as orientation or crystallization. Here, we describe weight loss, solvent sorption. Fourier transform infrared (FTIR), and wide-angle x-ray scattering (WAXS) studies during thermal imidization proceeds nearly to completion before significant crystallization occurs. The experimental data are interpreted in the terms of a triangular phase diagram that makes it possible to plot the processing pathway during the conversion from poly(amic acid) solution to solid poly(imide). In constructing this triangular phase diagram the extent of imidization (i.e., the composition of the poly(amic acid-co-imide) copolymers during conversion) is treated as an independent thermodynamic variable. The form of the triangular phase diagram can be predicted from the Flory-Huggins lattice theory of mixing. There is inevitably a two-phase region present due to the relatively poor solubility of the poly(imide) in the poly(amic acid) solvent (NMP). The specific processing pathway taken depends on the relative amount of solvent loss and imidization during conversion. Further datails about the triangular phase diagrams of poly(imides) will require such studies as solvent

swelling at intermediate stages of conversion.

Marie-Christine Jones, Tao Jiang, and David C. Martin,"Microstructural Characterization of Cross-linkable p-Phenylene Terephthalamide-Terephthalic Acid Derivative (PPTA-co-XTA) Copolymer Fibers", Macromoleules, 27, 6507, 1994.

We are studying the microstructure of PPTA-co-XTA copolymer fibers. XTA is a variant of terephthalic acid (TA) with a benzocyclobutene (BCB) cross-linked moiety which becomes reactive above the synthesis and processing temperatures but below the degradation temperature. The fibers were dry-jet wet spun from lyotropic liquid crystalline solutions and heat-treated at various temperatures to induce structural reorganization and cross-linking. The microstructure was examined by wide-angle X-ray diffractionand molecular modeling. The copolymers retain the ability to crystallize and form well-oriented fibers. The BCB units are accommodated by a gradual increase in the distance between hydrogen-bonded sheets, the a dimension of the two-chain unit cell. The BCB units of high XTA content copolymers segregate into (100) planes. The a, b, and c dimensions of the unit cell of un-cross-linked PPXTA are respectively 0.91, 0.47, and 1.24 nm. Cross-linking does not significantly change the diffraction patterns, suggesting that the reaction may occur preferentially within the grain boundaries between crystallites.

Jennifer Rigney, Monica D. Little, and David C. Martin, "Swelling Studies of Crosslinked Poly(p- phenylene Terephthalamide Copolymers in Sulfuric Acid", Journal of Polymer Science: Polymer Physics Edition, 32, 1017-1021, 1994.

In an attempt to improve the mechanical properties of extended chain polymers such as poly (p -phenylene terephthalamide) (PPTA), a crosslinkable terephthalic acid derivative (XTA) has been developed which can be incorporated into copolymers in various concentrations and activated after polymerization. The crosslinking of PPTA-co-XTA copolymer articles was investigated through a series of swelling experiments in concentrated H2SO4. The data show a systematic decrease in equilibrium swelling with increasing XTA content, indicating the XTA units are in fact acting as crosslink sites. Values for crosslink density were calculated from the Flory-Rehner theory of polymer swelling and compared with previous findings on crosslinked rigid polymer network systems. The effective number of crosslinks per XTA unit (efficiency) predicted by the Flory-Rehner theory increases and then decreases with %XTA. The decrease in crosslinking efficiency at high XTA concentrations is consistant with differential scanning calorimetry data which show the enthalpy of XTA reaction decreasing slightly with %XTA. The deviations at low%XTA may represent a failure of the Flory-Rehner theory to properly describe the rubberly elasticity of extended chain polymers.

J. Philip Anderson, Joseph Cappello, and David C. Martin, "Morphology and Primary

Crystal Structure of a Silk-Like Protein Polymer Synthesized by Genetically Engineered E. Coli Bacteria", Biopolymers, 34(8), 1049-1058, 1994.

The morphology and primary crystal structure of SLPF, a protein polymer produced by genetically engineered Escherichia coli bacteria, were characterized. SLPF is a segmented copolymer consisting of amino acid sequence blocks modeled on the crystalline segments of silk fibroin and the cell attachment domain of human fibronectin. Wide angle x-ray scattering (WAXS), transmission electron microscopy (TEM), selectedarea electron diffraction (SAED), and molecular simulations were used to analyxe the primary crystal structure of SLPF. TEM experiments conducted on SLPF droplets cast from formic acid on amorphous carbon film demonstrated that these protein films have a microstructure formed of wooden sheaves. The sheaves are composed of well-defined whisker crystallites. The width of whiskers, 11.8 +/- 2.2 nm, may be correlated to the length of the silk-like segment in SLPF as predicted by molecular simulations. WAXS data, TEM images, SAED, patterns, molecular simulations, and theoretical diffraction patterns all were consistant with the crankshaft model proposed for Silk I by Lotz and Keith.

Kenneth A. Walker, Larry J. Markoski, Gary A. Deeter, Gary E. Spilman, David C. Martin, and Jeffery S. Moore, "Crosslinking Chemistry for High-Performance Polymer Networks", Polymer, 35(23), 5012-5017, 1994.

A new thermally reactive monomer has been designed and synthesized that brings novel crosslinking chemistry to high performance polymers. This monomer (XTA) is a derivative of terephthalic acid and was based on the thermal chemistry of benzocyclobutene. Various model compounds have been synthesized to investigate substituent effects on benzocyclobutene reactivity. Irreversible reaction exotherms around 350oC were observed in these model compounds using differential scanning calorimetry. Based on these studies, polyaramid and poly(aryl ether ketone) XTA copolymers were synthesized. The formation of an insoluble network resulted after heat treatment of these polymers.

Jaime Ojeda and David C. Martin, "High Resolution Microscopy of PMDA-ODA Poly(imide) Single Crystals", Macromolecules, 26, 6557-6565, 1993.

Single crystals of the poly(imide) PMDA-ODA were grown from a 1.4% by weight solution of the precursor poly(amic acid) in 1-methyl-2-pyrrolidinone (NMP) solvent. The morphology of the crystals was examined by high resolution electron (HREM) and atomic force microscopies (AFM). The crystals formed spherulitic bundles of well-defined lamellae similar to that typically observed in semicrystalline polymers. The crystallographic growth direction was found to be (010) in all cases. The nucleation and growth patterns of these crystals permitted imaging of the lateral ((100) 0.6-nm and (010) 0.4-nm) packing directions as well as that along the chain axis. High contrast 1.6-nm (002) lattice fringes seen within the polymer lamellae provided direct evidence of the crystalline perfection and for screw dislocation mediated crystal growth and lamellar branching. The lamellar crystal thickness was found to be 10.2 +/- 0.5 nm, corresponding to six PMDA-ODA repeat units along the (c ) chain axis. Evidence from (001) zone HREM images and electron diffraction patterns indicated that the crystallographic angle fluctuated locally from 81 to 99o. This was consistant with molecular simulations indicating that the crystal energy of PMDA-ODA was relatively insensitive to fluctuations over a similar range of angles. The theoretical simulations also indicate that fluctuations in the crystallographic angle should be accompanied by simultaneous variations in the molecular setting angle.

Jun Liao and David C. Martin , " Direct Imaging of the Diacetylene Solid-State Monomer-Polymer Phase Transformation", Science, 260, 1489-1492, 1993.

The solid-state phase transformation from 1,6-di(N-carbazolyl)-2-4-hexadiyne (DCHD) diacetylene monomer to polymer has been studied dynamically by low-dose selected area electron diffraction and high-resolution electron microscopy. The total exposure required to induce polymerization is five orders of magnitude smaller than the critical dose for electron beam damage. The phase transformation is quasi-homogeneous, with the lattice parameters changing continuously as a function of beam dose. Characteristic streaking that developes in the selected area electron diffraction patterns in the (200) reciprocal directions during the intermediate stages of the transformation provides information about the defect-mediated mechanisms of this reaction.

David C. Martin, "Defects in Polymer Solids", Trends in Polymer Science, 1(6), 178-

183, 1993.

High-resolution structural characterization techniques such as low dose lattice imaging and atomic force microscopy have now made it possible to reveal the molecular organization near defects in ordered polymers solids. With access to information about defect structure, it is now necessary to establish how these defects influence macroscopic properties. This will require schemes to isolate specific defects and analyse their behavior in detail. We will also need to generate more sophisticated models of the response of materials to defects in order to evaluate the experimental data obtained. A better fundamental understanding of what defects are and how they can be controlled should lead to an improved exploitation of polymer materials in a variety of applications.

Larry J. Markoski, Kenneth A. Walker, Gary E. Spilman, David C. Martin, and Jeffrey S. Moore, "Cross-Linkable Copolymers of Poly(p -phenyleneterephthalamide)", Chemistry of Materials, 5, 248-250, 1993.

No Abstract.

Patricia M. Wilson and David C. Martin, "Dislocation Mediated Lattice Bending in 1,6-di (N-Carbazolyl)-2,4 hexadiyne (DCHD) Polydiacetylene Droplets", Journal of

Materials Research, 7(11), 3150-3158, 1992.

Droplets of 1,6-di (N-carbazolyl)-2,4 hexadiyne (DCHD) polydiacetylene were prepared by room temperature evaporation of dilute (0.01 wt. %) solution of the monomer in chloroform onto amorphous carbon-coated mica substrates. High Resolution Electron Microscopy (HREM) and Selected Area Electron Diffraction (SAED) revealed small crystallographically textured droplets (~1micrometer diameter) with cracks parallel to the (001) chain direction. The droplet geometry allowed us to investigate the organization of the polymer near surfaces. It was found that the curvature of the droplet edge caused a local bending of the polymer crystal lattice. Direct imaging of the molecular structure near the droplet surface revealed that the mechanism of the lattice bending was by the formation of edge dislocations. Dislocations were etched in some droplets to gain information about perturbations in structure and reactivity near the core.

David C. Martin, "Intermolecular Twist Defects in Extended-Chain Polymers",

Macromolecules, 25, 5171-5177, 1992.

Here the geometry and general properties of intermolecular twist defects in extended-chain polymer fibers are introduced. These defects are conceived as a total twisting of two or more polymer molecules about one another in the solid state. The structure and impact on mechanical properties of intermolecular twist defects in extended-chain polymer solids were explored using molecular mechanics simulations (PolyGraf and CERIUS software packages on a Silicon Graphics 4D25G workstation). The intermolecular twist defects were topologically entrapped in the molecular simulation by first creating a two-chain unit cell under triply-periodic boundary conditions and then connecting the tail of chain 1 to the head of chain 2 and vice versa. The distance between defects (the reciprocal of which is the defect density) was systematically varied by increasing the length of the simulation in the chain direction. The characteristics of these intermolecular twist defects were then examined for a particularly important extended-chain polymer system: poly(p -phenylenebenzobisoxazole) (PBZO). The simulation results indicate that for PBZO the internal energy of these defects is approxamately 100 kcal/mol, primarily due to an increase in the energy of bond torsions. An estimate of the change in the modulus of PBZO fibers as a function of the twist defect density is also obtained. Introducing one defect at every lattice site causes a reduction in the theoretical modulus by a factor of approxamately 2. Other salient freatures of these defects such as the distinction between left and right handedness, mechanisms for motion, and the influence on the slip behavior are also discussed. Finally, these results are compared to a constitutive relationship derived from the elastic analysis of twisted wire rope.

David C. Martin, Larry L. Berger, and Kenncorwin H. Gardner, "Structural Evolution of a Model Poly(imide): Organization Near Surfaces", Macromolecules, 24, 3921-3928,

1991.

Details of the molecular organization occuring during imidization of the poly(amic acid) PMDA-12C at temperatures below the bulk melting point were examined. In particular, the effects of surface constraints were investigated by studying structural evolution in thin droplets. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) experiments on as-cast and imidized droplets illustrated the development of surface roughness and fluctuations in mass thickness. High-resolution electron microscopy (HREM) studies near the droplet edge showed discrete crystallites containing uniformly spaced 1.8-nm (001) fringes, which correspond to the repeat distance along the polymer backbone. The projected size, shape, orientation, and relative population of the crystaallites were analyzed quantitatively. The crystallites were found to be slightly extended in the axial direction, withan average axial dimension of 53 +/- 23 nm and average lateral dimension of 38 +/- 13 nm. The polymer chains within 100 nm of the droplet edge were found to be strongly oriented in the plane of the droplet and weakly oriented parallel to the droplet edge. Certain crystallites apperared to contain internal bending deformation (with the radius of curvature as small as 50 nm). Evidence for different types of grain boundaries between adjacent interfaces and their possible influence on the physical properties of crystallizable polymers are discussed.

David C. Martin and Edwin L. Thomas, "Micromechanisms of Kinking in Rigid-Rod

Polymer Fibers", Journal of Materials Science, 26, 5171-5183, 1991.

The tensile strengths of fibres of the rigid-rod polymers poly(paraphenylene benzobisthiazole) (PBZT) and poly(paraphenylene benzobisoxazole) (PBZO) are excellent, and therefore are of particular interest for high-performance structural applications. However, these fibres are a factor of ten weaker in compression, with failure occuring by strain localization in waell-defined kink bands. Here, we study the morphology of PBZT and PBZO kink bands in detail, in order to help elucidate the molecular mechanismsinvoled in this deformation process. We found that the typical dimensions of a kink in the direction of the fibre axis (~30 nm) were smaller than the length of an average PBZT or PBZO molecule (100 nm). Also, the boundary between the kinked and unkinked regions was well-defined. Low-dose, high-resolution electron microscopy (HREM) of the kink interior revealed local, high-angle changes in chain orientation, indicative of covalent bondbending or breaking. The kink boundaries exhibit "sharp" or "smooth" features which seem to be related to the local tensile or compressive nature of the stress field. A model for kink nucleation and propagation in terms of partial dislocations is presented and discussed. A stress analysis using this model has been developed, and comparison with experimental data suggests that kinks tend to propagate toward regions of higher compressive stress. This observation is interpretated in terms of dislocation pinning (in areas of hydrostatic tension) and the nucleation of dislocation pairs (in areas of hydrostatic compression) due to the asymmetric nature of the intermolecular energy potential. Finally, practical methods for improving compressive strength based on these mechanistic insights are proposed.

David C. Martin and Edwin L. Thomas, "Grain Boundaries in Extended-Chain Polymers:

Theory and Experiment", Philosophical Magazine A, 64(4), 903-922, 1991.

A general geometrical classification scheme for grain boundaries in extended-chain polymers is presented. The analysis is an extension of a scheme originally presented by Bevis to describe deformation twins in polymers. Bevis recognized the importance of the orientation of the covalently bonded chain backbone within the crystallite, and referred to boundaries as 'chain invariant' or 'chain rotation' depending on whether chains in adjacent domains were parallel or not. We consider an additional important parameter: the orientation of the grain boundary plane. We classify those grain boundaries which are parallel to the two chain directions as 'lateral', and those which are not 'axial'. These two parameters lead directly to four types of grain boundaries which are, in order of increasing energy: lateral chain invariant, lateral chain rotation, axial chain invariant, and axial chain rotation. Experimental evidence for these different types of boundaries are presented from High Resolution Electron Microscopy (HREM) studies of the rigid-rod polymer poly(paraphenylene benzobisoxazole) (PBZO or PBO). Possible molecular mechanisms for grain boundary motion are also discussed.

David C. Martin and Edwin L. Thomas, "Ultrastructure of Poly(p-

phenylenebenzobisoxazole) Fibers", Macromolecules,24, 2450-2460, 1991.

The ultrastructureof poly(p -phenylenebenzobisozazole) (PBZO or PBO) was studied as a function of processing condition by wide-angle X-ray scattering (WAXS), selected-area electron diffraction (SAED), dark-field transmission electron microscopy (HREM). The development of single-crystal texturing in thin films made it possible to index the PBZO scattering patterns to a nonprimitive (N=2) monoclinic space group Pc (No. 7). The new unit cell parameters are a=1.120 nm, b =0.354 nm, c =1.205 nm, and p x1 =1.66 g/cm3, with neighboring chains in the a direction placed at relative axial translations of +/- .25c . HREM images of the 0.55 nm (200) and 0.35 nm (010) lateral spacings between PBZO molecules enabled the crystallite size, shape, and relative orientations to be directly determined. Defects within and between PBZO crystallites were observed, and molecular models are presented that are consistent with these observations.

C. Robin Hwang, Michael F. Malone, Richard J.Farris, David C. Martin, and Edwin L.

Thomas, "Microstructure and Mechanical Properties of In-Situ Network Composite Fibres of PBZT with Nylon", Journal of Material Science, 26, 2365-2371, 1991.

A method of preparing composite fibres by infiltrating nylon into swollen poly(p -phenylenebenzobisthiazole) (PBZT) fibre is described. PBZT fibre forms a microfibrillar network structure during the coagulation process. In-situ network composite (IC) fibres may be prepared by exchanging the coagulant with a solution containing the desired matrix material. These new composite fibres exhibit nearly identical mechanical properties and similar thermomechanical properties to those of so-called molecular composite (MC) fibres prepared from isotropic solutions of PBZT and nylon in methane sulphonic acid (MSA). The mechanical prooperties of these fibres were determined before and after heat treatment under tension. The structure of pure PBZT and its composite fibres (ICs' and MCs') were characterized useing nitrogen adsorption (Brunauer-Emmett-Teller (BET) experiments), small-angle X-ray scattering, and scanning and transmission electron microscopy (SEM and TEM, respectively). The structure of both composite fibers was found to be a microfibrillar network of PBZT in a matrix of amorphous nylon. The average diameters of the PBZT microfibrils were in the range of 10 to 20 nm for the in-situ network composites and approximately 4 nm for molecular composites.

R. Piner, R. Reifenberger, D. C. Martin, E. L. Thomas, R. P. Apkarian, "A Scanning Tunneling Microscope Study of Single Crystal Polyethylene", Journal of Polymer Science: Part C: Polymer Letters, 28(13), 399, 1990.

The scanning tunneling microscope has been used to image single crystal polyethylene lamallae coated with thin Au or Cr overlayers. The images show a variety of different morphologies ranging from single crystal lamella resting on atomically flat, highly oriented pyrolitic graphite substrates to large pyramidal structures formed by a multilayer growth process. Small outgrowth structures were observed on the top surface of many individual lamellae and were found to be in registry with the edge of the underlying "seed" lamella. The STM studies show evidence for sectorization of the single crystal lamella as well as plastic deformation of overlapping lamellae involving c-axis slip.

Michael A. Masse, David C. Martin, Edwin L. Thomas, Frank E. Karasz, and Jurgen Petermann, "Crystal Morphology in Pristine and Doped Films of Poly(p -phenylene Vinylene)", Journal of Materials Science, 25, 311-320, 1990.

The crystal morphology of orientated films of poly(p-pphenylene vinylene) (PPV) has been investigated using electron microscopy sand X-ray diffraction. An X-ray diffraction rotation series confirmed the existence of fibre symmetry in bulk orientated films. Dark-field imaging by transmission electron microscopy (TEM) revealed small diffracting regions of the order of 7 nm in size with an aspect ratio near 1. These diffracting regions were shown by high resolution transmission electron microscopy (HREM) to be composed of small crystallites with an average size of 5 nm. Imaging of the lateral packing by HREM allowed the evaluation of local variations in crystallite orientation. This HREM method of orientation function determination compares well to bulk methods (e.g. wide-angle X-ray scattering, infared dichroism) for PPV of similar draw ratio. A micellar model is presented to describe the crystalline morphology of orientated PPV. The model presents PPV as a highly connected network of small crystallites. The well-formed crystalline regions are thought to compose approximately 50% of the sample volume with the remainder of the volume being grain boundaries. Doping by SSF5

led to the formation of an electron-dense overlayer, thought to be arsenic oxide, which prohibited dark-field imaging of the crystallites. After doping with H2SO4, crystallites of the electrically conductive phase were observed. The general morphological character is preserved in the conversion from insulating to conducting forms. For the conditions employed, the doped diffracting regions were 4 nm in size and retained the orientation initially present in the pristine film.

David M. Anderson, David C. Martin, and Edwin L. Thomas, "Maximum Entropy Data

Restoration Using Both Real- and Fourier-Space Analysis", Acta Crystallographica,

A45, 686-698, 1989.

An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-nose ratio for periodic information in Foourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts under-lying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introdued that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases with various types of added noise aand in examples of normal and high-resolution electron-microscopy images, dramatic improvement can be obtained from two to four stages of iteration, even in cases where traditional ME restoration provides little improvement. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features presentin the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated.

David C. Martin, Glen A. Novak, and Michael G. Wyzgoski, "Fatique Fracture of

Reaction Injection Molded (RIM) Nylon Composites", Journal of Applied Polymer

Science, 37, 3029-3056, 1989.