900 resultados para Conductive polymer composites


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Cellulose fibers obtained from the textile industry (lyocell) were investigated as a potential reinforcement for thermoset phenolic matrices, to improve their mechanical properties. Textile cotton fibers were also considered. The fibers were characterized in terms of their chemical composition and analyzed using TGA, SEM, and X-ray. The thermoset (non-reinforced) and composites (phenolic matrices reinforced with randomly dispersed fibers) were characterized using TG, DSC, SEM, DMTA, the Izod impact strength test, and water absorption capacity analysis. The composites that were reinforced with lyocell fibers exhibited impact strengths of nearly 240 Jm(-1), whereas those reinforced with cotton fibers exhibited impact strengths of up to 773 Jm(-1). In addition to the aspect ratio, the higher crystallinity of cotton fibers compared to lyocell likely plays a role in the impact strength of the composite reinforced by the fibers. The SEM images showed that the porosity of the textile fibers allowed good bulk diffusion of the phenolic resin, which, in turn, led to both good adhesion of fiber to matrix and fewer microvoids at the interface.

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A tannin-phenolic resin (40 wt% of tannin, characterized by H-1 nuclear magnetic resonance (NMR) and C-13 NMR, Fourier transform infrared, thermogravimetry, differential scanning calorimetry) was used to prepare composites reinforced with sisal fibers (30-70 wt%). Inverse gas chromatography results showed that the sisal fibers and the tannin-phenolic thermoset have close values of the dispersive component and also have predominance of acid sites (acid character) at the surface, confirming the favoring of interaction between the sisal fibers and the tannin-phenolic matrix at the interface. The Izod impact strength increased up to 50 wt% of sisal fibers. This composite also showed high storage modulus, and the lower loss modulus, confirming its good fiber/matrix interface, also observed by SEM images. A composite with good properties was prepared from high content of raw material obtained from renewable sources (40 wt% of tannin substituted the phenol in the preparation of the matrix and 50 wt% of matrix was replaced by sisal fibers). (C) 2012 Elsevier Ltd. All rights reserved.

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Thermoplastic starch (TPS) from industrial non-modified corn starch was obtained and reinforced with natural strands. The influence of the reinforcement on physical-chemical properties of the composites obtained by melt processing has been analyzed. For this purpose, composites reinforced with different amounts of either sisal or hemp strands have been prepared and evaluated in terms of crystallinity, water sorption, thermal and mechanical properties. The results showed that the incorporation of sisal or hemp strands caused an increase in the glass transition temperature (T-g) of the TPS as determined by DMTA. The reinforcement also increased the stiffness of the material, as reflected in both the storage modulus and the Young's modulus. Intrinsic mechanical properties of the reinforcing fibers showed a lower effect on the final mechanical properties of the materials than their homogeneity and distribution within the matrix. Additionally, the addition of a natural latex plasticizer to the composite decreased the water absorption kinetics without affecting significantly the thermal and mechanical properties of the material. (c) 2012 Elsevier Ltd. All rights reserved.

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Composites of high-density biopolyethylene (HDBPE) obtained from ethylene derived from sugarcane ethanol and curaua fibers were formed by first mixing in an internal mixer followed by thermopressing. Additionally, hydroxyl-terminated polybutadiene (LHPB), which is usually used as an impact modifier, was mainly used in this study as a compatibilizer agent. The fibers, HDBPE and LHPB were also compounded using an inter-meshing twin-screw extruder and, subsequently, injection molded. The presence of the curaua fibers enhanced some of the properties of the HDBPE, such as its flexural strength and storage modulus. SEM images showed that the addition of LHPB improved the adhesion of the fiber/matrix at the interface, which increased the impact strength of the composite. The higher shear experienced during processing probably led to a more homogeneous distribution of fibers, making the composite that was prepared through extruder/injection molding more resistant to impact than the composite processed by the internal mixer/thermopressing. (c) 2012 Elsevier Ltd. All rights reserved.

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Composites formed of a polymer-embedded layer of sub-10 nm gold nanoclusters were fabricated by very low energy (49 eV) gold ion implantation into polymethylmethacrylate. We used small angle x-ray scattering to investigate the structural properties of these metal-polymer composite layers that were fabricated at three different ion doses, both in their original form (as-implanted) and after annealing for 6 h well above the polymer glass transition temperature (150 degrees C). We show that annealing provides a simple means for modification of the structure of the composite by coarsening mechanisms, and thereby changes its properties. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4720464]

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The aim of this study was to evaluate the compressive strength of microhybrid (FiltekTM Z250) and nanofilled (FiltekTM Supreme XT) composite resins photo-activated with two different light guide tips, fiber optic and polymer, coupled with one LED. The power density was 653 mW cm-2 when using the fiber optic light tip and 596 mW cm-2 with the polymer. After storage in distilled water at 37± 2 °C for seven days, the samples were subjected to mechanical testing of compressive strength in an EMIC universal mechanical testing machine with a load cell of 5 kN and speed of 0.5 mm min-1. The statistical analysis was performed using ANOVA with a confidence interval of 95% and Tamhane’s test. The results showed that the mean values of compressive strength were not influenced by the different light tips (p > 0.05). However, a statistical difference was observed (p < 0.001) between the microhybrid composite resin photo-activated with the fiber optic light tip and the nanofilled composite resin. Based on these results, it can be concluded that microhybrid composite resin photo-activated with the fiber optic light tip showed better results than nanofilled, regardless of the tip used, and the type of the light tip did not influence the compressive strength of either composite. Thus, the presented results suggest that both the fiber optic and polymer light guide tips provide adequate compressive strength to be used to make restorations. However, the fiber optic light tip associated with microhybrid composite resin may be an interesting option for restorations mainly in posterior teeth.

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Objective: The aim of this study was to evaluate the degree of conversion and hardness of different composite resins, photo-activated for 40 s with two different light guide tips, fiber optic and polymer. Methods: Five specimens were made for each group evaluated. The percentage of unreacted carbon double bonds (% C=C) was determined from the ratio of absorbance intensities of aliphatic C=C (peak at 1637 cm-1) against internal standard before and after curing of the specimen: aromatic C-C (peak at 1610 cm-1). The Vickers hardness measurements were performed in a universal testing machine. A 50 gf load was used and the indenter with a dwell time of 30 seconds. The degree of conversion and hardness mean values were analyzed separately by ANOVA and Tukey's test, with a significance level set at 5%. Results: The mean values of degree of conversion for the polymer and fiber optic light guide tip were statistically different (P<.001). The hardness mean values were statistically different among the light guide tips (P<.001), but also there was difference between top and bottom surfaces (P<.001). Conclusions: The results showed that the resins photo-activated with the fiber optic light guide tip promoted higher values for degree of conversion and hardness.

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The main reasons for the attention focused on ceramics as possible structural materials are their wear resistance and the ability to operate with limited oxidation and ablation at temperatures above 2000°C. Hence, this work is devoted to the study of two classes of materials which can satisfy these requirements: silicon carbide -based ceramics (SiC) for wear applications and borides and carbides of transition metals for ultra-high temperatures applications (UHTCs). SiC-based materials: Silicon carbide is a hard ceramic, which finds applications in many industrial sectors, from heat production, to automotive engineering and metals processing. In view of new fields of uses, SiC-based ceramics were produced with addition of 10-30 vol% of MoSi2, in order to obtain electro conductive ceramics. MoSi2, indeed, is an intermetallic compound which possesses high temperature oxidation resistance, high electrical conductivity (21·10-6 Ω·cm), relatively low density (6.31 g/cm3), high melting point (2030°C) and high stiffness (440 GPa). The SiC-based ceramics were hot pressed at 1900°C with addition of Al2O3-Y2O3 or Y2O3-AlN as sintering additives. The microstructure of the composites and of the reference materials, SiC and MoSi2, were studied by means of conventional analytical techniques, such as X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (SEM-EDS). The composites showed a homogeneous microstructure, with good dispersion of the secondary phases and low residual porosity. The following thermo-mechanical properties of the SiC-based materials were measured: Vickers hardness (HV), Young’s modulus (E), fracture toughness (KIc) and room to high temperature flexural strength (σ). The mechanical properties of the composites were compared to those of two monolithic SiC and MoSi2 materials and resulted in a higher stiffness, fracture toughness and slightly higher flexural resistance. Tribological tests were also performed in two configurations disco-on-pin and slideron cylinder, aiming at studying the wear behaviour of SiC-MoSi2 composites with Al2O3 as counterfacing materials. The tests pointed out that the addition of MoSi2 was detrimental owing to a lower hardness in comparison with the pure SiC matrix. On the contrary, electrical measurements revealed that the addition of 30 vol% of MoSi2, rendered the composite electroconductive, lowering the electrical resistance of three orders of magnitude. Ultra High Temperature Ceramics: Carbides, borides and nitrides of transition metals (Ti, Zr, Hf, Ta, Nb, Mo) possess very high melting points and interesting engineering properties, such as high hardness (20-25 GPa), high stiffness (400-500 GPa), flexural strengths which remain unaltered from room temperature to 1500°C and excellent corrosion resistance in aggressive environment. All these properties place the UHTCs as potential candidates for the development of manoeuvrable hypersonic flight vehicles with sharp leading edges. To this scope Zr- and Hf- carbide and boride materials were produced with addition of 5-20 vol% of MoSi2. This secondary phase enabled the achievement of full dense composites at temperature lower than 2000°C and without the application of pressure. Besides the conventional microstructure analyses XRD and SEM-EDS, transmission electron microscopy (TEM) was employed to explore the microstructure on a small length scale to disclose the effective densification mechanisms. A thorough literature analysis revealed that neither detailed TEM work nor reports on densification mechanisms are available for this class of materials, which however are essential to optimize the sintering aids utilized and the processing parameters applied. Microstructural analyses, along with thermodynamics and crystallographic considerations, led to disclose of the effective role of MoSi2 during sintering of Zrand Hf- carbides and borides. Among the investigated mechanical properties (HV, E, KIc, σ from room temperature to 1500°C), the high temperature flexural strength was improved due to the protective and sealing effect of a silica-based glassy phase, especially for the borides. Nanoindentation tests were also performed on HfC-MoSi2 composites in order to extract hardness and elastic modulus of the single phases. Finally, arc jet tests on HfC- and HfB2-based composites confirmed the excellent oxidation behaviour of these materials under temperature exceeding 2000°C; no cracking or spallation occurred and the modified layer was only 80-90 μm thick.

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In the present study, thin functional conducting polyaniline (PANI) films, either doped or undoped, patterned or unpatterned, were prepared by different approaches. The properties of the obtained PANI films were investigated in detail by a combination of electrochemistry with several other techniques, such as SPR, QCM, SPFS, diffraction, etc. The sensing applications (especially biosensing applications) of the prepared PANI films were explored. Firstly, the pure PANI films were prepared by the electropolymerisation method and their doping/dedoping properties in acidic conditions were investigated in detail by a combination of electrochemistry with SPR and QCM. Dielectric constants of PANI at different oxidation states were obtained quantitatively. The results obtained here laid a good foundation for the following investigations of PANI films in neutral pH conditions. Next, PANI multilayer films doped by a variety of materials were prepared by the layer-by-layer method in order to explore their biosensing applications, because of the loss of redox activity of pure PANI in neutral pH conditions. The dopants used include not only the traditionally used linear polyelectrolytes, but also, for the first tim, some other novel materials, like modified gold nanoparticles or modified carbon nanotubes. Our results showed that all the used dopants could form stable multilayer films with PANI. All the obtained PANI multilayer films showed good redox activity in a neutral pH environment, which makes them feasible for bioassays. We found that all the prepared PANI multilayer films can electrocatalyze the oxidation of NADH in neutral conditions at a low potential, although their catalytic efficiencies are different. Among them, PANI/carbon nanotube system showed the highest catalytic efficiency toward the oxidation of NADH, which makes it a good candidate as a NADH sensor. Besides, because some of the prepared PANI multilayer systems were end-terminated with –COOH groups (like PANI/Au nanoparticles system), which can be utilized to easily link biomolecules for biosensing applications. Here, we demonstrated, for the first time, to use the prepared PANI multilayer films for the DNA hybridisation detection. The detection event was monitored either by direct electrochemical method, or by enzyme-amplified electrochemical method, or by surface plasmon enhanced fluorescence spectroscopic method. All the methods can effectively differentiate non-complementary DNA from the complementary ones, even at the single-base mismatch level. It should also be noted that, our success in fabricating PANI multilayer films with modified Au nanoparticles or carbon nanotubes also offered another novel method for incorporating such novel materials into (conducting) polymers. Because of the unique electrochemical and optical properties of each component of the obtained PANI multilayer films, they should also find potential applications in many other fields such as microelectronics, or for electrochromic and photovoltaic devices. Finally, patterned PANI films were fabricated by the combination of several patterning techniques, such as the combination of electrocopolymerization with micromolding in capillaries (EP-MIMIC), the combination of microcontact printing with the layer-by-layer technique (µCP-LBL), and the polystyrene (PS) template induced electropolymerisation method. Using the obtained stripe-shaped PANI/PSS film, a redox-switchable polymer grating based on the surface-plasmon-enhanced mode was constructed and its application in the field of biosensing was explored. It was found that the diffraction efficiency (DE) of the grating was very sensitive to the applied potential (i.e. redox state of the film) as well as the pH environment of the dielectric medium. Moreover, the DE could also be effectively tuned by an electrocatalytic event, such as the electrocatalytic oxidation of NADH by the grating film. By using PS colloidal crystal assemblies as templates, well-ordered 3D interconnected macroporous PANI arrays (PANI inverse opals) were fabricated via electropolymerisation method. The quality of the obtained inverse opals was much higher than those reported by chemical synthesis method. By electrochemical method, the structures of the prepared inverse opals can be easily controlled. To explore the possible biosensing applications of PANI inverse opals, efforts were also done toward the fabrication of PANI composite inverse opals. By selecting proper dopants, high quality inverse opals of PANI composites were fabricated for the first time. And the obtained opaline films remained redox-active in neutral pH conditions, pointing to their possible applications for electrobioassays.

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ABSTRACT: In this work, proton conducting copolymers, polymer blends and composites containing phosphonic acid groups have been prepared. Proton conduction mechanisms in these materials are discussed respectively in both, the anhydrous and humidified state. Atom transfer radical copolymerization (ATRCP) of diisopropyl-p-vinylbenzyl phosphonate (DIPVBP) and 4-vinyl pyridine (4VP) is studied for the first time in this work. The kinetic parameters are obtained by using the 1H-NMR online technique. Proton conduction in poly(vinylbenzyl phosphonic acid) (PVBPA) homopolymer and its statistical copolymers with 4-vinyl pyridine (poly(VBPA-stat-4VP)s) are comprehensively studied in both, the “dry” and “wet” state. Effects of temperature, water content and polymer composition on proton conductivities are studied and proton transport mechanisms under various conditions are discussed. The proton conductivity of the polymers is in the range of 10-6-10-8 S/cm in nominally dry state at 150 oC. However, proton conductivity of the polymers increases rapidly with water content in the polymers which can reach 10-2 S/cm at the water uptake of 25% in the polymers. The highest proton conductivity obtained from the polymers can even reach 0.3 S/cm which was measured at 85oC with 80% relative humidity in the measuring atmosphere. Poly(4-vinyl pyridine) was grafted from the surface of SiO2 nanoparticles using ATRP in this work for the first time. Following this approach, silica nanoparticles with a shell of polymeric layer are used as basic particles in a polymeric acidic matrix. The proton conductivities of the composites are studied under both, humidified and dry conditions. In dry state, the conductivity of the composites is in the range of 10-10~10-4 S/cm at 150 oC. While in humid state, the composites show much higher proton conductivity. The highest proton conductivity obtained with the composites is 0.5 S/cm measured at 85oC with 80% relative humidity in the measuring atmosphere. The miscibility of poly (vinyl phosphonic acid) and PEO is studied for the first time in this work and a phase diagram is plotted based on a DSC study and optical microscopy. With this knowledge, homogeneous PVPA/PEO mixtures are prepared as proton-conducting polymer blends. The mobility of phosphonic acid groups and PEO in the blends is determined by 1H-MAS-NMR in temperature dependent measurements. The effect of composition and the role of PEO on proton conduction are discussed.

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Conjugated polymers and conjugated polymer blends have attracted great interest due to their potential applications in biosensors and organic electronics. The sub-100 nm morphology of these materials is known to heavily influence their electromechanical properties and the performance of devices they are part of. Electromechanical properties include charge injection, transport, recombination, and trapping, the phase behavior and the mechanical robustness of polymers and blends. Electrical scanning probe microscopy techniques are ideal tools to measure simultaneously electric (conductivity and surface potential) and dielectric (dielectric constant) properties, surface morphology, and mechanical properties of thin films of conjugated polymers and their blends.rnIn this thesis, I first present a combined topography, Kelvin probe force microscopy (KPFM), and scanning conductive torsion mode microscopy (SCTMM) study on a gold/polystyrene model system. This system is a mimic for conjugated polymer blends where conductive domains (gold nanoparticles) are embedded in a non-conductive matrix (polystyrene film), like for polypyrrole:polystyrene sulfonate (PPy:PSS), and poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS). I controlled the nanoscale morphology of the model by varying the distribution of gold nanoparticles in the polystyrene films. I studied the influence of different morphologies on the surface potential measured by KPFM and on the conductivity measured by SCTMM. By the knowledge I gained from analyzing the data of the model system I was able to predict the nanostructure of a homemade PPy:PSS blend.rnThe morphologic, electric, and dielectric properties of water based conjugated polymer blends, e.g. PPy:PSS or PEDOT:PSS, are known to be influenced by their water content. These properties also influence the macroscopic performance when the polymer blends are employed in a device. In the second part I therefore present an in situ humidity-dependence study on PPy:PSS films spin-coated and drop-coated on hydrophobic highly ordered pyrolytic graphite substrates by KPFM. I additionally used a particular KPFM mode that detects the second harmonic electrostatic force. With this, I obtained images of dielectric constants of samples. Upon increasing relative humidity, the surface morphology and composition of the films changed. I also observed that relative humidity affected thermally unannealed and annealed PPy:PSS films differently. rnThe conductivity of a conjugated polymer may change once it is embedded in a non-conductive matrix, like for PPy embedded in PSS. To measure the conductivity of single conjugated polymer particles, in the third part, I present a direct method based on microscopic four-point probes. I started with metal core-shell and metal bulk particles as models, and measured their conductivities. The study could be extended to measure conductivity of single PPy particles (core-shell and bulk) with a diameter of a few micrometers.

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Several CFCC (Continuous Fiber Composite Ceramics) production processes were tested, concluding that PIP (Polymer Impregnation, or Infiltration, Pyrolysis) and CBC (Chemically Bonded Ceramics) based procedures have interesting potential applications in the construction and transportation fields, thanks to low costs to get potentially useful thermomechanical performances. Among the different processes considered during the Doctorate (from the synthesis of new preceramic polymers, to the PIP production of SiC / SiC composites) the more promising results came from the PIP process with poly-siloxanes on basalt fabrics preforms. Low processing time and costs, together with fairly good thermomechanical properties were demonstrated, even after only one or two PIP steps in nitrogen flow. In alternative, pyrolysis in vacuum was also tested, a procedure still not discussed in literature, but which could originate an interesting reduction of production costs, with only a moderate detrimental effect on the mechanical properties. The resulting CFCC is a basalt / SiCO composite that can be applied for continuous operation up to 600°C, also in oxidant environment, as TG and XRD demonstrated. The failure upon loading is generally pseudo-plastic, being interlaminar delamination the most probable rupture mechanism. . The strength depends on several different factors (microstructure, polymer curing and subsequent ceramic phase evolution, fiber pull-out, fiber strength, fiber percentage) and can only be optimized empirically. In order to be open minded in selecting the best technology, also CBC (Chemically Bonded Ceramics) matrixes were considered during this Doctorate, making some preliminary investigations on fire-resistant phosphate cements. Our results on a commercial product evidenced some interesting thermomechanical capabilities, even after thermal treatments. However the experiments showed also phase change and possible cracking and deformations even on slow drying (at 130°C) and easy rehydration upon exposure to environmental humidity.

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The behaviour of a polymer depends strongly on the length- and time scale as well as on the temperature rnat which it is probed. In this work, I describe investigations of polymer surfaces using scanning probe rnmicroscopy with heatable probes. With these probes, surfaces can be heated within seconds down to rnmicroseconds. I introduce experiments for the local and fast determination of glass transition and melting rntemperatures. I developed a method which allows the determination of glass transition and melting rntemperatures on films with thicknesses below 100 nm: A background measurement on the substrate was rnperformed. The resulting curve was subtracted from the measurement on the polymer film. The rndifferential measurement on polystyrene films with thicknesses between 35 nm and 160 nm showed rncharacteristic signals at 95 ± 1 °C, in accordance with the glass transition of polystyrene. Pressing heated rnprobes into polymer films causes plastic deformation. Nanometer sized deformations are currently rninvestigated in novel concepts for high density data storage. A suitable medium for such a storage system rnhas to be easily indentable on one hand, but on the other hand it also has to be very stable towards rnsurface induced wear. For developing such a medium I investigated a new approach: A comparably soft rnmaterial, namely polystyrene, was protected with a thin but very hard layer made of plasma polymerized rnnorbornene. The resulting bilayered media were tested for surface stability and deformability. I showed rnthat the bilayered material combines the deformability of polystyrene with the surface stability of the rnplasma polymer, and that the material therefore is a very good storage medium. In addition we rninvestigated the glass transition temperature of polystyrene at timescales of 10 µs and found it to be rnapprox. 220 °C. The increase of this characteristic temperature of the polymer results from the short time rnat which the polymer was probed and reflects the well-known time-temperature superposition principle. rnHeatable probes were also used for the characterization of silverazide filled nanocapsules. The use of rnheatable probes allowed determining the decomposition temperature of the capsules from few rnnanograms of material. The measured decomposition temperatures ranged from 180 °C to 225 °C, in rnaccordance with literature values. The investigation of small amounts of sample was necessary due to the rnlimited availability of the material. Furthermore, investigating larger amounts of the capsules using rnconventional thermal gravimetric analysis could lead to contamination or even damage of the instrument. rnBesides the analysis of material parameters I used the heatable probes for the local thermal rndecomposition of pentacene precursor material in order to form nanoscale conductive structures. Here, rnthe thickness of the precursor layer was important for complete thermal decomposition. rnAnother aspect of my work was the investigation of redox active polymers - Poly-10-(4-vinylbenzyl)-10H-rnphenothiazine (PVBPT)- for data storage. Data is stored by changing the local conductivity of the material rnby applying a voltage between tip and surface. The generated structures were stable for more than 16 h. It rnwas shown that the presence of water is essential for succesfull patterning.

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In this communication, solid-state/melt extrusion (SSME) is introduced as a novel technique that combines solid-state shear pulverization (SSSP) and conventional twin screw extrusion (TSE) in a single extrusion system. The morphology and property enhancements in a model linear low-density polyethylene/organically modified clay nanocomposite sample fabricated via SSME were compared to those fabricated via SSSP and TSE. The results show that SSME is capable of exfoliating and dispersing the nanofillers similarly to SSSP, while achieving a desirable output rate and producing extrudate similar in form to that from TSE.

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EPON 862 is an epoxy resin which is cured with the hardening agent DETDA to form a crosslinked epoxy polymer and is used as a component in modern aircraft structures. These crosslinked polymers are often exposed to prolonged periods of temperatures below glass transition range which cause physical aging to occur. Because physical aging can compromise the performance of epoxies and their composites and because experimental techniques cannot provide all of the necessary physical insight that is needed to fully understand physical aging, efficient computational approaches to predict the effects of physical aging on thermo-mechanical properties are needed. In this study, Molecular Dynamics and Molecular Minimization simulations are being used to establish well-equilibrated, validated molecular models of the EPON 862-DETDA epoxy system with a range of crosslink densities using a united-atom force field. These simulations are subsequently used to predict the glass transition temperature, thermal expansion coefficients, and elastic properties of each of the crosslinked systems for validation of the modeling techniques. The results indicate that glass transition temperature and elastic properties increase with increasing levels of crosslink density and the thermal expansion coefficient decreases with crosslink density, both above and below the glass transition temperature. The results also indicate that there may be an upper limit to crosslink density that can be realistically achieved in epoxy systems. After evaluation of the thermo-mechanical properties, a method is developed to efficiently establish molecular models of epoxy resins that represent the corresponding real molecular structure at specific aging times. Although this approach does not model the physical aging process, it is useful in establishing a molecular model that resembles the physically-aged state for further use in predicting thermo-mechanical properties as a function of aging time. An equation has been predicted based on the results which directly correlate aging time to aged volume of the molecular model. This equation can be helpful for modelers who want to study properties of epoxy resins at different levels of aging but have little information about volume shrinkage occurring during physical aging.