Molecular Modeling Approach to Prediction of Thermo-Mechanical Behavior of Thermoset Polymer Networks
|
|
- Carmella Simmons
- 6 years ago
- Views:
Transcription
1 pubs.acs.org/macromolecules Molecular Modeling Approach to Prediction of Thermo-Mechanical Behavior of Thermoset Polymer Networks Natalia B. Shenogina,*, Mesfin Tsige,*, Soumya S. Patnaik, and Sharmila M. Mukhopadhyay Department of Mechanical and Materials Engineering, Wright State University, Dayton, Ohio, United States Department of Polymer Science, University of Akron, Akron, Ohio, United States Propulsion Directorate, Air Force Research Laboratory, Dayton, Ohio, United States ABSTRACT: Molecular dynamics and molecular mechanics simulations have been used to study thermo-mechanical response of highly cross-linked polymers composed of epoxy resin DGEBA and hardener DETDA. The effective cross-linking approach used in this work allowed construction of a set of stress-free molecular models with high conversion degree containing up to atoms. The generated structures were used to investigate the influence of model size, length of epoxy strands, and degree of cure on thermo-mechanical properties. The calculated densities, coefficients of thermal expansion, and glass transition temperatures of the systems are found to be in good agreement with experimental data. The computationally efficient static deformation approach we used to calculate elastic constants of the systems successfully compensated for the large scattering of the mechanical properties data due to nanoscopically small volume of simulation cells and allowed comparison of properties of similar polymeric networks having minor differences in structure or chemistry. However, some of the elastic constants obtained using this approach were found to be higher than in real macroscopic samples. This can be attributed to both finite-size effect and to the limitations of the static deformation approach to account for dynamic effects. The observed dependence of properties on system size, in this work, can be used to estimate the contribution of large-scale defects and relaxation events into macroscopic properties of the thermosetting materials. 1. INTRODUCTION Chemically cross-linked thermosetting polymer networks are useful in many applications such as coatings, adhesives and matrix components in high performance composites. 1 Epoxy resins cross-linked with amine curing agents are popular materials due to their outstanding thermo-mechanical properties such as high-temperature performance, high stiffness and fracture strength. Optimizing of the processing conditions, designing of the new structures with the required properties as well as better understanding of the physical phenomena in polymers imply extensive trial-and-error experimental studies which can be both expensive and time-consuming. In order to reduce the experimental efforts in synthesis and optimization of material properties, computer simulations of the systems of interest can be very useful. Such simulations allow systematic variation of structural or physical parameters of the materials and can significantly lower experimental costs in predicting the properties of new materials. These approaches may eventually allow for screening of a greater breadth of potential resin chemistries than those that can be tried by experimental testing alone. Among various computational approaches, finite element simulations 2,3 are successfully employed to study large-scale events in polymeric materials. However, such methods are often limited by the lack of realistic parameters for inputs to constitutive relations. Two other popular computational approaches used to simulate polymeric systems are Monte Carlo simulations 4 10 and molecular dynamics (MD) simulations using a bead spring model, where each bead represents one or several polymer groups While these methods can predict some general trends in the behavior of polymer networks and generate useful insight into the dependence of Received: April 13, 2012 Revised: May 25, 2012 Published: June 7, American Chemical Society 5307
2 the physical properties on the cross-link networks, these studies are not capable of providing specific correlation with the chemical structure of the resin system. However thermomechanical properties of thermosetting networks are known to be significantly dependent on the molecular-level details of the structure. Detailed microscopic information on the physical properties of thermosetting polymers can be obtained from atomistic simulations, which may lead to predictions in quantitative agreement with experiments. Several groups have developed atomistic level methods of constructing models of highly crosslinked polymer networks, and used them to predict their properties More notably, Yarovsky and Evans 19 proposed a cross-linking technique in which all cross-linking reactions were carried out in one step (so-called static approach). The structure obtained using this method had conversion degree much lower than in real curing reactions. Alternatively, Wu and Xu 21 used cross-linking procedure that allows the formation of one cross-link per step and calculated elastic moduli of the resulting structures. However, this improved approach could become computationally inefficient with increasing the system size. Heine et al. 20 used a dynamic cross-linking approach based on a cutoff distance criterion and relaxation procedure of the cross-linked structure with a modified potential. Komarov et al. 23 employed four-step reverse mapping procedure to perform cross-linking at coarse-grained level and study properties of the resulting structures on the fully atomistic level as a function of the conversion degree. Varshney et al. 24 combined the dynamic cross-linking approach proposed by Heine et al. 20 and the relaxation procedure consisting of cycles of energy minimization and molecular dynamics equilibration stages that was proposed by Wu and Xu, 21 used new method of multistep bond formation and calculated some thermodynamic and structural properties. Li and Strachan 26,27 proposed the cross-linking procedure with charge evolution in the course of chemical reaction and obtained thermo-mechanical properties using their cross-linked models. Whereas these earlier studies provided a significant progress in atomistic computer simulations of highly cross-linked polymer networks, the systems studied were relatively small in size (less than atoms). This is a limitation since it is known that the size of the system can substantially influence the properties obtained by molecular dynamics simulations. In the present work we have addressed this issue by constructing a significantly larger set of all-atom models, containing up to atoms. We have used a method developed by Accelrys, Inc. 30 which uses a cross-linking procedure that combines several approaches that allow construction of thermosetting networks having structural characteristics close to those in real systems. These include capture sphere growth approach 29 and effective relaxation technique 21 in combination with monitoring of local stresses in the resulting networks on-the-fly. This combination of approaches yields systems with high conversion degrees and also free of stresses and geometrical distortions. The resulting polymer networks have been used in the present study to investigate the influence of model size, extent of curing and length of epoxy strands on the thermo-mechanical properties of epoxy-based polymer networks. The focus has been on a resin-hardener system that is widely used in engineering applications: the resin selected is DGEBA (diglycidylether of bisphenol A) and the aromatic amine hardener selected is EPI-Cure-W (diethylenetoluenediamine, DETDA). While some authors 23,26 28 have recently reported simulations showing the influence of the conversion degree on the properties of thermosetting polymers, there is no previous report in the literature that systematically investigated the effect of resin chain length on the thermo-mechanical properties of epoxy networks to the best of our knowledge. The paper is organized as follows. In the next section, we briefly review our simulation methodology, including the systems of interest and the approach we used in building the polymer networks. We present and discuss our results for physical properties of the system in section 3 and for mechanical properties including the effect of resin chain length in section 4. In the last section, we summarize our results as well as the advantages and limitations of the methods used in this study. 2. METHODOLOGY 2.1. Systems of Interest. The molecular structures of the epoxy monomer and curing agent molecule are shown in Figure 1, parts a and b. To simulate the cross-linking reaction, the Figure 1. (a) Epoxy resin: DGEBA (diglycidyl ether of bisphenol A) with activated reactive sites (yellow). (b) Aromatic amine hardener: DETDA (diethylene toluene diamine). Reactive sites (amine groups) are highlighted in yellow. (c) The reactive sites in the epoxy resin are activated by opening the epoxy rings at the ends of the molecule. (d) Amine groups in curing agent react with opened epoxy rings at the ends of resin molecules. reactive sites in the epoxy resin are activated by opening the epoxy rings at the ends of the molecule as shown in Figure 1c. Each of the amine groups in curing agent can react with two resin molecules as terminal carbon atoms of a resin molecule react with the nitrogen atoms of the amine hardener (Figure 1d). In the present work, we simulate stoichiometrically balanced compositions of the epoxy resin and hardener molecules; i.e., in all our systems, the number of the resin molecules is two times that of the hardener ones, which allows a theoretical conversion of 100%. 5308
3 To study the effect of system size on the thermo-mechanical properties of the thermosetting polymers, we constructed seven different system sizes ranging from (32, 16) to (512, 256), where the numbers in the parentheses represent the number of the epoxy resin and hardener molecules respectively, which corresponds to approximately 2200 to atoms in the simulation cells. Furthermore, to investigate the effect of resin chain length on the physical and mechanical properties of this class of materials, we also built the structures using short resin oligomers with various degree of polymerization, consisting of one, two and four monomer epoxy molecules (mono-, di-, and tetramers, respectively). In addition, in order to examine the role of the degree of curing on the properties of the system, structures with degrees of conversion ranging from 50% to 100% are selected during the curing process described below. We would like to also add that for better prediction of the mechanical properties of the thermosetting material under investigations using molecular dynamics (MD) simulation, we generated up to 70 topologically independent structures for each configuration with a given system size, degree of conversion and resin chain length. The details of this approach will be discussed in the mechanical properties section Simulation Details. The initial mixtures of reactants were built by packing activated epoxy resin and curing agent molecules into a cubic simulation cell followed by a geometry optimization using the Amorphous Cell module of the Materials Studio commercial package. 30 All subsequent MD simulations were performed using the Discover module of the Materials Studio software. In all our simulations, 3D periodic boundary conditions were imposed to a cubic simulation cell in order to avoid introducing artificial surface effects. Interatomic interactions are described using the second-generation COMPASS force field 31 due to its high accuracy in predicting the properties of polymeric materials. Wu and Xu 21 validated COMPASS force field for predicting the elastic moduli of highly cross-linked polymer networks. These properties were found to be in better agreement with experiment than previous calculations of these properties using DREIDING force field. In addition, Tack and Ford 32 showed that density prediction of thermosetting polymer using COMPASS is better than that using the cff91 force field Building of Polymer Networks. Earlier attempts to construct realistic models of highly cross-linked polymer networks encountered difficulties resulting from high internal stresses and unrealistic geometry distortions (see, for example, Yarovsky and Evans 19 ). As a consequence, these models produced markedly different predictions with properties of thermosetting polymers that are often far from the experimental values. In this study we used the methodology that is currently most reliable for creating models of free of stresses and geometrical distortions and yet reaching the levels of degree of conversion consistent with those typical in real systems. To build polymer networks with high degree of conversion, we used Accelrys software. 30 This software employs the capture sphere growth approach that was originally elaborated by Eichinger 29 and was successfully used for generating the topology of lightly cross-linked elastomers. In this approach, a cross-linked system is developed by growing the radius of a sphere around each cross-link site and bonds are formed between reactive atoms whenever a valid atom falls within the sphere of another one. In the case of densely cross-linked polymers, the network potential energy has a significant influence on the properties of the material. Hence, to create thermosetting polymer with realistic material properties, additional measures were taken to ensure undistorted geometry of the molecules with low internal stresses. In order to minimize the presence of internal stresses and geometric distortions during cross-linking, energetic and structural information are analyzed on-the-f ly after each cross-linking cycle. Unrealistically high stretching energy of any of the individual bonds in the system can be considered as a sensitive measure of the distortion. It usually happens when a defect is introduced in the course of the cross-linking reaction. In the present work, when a dramatic increase in the maximum bond stretching energy is detected at any stage of the cross-linking procedure, the structure is rejected in favor of others with low internal stresses. In actual chemical reactions, the reactive groups diffuse through the mixture and bond as they approach to each other at the appropriate distance. Equilibrating the mixture at high temperature enhances the movement of the reactive groups toward each other. However, in the case of a dramatic increase in molecular weight that usually occurs in the course of the cross-linking reaction, the diffusion takes much longer time and is currently beyond the reach of all-atom molecular dynamics approach. To circumvent this limitation and to relieve network stresses within a reasonable computational time, the equilibration can be supplemented with energy minimization of the structure that allows quick changes in geometry which otherwise would take long time in dynamic simulations. Thus, to mimic the diffusion in actual cross-linking reactions our model systems are subjected cascades of both energy minimization and constant volume and temperature equilibration after each cross-linking cycle. 21 Cross-Linking Procedure. In the present study, the initial amorphous structures of the uncross-linked DGEBA/DETDA mixtures were built using Accelrys amorphous builder which uses a Monte Carlo packing algorithm based on the rotational isomeric states model. 33 The DGEBA and DETDA molecules in stoichiometrically perfect proportions were added to a cubic periodic simulation box by growing the molecules segment by segment, taking into account both energy of interaction with all atoms in the box and chain conformations. As both epoxy and amine hardener molecules contain aromatic rings, a special care was taken to check ring spearing during the construction of the amorphous mixture. The formation of thermosetting polymer network starts with the equilibration of reactant mixture. In order to enhance molecular mobility in the course of chemical reaction and hence accelerate the network formation the curing is carried out at elevated temperature of 480 K. The cross-linking cycle begins with determination of the available reactive sites, i.e., terminal carbons of the activated epoxy molecules and nitrogen atoms of the amine hardener. During the simulation, distances between these reactive sites are calculated and those reactive sites falling within the current reaction radius are identified. The initial cutoff of chemical reaction is set to 5 Å and increase the cutoff radius by a small value (0.5 Å) after each crosslinking cycle. New bonds between the identified reactive atoms are created and surplus hydrogen atoms are removed from both epoxy and amine group reactive sites. The partial charges and atom types of the atoms that participated in the chemical 5309
4 reaction process are also modified after the reaction. The cycle recurs until the specified maximum cutoff radius is achieved or all available sites are reacted. Unreated epoxy rings remain open. After each cross-linking cycle a relaxation procedure is applied as described in the above section and structural and energetic characteristics of the obtained configuration are evaluated. If the maximum bond stretching energy detected after relaxation remains unusually high, the reaction stops. Otherwise, the cross-linking cycle continues Determining Thermal Properties of the Network. As described above, to enhance molecular motions and reduce stresses in the models, a curing reaction was conducted at an elevated temperature of 480 K that is above the experimental glass transition region for this material. To study thermal response of the constructed networks, we applied stepwise constant pressure cooling procedure performing a sequence of constant pressure and temperature molecular dynamics simulation runs at a set of temperatures. Here we implemented Andersen thermostat and Berendsen barostat to control temperature and pressure in our simulations. Cooling of the model systems was carried out in steps of 10 K with 100 ps equilibration run at each temperature within the temperature range of 623 to 223 K. The volume at each temperature was then computed by averaging results from at least five randomly picked epoxy structures and is used to construct volume temperature plots from which a set of physical properties are calculated as described below. Figure 2 shows a representative specific volume temperature plot of the cooling process. As can be seen in Figure 2, the Figure 2. Representative specific volume temperature plot for epoxy system containing (512, 256) DGEBA/DETDA molecules cured to 90%. The small error bars are evidence of small variation of the specific volume between the 5 structures used to generate the data. volume continuously decreases with decrease in temperature and a linear analysis was then used to predict the behavior observed at high and low temperature regions. To determine the properties of interest we perform linear fits of these two regions using: V = V + α T ( K) G G G (1) V = V + α T ( K) R R R (2) where T indicates temperature, V G and V R are specific volumes in glassy and rubbery regions, while the slopes of these regions, 5310 α G and α R correspond to the volumetric coefficients of thermal expansion (CTE) in glassy and rubbery regions, respectively. Glass transition temperatures were determined at the point of the change in the slope (represented by the intersection of the solid lines in the Figure 2). To validate the temperature ranges in which we perform linear fits, we varied the boundaries of these ranges and found that linear fits obtained are within the error bars of the volume-temperature plot and bring negligible changes in glass transition temperature. Furthermore, for mechanical characterization of the material both in glassy and rubbery states the systems should be equilibrated to the temperatures of interest. In this work we have chosen two temperatures, 298 and 480 K, which are above and below the glass transition region of a given structure, respectively. First, we determined densities at these two temperatures from volume temperature plots that were generated by averaging data from five randomly picked structures for each extent of the reaction. Then all the structures were equilibrated to these two predefined temperatures and corresponding densities for mechanical properties characterization of the material under investigation. 3. PHYSICAL PROPERTIES 3.1. Results. A. Glass Transition Temperature. The results of our glass transition temperature investigation are presented in Figure 3a where the glass transition temperature is plotted as a function of the extent of the reaction for the seven different system sizes ranging from (32, 16) to (512, 256) DGEBA/ DETDA molecules represented by different colors. As expected 34 we observe an increase in glass transition temperature with increase in degree of curing. In general, the dependence of T g on the degree of curing shows better defined trends with increasing the system size giving about 50 K divergence in values for the smallest and the largest system at high conversion degrees. However, even for the largest system size, small sampling size is prone to larger error bars resulting in higher standard deviations. These range from 3 K at low curing degrees to 21 K at 95% of curing. As the confidence interval for high extents of the reaction is wide, it makes it very hard to draw any definite conclusion about the shape of the curve in Figure 3a at high degrees of curing. The experimental values of the glass transition temperature for this material reported by different groups under different conditions also have wide variation of about 35K (441 to 476 K) and are shown in Figure 3a as open symbols. We see that our simulation results for extent of reactions higher than 90% are within the range of the reported experimental values. B. Volumetric Coefficient of Thermal Expansion. Figure 3b shows the results of the coefficients of thermal expansion (CTE) calculations for the glassy and rubbery regions at different degrees of reaction for the seven different system sizes mentioned above. In both the glassy and rubbery regions, the CTE monotonically decreases with increase in extent of curing. In addition, CTE shows well observable dependence on system size and, on average, it increases with increase in number of atoms in the model. Experimental values for fully cured structure at glassy and rubbery states 38 are also shown in Figure 3b as open symbols. The CTE values obtained from our simulations for high degrees of curing are slightly below but in a reasonable agreement with experiment and will be discussed later. C. Density. In Figure 3c, the dependence of density on the extent of curing reaction at temperatures below and above T g
5 Figure 3. (a) Glass transition temperature, (b) volumetric coefficients of thermal expansion in glassy state (squares) and rubbery state (circles), and (c) density in glassy state (squares) and rubbery state (circles) as a function of the extent of the reaction for the atomic structures ranging from (32, 16) to (512, 256) DGEBA/DETDA molecules. In all cases the open symbols represent experimental values and are taken from the following: (a) square, Jansen et al.; 35 triangle, Ratna et al.; 36 circle, Shen et al.; 37 rhomb, Liu et al.; 38 (b) in glassy (square) and rubbery (circle) states; 38 (c) in glassy state (square). 39 The color codes are as follows: orange (32, 16); cyan (64, 32); black (96, 48); red (128, 64); green, (256, 128); blue (432, 216); magenta (512, 256). for seven different system sizes is shown. As expected the density increases in the course of the reaction and the rate of increase shows noticeable dependence on temperature. In addition, at a given extent of reaction the density, on average, decreases with increase in system size. The density at the highest extent of the reaction is in excellent agreement with experimental data (less than 2% difference). 39 D. Properties of the Structures with Different Chain Length of the Epoxy Strands. The dependencies of glass transition temperature, coefficients of thermal expansion, and density on the extent of the reaction for different chain length of the epoxy strands are shown in Figure 4, parts a c. In this work we compared three kinds of systems which were constructed using 512 monomers, 256 dimers and 128 tetramers of the epoxy resin DGEBA of respectively (512, 256), (256, 128) and (128, 64) systems. All properties under consideration show observable dependence on the resin chain length. The slopes of the conversion dependencies are maximum ones for the structures cured with epoxy monomers. Besides, better correspondence of densities and coefficients of thermal expansion with experimental values is observed for longer epoxy strands Discussion. A. Cooling Rate Effect. The transition between liquid and glass is not a transition between two states that are in thermodynamic equilibrium. It is a dynamic transition from an ergodic to a nonergodic state. Glass is a kinetically locked state of the material and its properties (density, CTE, T g ) are strongly dependent on its thermal history. The properties presented above strongly depend on the rate of cooling which reflects the fact that highly cross-linked polymer structures do not immediately respond to changes in temperature. In particular, exceptionally high cooling rates used in MD simulations usually result in densities that are lower than experimentally observed values 39 as the structure freezes before its molecules get into more compact equilibrium configuration. For the same reason, the CTE values from simulation are usually lower than those estimated by experiment. 39 It was shown in many DSC experimental studies (see, for example, review by Wunderlich 40 ) that glass transition temperature depends not only on the rate of temperature change but also on the sign of its change. In other words, glass transition occurs at different temperatures at cooling and heating of the same sample giving lower T g values at cooling and higher ones at heating. Moreover, it was shown by experiments that hysteresis increases with increasing the rate of temperature change. Thus, we could expect that cooling cycles done using molecular dynamics simulations, as in the present work, may also yield lower glass transition temperature than that of heating cycles. B. System Size Effect. Glass transition temperatures obtained in our simulations (Figure 3a) show strong dependence on system size at high extents of the reaction. Indeed, the smaller the volume, the lesser structural rearrangements it can accommodate. So glass transition temperatures of smaller model structures (with periodic boundaries, i.e. without free surfaces) are higher than that of larger ones. The same reason is valid for the size dependence of the coefficients of thermal expansion. An increase in the coefficients of thermal expansion is observed when the simulation cell size is increased. Similarly, as larger volumes in atomic scale take more time to equilibrate, the densities of larger systems obtained from our simulations are slightly lower. C. Effect of Chain Length of the Resin Strands. The dependence of T g on resin chain length is not as clear as the trends seen for CTE and density. The observed dependence of 5311
6 Note that the structures built using epoxy monomers contain about atoms, while dimer structures have atoms and tetramer structures have atoms. As these systems are not of the same size, quantitative comparison of absolute values of the properties is not advisible since they are influenced by both chain length and size of the simulation cell. However, comparison of the individual slopes is still informative, and worth noting. Figure 4. (a) Glass transition temperature, (b) volumetric coefficient of thermal expansion, and (c) density as a function of the extent of the reaction for the atomic structures built using monomers (black), dimers (red), and tetramers (green) of the epoxy resin. The open symbols in part b represent experimental values in glassy (square) and rubbery (circle) states, 38 and in part c, the open square represents experimental value. 39 CTE and density on the chain length of the resin strands can be understood using following considerations. For infinitely long strands the cross-linking density tends to zero and any of the properties discussed above should not show any observable dependence on the degree of conversion. Moreover, it is known that small amount of resin oligomers is always present in commercial products. Our results for density and coefficients of thermal expansion for oligomer-based structures match better with experimental values and clearly show the correct trend. 4. MECHANICAL PROPERTIES OF THE HIGHLY CROSS-LINKED POLYMERIC NETWORKS 4.1. Approach Used in the Mechanical Properties Calculations. Any small volume element of an amorphous material in atomic scale can be characterized by a unique distribution of matter within it and consequently displays unique properties that sometimes can be pretty far from the macroscopic properties of the sample. It means that a macroscopically homogeneous amorphous material can be viewed as heterogeneous at the nanoscale. We can thus partition the macroscopic sample into many small elements and take an average of the properties of the individual elements to predict the macroscopic properties of the material. In this work we estimate elastic constants of the thermosetting polymer by calculating elastic constants for a number of nanoscopically small simulation cells with subsequent averaging of the obtained properties. Simple averaging of the stiffness and compliances matrices gives so cold Voigt and Reuss bounds representing upper and lower bounds of the elastic constants of the material. However, these bounds are often pretty broad for polymer networks while the aim of this study is to be able to distinguish between properties of very similar materials, e.g., materials with extent of reaction differing by 5%. For this purpose, in the present work we used two different bound estimation techniques to study statistical variation of elastic constants. The simplest, but not necessarily the best, is rough estimation technique giving Voigt and Reuss bounds mentioned above. The second technique proposed by Hill and Walpole is more sophisticated but gives significantly narrower bounds. To calculate elastic constants, we used Accelrys software 30 which implements the static approach. 45 First, three tensile and three shear deformations of a small magnitude were applied to the systems in three directions with subsequent energy minimization. The obtained stress tensor is then used to calculate stiffness and compliance matrices C ij and S ij of the simulation cells followed by estimation of Voigt Reuss and Hill Walpole bounds. Finally, assuming isotropic symmetry of the model, these stiffness and compliances matrices are used to calculate two Lame elastic constants from which Young s, shear, and bulk moduli and Poisson s ratio are calculated. 44 Because of high computational efficiency, this methodology allows one to analyze the elastic constants of a large number of nanoscopically small volume elements giving narrow bounds of the material properties. Such statistical treatment allows mimicking the effect of nanoscopic heterogeneities that are always present in real macroscopic samples and partially overreach the size limitation of the molecular dynamic simulation method. For this purpose we generated batches of up to 70 topologically distinct thermosets for each extent of the reaction. To the best of our knowledge, we are not aware of any all-atom molecular modeling that treated such a great number of statistical data (while using large simulation cells of up to atoms) to calculate elastic constants. 5312
7 Figure 5. Elastic moduli at 298 K(squares) and 480 K (circles) as a function of the extent of the reaction for the atomic structures ranging from (96, 48) to (512, 256) DGEBA/DETDA molecules: (a) Young s modulus; (b) Poisson s ratio; (c) bulk modulus; (d) shear modulus. Error bars represent Hill Walpole bounds. Color codes are black (96, 48), red (128, 64), green (256, 128), blue (432, 216), and magenta (512, 256) Results. The dependence of the elastic moduli on the extent of reaction at two temperatures for five different system sizes ranging from (96, 48) to (512, 256) DGEBA/DETDA molecules are shown in Figures 5a-d. As expected Hill-Walpole bounds are significantly narrower than Viogt and Reuss ones so in all our elastic moduli plots we show only Hill-Walpole bounds, where the size of the error bars reflect the width of the bounds. The elastic moduli for small systems containing (32, 16) and (64, 32) molecules are not shown here due to considerable scattering and extremely wide bounds. As expected, the results from our simulation demonstrate the pronounced increase in Young s, bulk and shear moduli with extent of curing at both temperatures. However, the values of the Young s modulus determined from our simulation are above the experimental value (2.71 GPa) at high extents of the cross-linking reaction. 46 The Young s, bulk and shear moduli values are lower at the elevated temperature, which is evidence of the reduced stiffness of the polymer with increase in temperature. Besides, these elastic constants demonstrate systematic dependence on the system size giving more accurate shapes of the curves and narrowing the bounds significantly with increase in system size. We do not detect any dependence of the Poisson s ratio on the extent of the reaction or system size. From our simulations we determined an average Poisson s ratio value of 0.31 at ambient temperature for all extensions and sizes of the simulation cell, which is in good agreement with experimental values for epoxy materials. 47 The dependence of mechanical properties on the length of the epoxy strands in the material are shown in Figure 6, parts a d. All elastic constants show a pronounced dependence on the length of the epoxy strands. The dependence of the Young s, bulk and shear moduli on the degree of conversion shows different slopes with the maximum slope corresponding to the structures with the shortest epoxy strands. For the structures with the shortest epoxy strands these moduli have higher value at high extent of the reactions. As expected, Poisson s ratio increases for the structures with longer epoxy strands showing the correct trend Discussion. A. Size Effect. In this study, we managed to successfully build models that are free of stresses and distorted geometry (bonds, angles etc.). However, these defects are not the only ones present in real polymers. For example, big voids and large-scale cooperative motions in macroscopic samples can lower the measured stiffness of the material. This phenomenon was observed experimentally e.g. by Shen et al. 37 and Possart et al. 48 The authors measured micrometerscale Young s modulus and compared it with macroscopic values obtained from tensile tests. In both studies Young s modulus measured at micrometer scales using nanoindentation test is higher than integral values measured at macroscale by tensile test. At nanoscale, the deviation from integral values is expected to be even more pronounced. Therefore, it is not surprising that simulation predictions at nanoscale are higher than those measured experimentally (at micro and macro scales). All the models we constructed for our MD simulations are nanoscopically small and nearly perfect. As a consequence, such structures cannot accommodate either big defects or large- 5313
8 Figure 6. Elastic moduli at 298 (squares) and 480 K (circles) as a function of the extent of the reaction for the atomic structures built using monomers (black), dimers (red) and tetramers(green) of the epoxy resin: (a) Young s modulus; (b) Poisson s ratio; (c) bulk modulus; (d) shear modulus. Error bars represent Hill Walpole bounds. scale motions and thus resulted in higher than experimentally measured Young s modulus values. B. Mechanical Properties at Temperatures above T g. At temperatures above glass transition we should expect to observe high value of Poisson s ratio that is close to 0.5 as well as a rubbery plateau modulus that is two or 3 orders of magnitude lower than the modulus at glassy state. However, the Young s moduli determined at 480 K from our simulations are slightly lower than the corresponding Young s moduli at room temperature, while Poisson s ratio takes distinctly lower values than that for perfectly incompressible material. Nevertheless, these results could be interpreted in terms of frequency dependence of elastic constants in amorphous polymers. Large-scale cooperative motions of big segments of the molecules characterize the rubbery state. However, static method of deformation does not accurately take into account the dynamic effects that are especially noticeable at high temperatures. Moreover, typical sizes of the simulation cells used in atomistic simulations could not accommodate these kinds of motions and thus resulting in higher Young s modulus values. Besides, these kinds of structure rearrangements could take macroscopic-scale time. So, one could say that elastic constants simulated in this study correspond to elastic constants measured at extremely high frequencies where relaxation motions are frozen. C. The Role of Epoxy Chain Length. The explanation given in section 3.1 on the observed dependence of material properties on the length of the resin strands composing the network is generally valid in explaining the mechanical properties dependence on this parameter. The shorter the strands the more sensitive the material property to changes in the conversion degree and the higher the slope of the dependence of the mechanical property on extent of reaction. Furthermore, the shortening of the distance between crosslinking sites increases the stiffness of the polymer network reducing the Poisson s ratio and raising the values of the remaining three moduli of the material. 5. SUMMARY AND CONCLUSIONS In the present study, we were able to generate a set of stressfree thermoset models with high degree of cure containing up to atoms. These models were used to predict the dependence of the thermo-mechanical properties of highly cross-linked polymers on several parameters: the extent of curing reaction, temperature, size of the model, and chain length of the resin strands. It was seen that densities, coefficients of thermal expansion, and glass transition temperatures of the systems are in good agreement with experimental data. However, some of the elastic constants from our model systems were found to be higher than in real macroscopic samples. The advantages and limitations of the methods used in this study are summarized as follows. A. Cross-Linking Method. The capture sphere growth approach employed in this study to build polymer networks allows one to achieve high extents of the reaction close to the real systems. The effective on-the-fly monitoring of the model quality and analysis of energetic and structural information 5314
9 enables to minimize the presence of internal stresses and geometric distortions in the produced structure. The relaxation procedure used to build thermoset structures has successfully helped to overreach time-scale limitations of the MD method. B. Static Deformation Approach for Mechanical Properties Calculation. Large number of samples averaged in the analysis of our data allows us to compensate for large scattering in mechanical properties data that is usually caused by unique distribution of matter in each nanoscopically small simulation cell. While this deformation method makes it possible to distinguish between properties of very similar materials that have minor differences, it may have difficulties in correctly predicting mechanical properties at high temperatures. Though simulated structures were equilibrated at predefined temperatures, this approach does not accurately take into account dynamic effects that become more important at elevated temperatures. C. Size and Time Scale Effects on Thermo-Mechanical Properties. Since systematic size effect on the material properties is observed one may extrapolate to predict properties at macroscopic sizes. However, due to size limitations of atomistic simulations, simulation cell could not accommodate large-scale events such as large voids and cooperative motions that are important in macroscopic-sized polymers. Therefore, the elastic constants obtained can be considered as properties for perfect highly cross-linked polymer networks with no large-scale events. Moreover, time scales used in all-atomistic molecular dynamics simulations of thermosetting polymers do not allow monitoring macroscopically long structural rearrangements, which are characteristic features of amorphous polymers. In this sense, the properties obtained in the present study allow to estimate contributions of dynamic effects as well as large-scale defects and relaxation events into the macroscopic properties of thermosetting materials. AUTHOR INFORMATION Corresponding Author * (N.B.S.) (M.T.) Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the Low Density Materials Program of the Air Force Office of Scientific Research Grant Number: FA The authors gratefully acknowledge Dr. Charles Lee (AFOSR) for valuable discussions, and the Air Force Research Laboratory DoD Supercomputing Resource Center High Performance Computing for computer time. REFERENCES (1) Pascault, J. P.; Williams, R. J. J. Epoxy Polymers: New Materials and innovations; Wiley-VCH: Weinheim, Germany, (2) Mackerle, J. Modell. Simul. Mater. Sci. Eng. 1997, 5, 615. (3) Mackerle, J. Modell. Simul. Mater. Sci. Eng. 2003, 11, 195. (4) Rohr, D. F.; Klein, M. T. Ind. Eng. Chem. Res. 1990, 29, (5) Schulz, M.; Frisch, H. L. J. Chem. Phys. 1994, 101, (6) Shy, L. Y.; Leung, Y. K.; Eichinger, B. E. Macromolecules 1985, 18, 983. (7) Cheng, K. C.; Chiu, W. Y. Macromolecules 1994, 27, (8) Carmesin, I.; Kremer, K. Macromolecules 1988, 21, (9) Jo, W. H.; Ko, M. B. Macromolecules 1994, 27, (10) Jo, W. H.; Ko, M. B. Macromolecules 1993, 26, (11) Stevens, M. J. Macromolecules 2001, 34, (12) Stevens, M. J. Macromolecules 2001, 34, (13) Tsige, M.; Stevens, M. J. Macromolecules 2004, 37, 630. (14) Tsige, M.; Lorenz, C. D.; Stevens, M. J. Macromolecules 2004, 37, (15) Mukherji, D.; Abrams, C. F. Phys. Rev. E 2009, 79, (16) Panico, M.; Narayanan, S.; Brinson, L. C. Modell. Simul. Mater. Sci. Eng. 2010, 18, (17) Prasad, A.; Grover, T.; Basu, S. IJEST 2010, 2, 17. (18) Doherty, D. C.; Holmes, B. N.; Leung, P.; Ross, R. B. Comput. Theor. Polym. Sci. 1998, 8, 169. (19) Yarovsky, I.; Evans, E. Polymer 2002, 43, 963. (20) Heine, D. R.; Grest, G. S.; Lorenz, C. D.; Tsige, M.; Stevens, M. J. Macromolecules 2004, 37, (21) Wu, C.; Xu, W. Polymer 2006, 47, (22) Fan, H. B.; Yuen, M. M. F. Polymer 2007, 48, (23) Komarov, P. V.; Chiu, Y. T.; Chen, S. M.; Khalatur, P. G.; Reineker, P. Macromolecules 2007, 40, (24) Varshney, V.; Patnaik, S. S.; Roy, A. K.; Farmer, B. L. Macromolecules 2008, 41, (25) Clancy, T. C.; Frankland, S. J. V.; Hinkley, J. A.; Gates, T. S. Polymer 2009, 50, (26) Li, C.; Strachan, A. Polymer 2010, 51, (27) Li, C.; Strachan, A. Polymer 2011, 52, (28) Bandyopadhyay, A.; Valavala, P. K.; Clancy, T. C.; Wise, K. E.; Odegard, G. M. Polymer 2011, 52, (29) Eichinger, B. E.; Akgiray, O. Computer Simulation of Polymer Network Formation. In Computer Simulation of Polymers; Colbourne, E. A., Ed.; Longman: Harlow, 1992, Chapter 9. (30) Accelrys Software inc.: Materials Studio. products/materials-studio/ (accessed Apr 10, 2012). (31) Sun, H. J. Phys. Chem. B 1998, 102, (32) Tack, J. L.; Ford, D. M. J. Mol. Graphics Modell. 2008, 26, (33) Theodorou, D. N.; Suter, U. W. Macromolecules 1985, 18, (34) Gao, J. G.; Li, Y. F.; Zhao, M.; Liu, G. D. J. Appl. Polym. Sci. 2000, 78, 794. (35) Jansen, B. J. P.; Tamminga, K. Y.; Meijer, H. E. H.; Lemstra, P. J. Polymer 1999, 40, (36) Ratna, D.; Manoj, N. R.; Varley, R.; Raman, R. K. S.; Simon, G. P. Polym. Int. 2003, 52, (37) Shen, L.; Wang, L.; Liu, T. X.; He, C. Macromol. Mater. Eng. 2006, 291, (38) Liu, W.; Varley, R. J.; Simon, G. P. Polymer 2006, 47, (39) Ratna, D.; Varley, R.; Singh, R. K.; Simon, G. P. J. Mater. Sci. 2003, 38, 147. (40) Wunderlich, B. J. Therm. Anal. Calorim. 2007, 89, 321. (41) Hill, R. J. J. Mech. Phys. Solids 1965, 13, 213. (42) Walpole, L.J. J. J. Mech. Phys. Solids 1966, 14, 151. (43) Walpole, L.J. J. J. Mech. Phys. Solids 1969, 17, 235. (44) Suter, U. W.; Eichinger, B. E. Polymer 2002, 43, 575. (45) Theodorou, D. N.; Suter, U. W. Macromolecules 1986, 19, 139. (46) Qi, B.; Zhang, Q. X.; Bannister, M.; Mai, Y. W. Compos. Struct. 2006, 75, 514. (47) Kalantar, J.; Drzal, L. T. J. Mater. Sci. 1990, 25, (48) Possart, G.; Presser, M.; Passlack, S.; Geiss, P. L.; Kopnarski, M.; Brodyanski, A.; Steinmann, P. Int. J. Adhes. Adhes. 2009, 29, 478.
MOLECULAR MODELING OF THERMOSETTING POLYMERS: EFFECTS OF DEGREE OF CURING AND CHAIN LENGTH ON THERMO-MECHANICAL PROPERTIES
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MOLECULAR MODELING OF THERMOSETTING POLYMERS: EFFECTS OF DEGREE OF CURING AND CHAIN LENGTH ON THERMO-MECHANICAL PROPERTIES N. B. Shenogina 1, M. Tsige
More informationA Molecular Modeling Approach to Predicting Thermo-Mechanical Properties of Thermosetting Polymers
A Molecular Modeling Approach to Predicting Thermo-Mechanical Properties of Thermosetting Polymers Natalia Shenogina, Wright State University Mesfin Tsige, University of Akron Soumya Patnaik, AFRL Sharmila
More informationPolymer 54 (2013) 3370e3376. Contents lists available at SciVerse ScienceDirect. Polymer. journal homepage:
Polymer 54 (2013) 3370e3376 Contents lists available at SciVerse ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer Molecular modeling of elastic properties of thermosetting polymers
More informationEffect of Resin Molecular Architecture on Epoxy Thermoset Mechanical Properties
Effect of Resin Molecular Architecture on Epoxy Thermoset Mechanical Properties The effect of resin molecular architecture on the small strain elastic constants of diamine-cured epoxy thermosets has been
More informationAtomistic Modeling of Cross-linked Epoxy Polymer
51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference18th 1-15 April 010, Orlando, Florida AIAA 010-811 Atomistic Modeling of Cross-linked Epoxy Polymer Ananyo Bandyopadhyay
More informationATOMISTIC MODELLING OF CROSSLINKED EPOXY POLYMER
ATOMISTIC MODELLING OF CROSSLINKED EPOXY POLYMER A. Bandyopadhyay 1, P.K. Valavala 2, G.M. Odegard 3 1. Department of Materials Science and Engineering, 512 M&M Building, Michigan Technological University,
More informationEffect of different crosslink densities on the thermomechanical properties of polymer nanocomposites
Effect of different crosslink densities on the thermomechanical properties of polymer nanocomposites *Byungjo Kim 1), Joonmyung Choi 2), Suyoung Yu 3), Seunghwa Yang 4) and Maenghyo Cho 5) 1), 2), 3),
More informationRelative Reactivity Volume Criterion for Cross-Linking: Application to Vinyl Ester Resin Molecular Dynamics Simulations
pubs.acs.org/macromolecules Relative Reactivity Volume Criterion for Cross-Linking: Application to Vinyl Ester Resin Molecular Dynamics Simulations Changwoon Jang, Thomas E. Lacy, Steven R. Gwaltney, Hossein
More informationMODELING THERMOSET POLYMERS AT THE ATOMIC SCALE: PREDICTION OF CURING, GLASS TRANSITION TEMPERATURES AND MECHANICAL PROPERTIES
MODELING THERMOSET POLYMERS AT THE ATOMIC SCALE: PREDICTION OF CURING, GLASS TRANSITION TEMPERATURES AND MECHANICAL PROPERTIES Jeffrey M Sanders a, Thomas JL Mustard b, David J Giesen a, Jacob Gavartin
More informationA Molecular Dynamic Modelling of Cross-Linked Epoxy Resin Using Reactive Force Field: Thermo-Mechanical Properties
Journal of Mechanics Engineering and Automation 5 (2015) 655-666 doi: 10.17265/2159-5275/2015.12.002 D DAVID PUBLISHING A Molecular Dynamic Modelling of Cross-Linked Epoxy Resin Using Reactive Force Field:
More informationMolecular modeling of crosslink distribution in epoxy polymers
Molecular modeling of crosslink distribution in epoxy polymers A. Bandyopadhyay and G.M. Odegard* Department of Mechanical Engineering Engineering Mechanics Michigan Technological University 1400 Townsend
More informationComputational prediction of the influence of crosslink distribution on the thermo-mechanical properties of epoxies
Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Reports - Open Dissertations, Master's Theses and Master's Reports 2011 Computational prediction
More informationMD Toughness Predictions for Hybrids for Extreme Environments. Logan Ward Summer Intern, JEOM Program Mentor: Dr. Mollenhauer RXBC
Examples (Former Interns) HIP Presentation Slide Example MD Toughness Predictions for Hybrids for Extreme Environments Logan Ward Summer Intern, JEOM Program Mentor: Dr. Mollenhauer RXBC Project Overview
More informationUSING MOLECULAR DYNAMICS COUPLED WITH HIGHER LENGTHSCALE SIMULATIONS FOR THE DEVELOPMENT OF IMPROVED COMPOSITE MATRIX MATERIALS
USING MOLECULAR DYNAMICS COUPLED WITH HIGHER LENGTHSCALE SIMULATIONS FOR THE DEVELOPMENT OF IMPROVED COMPOSITE MATRIX MATERIALS S. Christensen Boeing Research & Technology Box 3707 Seattle, WA 98124 MC:
More informationMOLECULAR MODELING OF PHYSICAL AGING IN EPOXY POLYMERS
THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MOLECULAR MODELING OF PHYSICAL AGING IN EPOXY POLYMERS A. Bandyopadhyay, G.M. Odegard* Michigan Technological University, Houghton, MI, USA *Corresponding
More informationModule-4. Mechanical Properties of Metals
Module-4 Mechanical Properties of Metals Contents ) Elastic deformation and Plastic deformation ) Interpretation of tensile stress-strain curves 3) Yielding under multi-axial stress, Yield criteria, Macroscopic
More informationMolecular modeling of EPON-862/graphite composites: Interfacial characteristics for multiple crosslink densities
Molecular modeling of EPON-862/graphite composites: Interfacial characteristics for multiple crosslink densities C.M. Hadden 1, B.D. Jensen 1, A. Bandyopadhyay 1, G.M. Odegard 1 *, A. Koo 2, R. Liang 2,
More informationGlass-Transition and Side-Chain Dynamics in Thin Films: Explaining. Dissimilar Free Surface Effects for Polystyrene and Poly(methyl methacrylate)
Supporting Information for Glass-Transition and Side-Chain Dynamics in Thin Films: Explaining Dissimilar Free Surface Effects for Polystyrene and Poly(methyl methacrylate) David D. Hsu, Wenjie Xia, Jake
More informationMolecular modeling of EPON-862/graphite composites: Interfacial characteristics for multiple crosslink densities
Molecular modeling of EPON-862/graphite composites: Interfacial characteristics for multiple crosslink densities C.M. Hadden 1, B.D. Jensen 1, A. Bandyopadhyay 1, G.M. Odegard 1 *, A. Koo 2, R. Liang 2,
More informationA Molecular Dynamics Simulation of a Homogeneous Organic-Inorganic Hybrid Silica Membrane
A Molecular Dynamics Simulation of a Homogeneous Organic-Inorganic Hybrid Silica Membrane Supplementary Information: Simulation Procedure and Physical Property Analysis Simulation Procedure The molecular
More informationMechanical properties of polymers: an overview. Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore
Mechanical properties of polymers: an overview Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore UGC-NRCM Summer School on Mechanical Property Characterization- June 2012 Overview of polymer
More informationChapter 3 Entropy elasticity (rubbery materials) Review basic thermal physics Chapter 5.1 to 5.5 (Nelson)
Chapter 3 Entropy elasticity (rubbery materials) Review basic thermal physics Chapter 5.1 to 5.5 (Nelson) Outline: 3.1 Strain, stress and Young modulus 3. Energy density 3.3 Typical stress-strain curve
More informationA Coarse-Grained Model for Epoxy Molding Compound
pubs.acs.org/jpcb A Coarse-Grained Model for Epoxy Molding Compound Shaorui Yang, Zhiwei Cui, and Jianmin Qu*,, Department of Mechanical Engineering and Department of Civil and Environmental Engineering,
More informationContinuum Modeling Techniques to Determine Mechanical Properties of Nanocomposites
International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Continuum Modeling Techniques to Determine Mechanical Properties of Nanocomposites Sonali Gholap 1, Dr. Dhananjay R. Panchagade
More informationMechanical Properties of Tetra-Polyethylene and Tetra-Polyethylene Oxide Diamond Networks via Molecular Dynamics Simulations
Supplemental Information Mechanical Properties of Tetra-Polyethylene and Tetra-Polyethylene Oxide Diamond Networks via Molecular Dynamics Simulations Endian Wang and Fernando A. Escobedo Table S1 Lennard-Jones
More informationMechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.
Mechanical Properties of Polymers Scope MSE 383, Unit 3-1 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Structure - mechanical properties relations Time-dependent mechanical
More informationSize exclusion chromatography of branched polymers: Star and comb polymers
Macromol. Theory Simul. 8, 513 519 (1999) 513 Size exclusion chromatography of branched polymers: Star and comb polymers Hidetaka Tobita*, Sadayuki Saito Department of Materials Science and Engineering,
More informationTHERMODYNAMIC AND MECHANICAL PROPERTIES OF EPON 862 WITH CURING AGENT DETDA BY MOLECULAR SIMULATION. A Thesis JEREMY LEE TACK
THERMDYNAMIC AND MECHANICAL PRPERTIES F EPN 862 WITH CURING AGENT DETDA BY MLECULAR SIMULATIN A Thesis by JEREMY LEE TACK Submitted to the ffice of Graduate Studies of Texas A&M University in partial fulfillment
More informationDiffusion of Water and Diatomic Oxygen in Poly(3-hexylthiophene) Melt: A Molecular Dynamics Simulation Study
Diffusion of Water and Diatomic Oxygen in Poly(3-hexylthiophene) Melt: A Molecular Dynamics Simulation Study Julia Deitz, Yeneneh Yimer, and Mesfin Tsige Department of Polymer Science University of Akron
More informationLab Week 4 Module α 1. Polymer chains as entropy springs: Rubber stretching experiment and XRD study. Instructor: Gretchen DeVries
3.014 Materials Laboratory December 9-14, 005 Lab Week 4 Module α 1 Polymer chains as entropy springs: Rubber stretching experiment and XRD study Instructor: Gretchen DeVries Objectives Review thermodynamic
More informationMolecule Dynamics Simulation of Epoxy Resin System
Molecule Dynamics Simulation of Epoxy Resin System Wu, Peilin Department of Physics, City University of Hong Kong. Lam, Tran Department of Biology, University of Pennsylvania. (RECSEM-2017, Joint Institute
More informationThe yielding transition in periodically sheared binary glasses at finite temperature. Nikolai V. Priezjev
The yielding transition in periodically sheared binary glasses at finite temperature Nikolai V. Priezjev 5 March, 2018 Department of Mechanical and Materials Engineering Wright State University Movies,
More informationAbvanced Lab Course. Dynamical-Mechanical Analysis (DMA) of Polymers
Abvanced Lab Course Dynamical-Mechanical Analysis (DMA) of Polymers M211 As od: 9.4.213 Aim: Determination of the mechanical properties of a typical polymer under alternating load in the elastic range
More informationExperimental Study of the Induced Residual Stresses During the Manufacturing Process of an Aeronautic Composite Material
Research Journal of Applied Sciences, Engineering and Technology 2(6): 596-602, 2010 ISSN: 2040-7467 Maxwell Scientific Organization, 2010 Submitted Date: July 28, 2010 Accepted Date: August 27, 2010 Published
More informationMolecular Scale Simulations on Thermoset Polymers: A Review
JOURNAL OF POLYMER SCIENCE WWW.POLYMERPHYSICS.ORG REVIEW Molecular Scale Simulations on Thermoset Polymers: A Review Chunyu Li, Alejandro Strachan Department of Materials Engineering and Birck Nanotechnology
More informationInfluence of representative volume element size on predicted elastic properties of polymer materials
Influence of representative volume element size on predicted elastic properties of polymer materials P K Valavala 1, G M Odegard 1 and E C Aifantis 2 1 Department of Mechanical Engineering-Engineering
More informationSTRONG CONFIGURATIONAL DEPENDENCE OF ELASTIC PROPERTIES OF A CU-ZR BINARY MODEL METALLIC GLASS
Chapter 3 STRONG CONFIGURATIONAL DEPENDENCE OF ELASTIC PROPERTIES OF A CU-ZR BINARY MODEL METALLIC GLASS We report the strong dependence of elastic properties on configurational changes in a Cu-Zr binary
More information(Refer Slide Time: 00:58)
Nature and Properties of Materials Professor Bishak Bhattacharya Department of Mechanical Engineering Indian Institute of Technology Kanpur Lecture 18 Effect and Glass Transition Temperature In the last
More informationVISCOELASTIC PROPERTIES OF POLYMERS
VISCOELASTIC PROPERTIES OF POLYMERS John D. Ferry Professor of Chemistry University of Wisconsin THIRD EDITION JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore Contents 1. The Nature of
More informationModule 7: Micromechanics Lecture 34: Self Consistent, Mori -Tanaka and Halpin -Tsai Models. Introduction. The Lecture Contains. Self Consistent Method
Introduction In this lecture we will introduce some more micromechanical methods to predict the effective properties of the composite. Here we will introduce expressions for the effective properties without
More informationSynergy of the combined application of thermal analysis and rheology in monitoring and characterizing changing processes in materials
Synergy of the combined application of thermal analysis and rheology in monitoring and characterizing changing processes in materials by A. Franck, W. Kunze, TA Instruments Germany Keywordss: synergy,
More information2. Amorphous or Crystalline Structurally, polymers in the solid state may be amorphous or crystalline. When polymers are cooled from the molten state
2. Amorphous or Crystalline Structurally, polymers in the solid state may be amorphous or crystalline. When polymers are cooled from the molten state or concentrated from the solution, molecules are often
More informationCoarse-Grained Molecular Dynamics Study of the Curing and Properties of Highly Cross-Linked Epoxy Polymers
pubs.acs.org/jpcb Coarse-Grained Molecular Dynamics Study of the Curing and Properties of Highly Cross-Linked Epoxy Polymers Amin Aramoon,*, Timothy D. Breitzman, Christopher Woodward, and Jaafar A. El-Awady*,
More informationModelling of viscoelastic properties of a curing adhesive
Computational Methods and Experiments in Materials Characterisation III 241 Modelling of viscoelastic properties of a curing adhesive J. de Vreugd 1, K. M. B. Jansen 1, L. J. Ernst 1 & J. A. C. M. Pijnenburg
More informationPacking grains by thermally cycling
Packing grains by thermally cycling One of the oldest and most intriguing problems in the handling of materials is how a collection of solid grains packs together. 1 While granular packing is normally
More informationSystematic Coarse-Graining and Concurrent Multiresolution Simulation of Molecular Liquids
Systematic Coarse-Graining and Concurrent Multiresolution Simulation of Molecular Liquids Cameron F. Abrams Department of Chemical and Biological Engineering Drexel University Philadelphia, PA USA 9 June
More informationComparison of COMPASS and PCFF in Calculating Mechanical Behaviors of Aramid Fiber by Means of Molecular Dynamics
AMSE JOURNALS-AMSE IIETA publication-2017-series: Modelling B; Vol. 86; N 2; pp 438-446 Submitted Mar. 04; Revised May 12, 2017; Accepted Jun. 12, 2017 Comparison of COMPASS and PCFF in Calculating Mechanical
More information3.22 Mechanical Properties of Materials Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 3.22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Quiz #1 Example
More informationElasticity Constants of Clay Minerals Using Molecular Mechanics Simulations
Elasticity Constants of Clay Minerals Using Molecular Mechanics Simulations Jin-ming Xu, Cheng-liang Wu and Da-yong Huang Abstract The purpose of this paper is to obtain the elasticity constants (including
More informationCHAPTER 4 MODELING OF MECHANICAL PROPERTIES OF POLYMER COMPOSITES
CHAPTER 4 MODELING OF MECHANICAL PROPERTIES OF POLYMER COMPOSITES 4. Introduction Fillers added to polymer matrices as additives are generally intended for decreasing the cost (by increase in bulk) of
More informationVIII. Rubber Elasticity [B.Erman, J.E.Mark, Structure and properties of rubberlike networks]
VIII. Rubber Elasticity [B.Erman, J.E.Mark, Structure and properties of rubberlike networks] Using various chemistry, one can chemically crosslink polymer chains. With sufficient cross-linking, the polymer
More informationRHEOLOGICAL AND MORPHOLOGICAL INFLUENCES ON THE VISCOELASTIC BEHAVIOUR OF POLYMER COMPOSITES
RHEOLOGICAL AND MORPHOLOGICAL INFLUENCES ON THE VISCOELASTIC BEHAVIOUR OF POLYMER COMPOSITES R. Gaertner 1 and 2, C. Gauthier 1, P. Franciosi 1, A. Khavandi 1 and M. Shaterzadeh 1 1 GEMPPM - UMR 5510,
More informationMicroporous Carbon adsorbents with high CO 2 capacities for industrial applications
Microporous Carbon adsorbents with high CO 2 capacities for industrial applications Santiago Builes, a,b Thomas Roussel,* b Camelia Matei Ghimbeu, c Julien Parmentier, c Roger Gadiou, c Cathie Vix-Guterl
More informationXI. NANOMECHANICS OF GRAPHENE
XI. NANOMECHANICS OF GRAPHENE Carbon is an element of extraordinary properties. The carbon-carbon bond possesses large magnitude cohesive strength through its covalent bonds. Elemental carbon appears in
More informationChapter 1 Introduction
Chapter 1 Introduction This thesis is concerned with the behaviour of polymers in flow. Both polymers in solutions and polymer melts will be discussed. The field of research that studies the flow behaviour
More information2.1 Strain energy functions for incompressible materials
Chapter 2 Strain energy functions The aims of constitutive theories are to develop mathematical models for representing the real behavior of matter, to determine the material response and in general, to
More informationA NEW GENERATION OF CONSTRUCTION MATERIALS: CARBON NANOTUBES INCORPORATED TO CONCRETE AND POLYMERIC MATRIX
A NEW GENERATION OF CONSTRUCTION MATERIALS: CARBON NANOTUBES INCORPORATED TO CONCRETE AND POLYMERIC MATRIX Javier Grávalos, Juan Manuel Mieres and Santiago González R&D Department, NECSO Entrecanales Cubiertas
More informationPrediction of Elastic Constants on 3D Four-directional Braided
Prediction of Elastic Constants on 3D Four-directional Braided Composites Prediction of Elastic Constants on 3D Four-directional Braided Composites Liang Dao Zhou 1,2,* and Zhuo Zhuang 1 1 School of Aerospace,
More informationMATERIALS SCIENCE POLYMERS
POLYMERS 1) Types of Polymer (a) Plastic Possibly the largest number of different polymeric materials come under the plastic classification. Polyethylene, polypropylene, polyvinyl chloride, polystyrene,
More informationSimulation of Cure Volume Shrinkage Stresses on Carbon/Vinyl Ester Composites in Microindentation Testing
8 th International LS-DYNA Users Conference Simulation Technology (3) Simulation of Cure Volume Shrinkage Stresses on Carbon/Vinyl Ester Composites in Microindentation Testing Tom Mase, Lanhong Xu, Lawrence
More informationDepartment of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
5 th Australasian Congress on Applied Mechanics, ACAM 2007 10-12 December 2007, Brisbane, Australia Toughening mechanisms in novel nano-silica epoxy polymers A.J. Kinloch 1, B.B. Johnsen 1, R.D. Mohammed
More informationThe bulk modulus of covalent random networks
J. Phys.: Condens. Matter 9 (1997) 1983 1994. Printed in the UK PII: S0953-8984(97)77754-3 The bulk modulus of covalent random networks B R Djordjević and M F Thorpe Department of Physics and Astronomy
More informationMolecular modeling of EPON 862-DETDA polymer
Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Reports - Open Dissertations, Master's Theses and Master's Reports 2012 Molecular modeling
More informationCase study: molecular dynamics of solvent diffusion in polymers
Course MP3 Lecture 11 29/11/2006 Case study: molecular dynamics of solvent diffusion in polymers A real-life research example to illustrate the use of molecular dynamics Dr James Elliott 11.1 Research
More informationMOLECULAR MODELING OF MECHANICAL PROPERTIES OF THE CHITOSAN BASED GRAPHENE COMPOSITES
U.P.B. Sci. Bull., Series B, Vol. 76, Iss. 1, 2014 ISSN 1454 2331 MOLECULAR MODELING OF MECHANICAL PROPERTIES OF THE CHITOSAN BASED GRAPHENE COMPOSITES Andreea Mădălina PANDELE 1, Mariana IONIŢĂ 2, Horia
More informationSIZE EFFECTS IN THE COMPRESSIVE CRUSHING OF HONEYCOMBS
43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con 22-25 April 2002, Denver, Colorado SIZE EFFECTS IN THE COMPRESSIVE CRUSHING OF HONEYCOMBS Erik C. Mellquistand Anthony M.
More informationplane in a cubic unit cell. Clearly label the axes. (b) Draw two directions in the ( 112)
Midterm Examination - Thursday, February 5, 8:00 9:5 AM Place all answers in a 8.5" x " Bluebook Allowed:, double-sided 8.5" x " page of notes must return with exam. Required: Picture ID when returning
More informationMultiscale modeling of failure in ABS materials
Institute of Mechanics Multiscale modeling of failure in ABS materials Martin Helbig, Thomas Seelig 15. International Conference on Deformation, Yield and Fracture of Polymers Kerkrade, April 2012 Institute
More informationComputational Analysis for Composites
Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics
More informationNon-conventional Glass fiber NCF composites with thermoset and thermoplastic matrices. F Talence, France Le Cheylard, France
20 th International Conference on Composite Materials Copenhagen, 19-24th July 2015 Non-conventional Glass fiber NCF composites with thermoset and thermoplastic matrices. Thierry Lorriot 1, Jalal El Yagoubi
More informationMATERIAL MECHANICS, SE2126 COMPUTER LAB 4 MICRO MECHANICS. E E v E E E E E v E E + + = m f f. f f
MATRIAL MCHANICS, S226 COMPUTR LAB 4 MICRO MCHANICS 2 2 2 f m f f m T m f m f f m v v + + = + PART A SPHRICAL PARTICL INCLUSION Consider a solid granular material, a so called particle composite, shown
More informationPhys 450 Spring 2011 Solution set 6. A bimolecular reaction in which A and B combine to form the product P may be written as:
Problem Phys 45 Spring Solution set 6 A bimolecular reaction in which A and combine to form the product P may be written as: k d A + A P k d k a where k d is a diffusion-limited, bimolecular rate constant
More informationCURE DEPENDENT CREEP COMPLIANCE OF AN EPOXY RESIN
CURE DEPENDENT CREEP COMPLIANCE OF AN EPOXY RESIN Daniel J. O Brien and Scott R. White 2 Department of Mechanical and Industrial Engineering, University of Illinois at Urbana- Champaign 206 West Green,
More informationShear Properties and Wrinkling Behaviors of Finite Sized Graphene
Shear Properties and Wrinkling Behaviors of Finite Sized Graphene Kyoungmin Min, Namjung Kim and Ravi Bhadauria May 10, 2010 Abstract In this project, we investigate the shear properties of finite sized
More informationInternational Journal of Basic & Applied Sciences IJBAS-IJENS Vol:14 No:04 9
International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:14 No:04 9 Investigation on a Practical Model to Explain the Temperature Change of a Deflating Balloon Yongkyun Lee*, Yongnam Kwon Korean
More informationA MOLECULAR DYNAMICS STUDY OF POLYMER/GRAPHENE NANOCOMPOSITES
A MOLECULAR DYNAMICS STUDY OF POLYMER/GRAPHENE NANOCOMPOSITES Anastassia N. Rissanou b,c*, Vagelis Harmandaris a,b,c* a Department of Applied Mathematics, University of Crete, GR-79, Heraklion, Crete,
More informationTOPIC 7. Polymeric materials
Universidad Carlos III de Madrid www.uc3m.es MATERIALS SCIENCE AND ENGINEERING TOPIC 7. Polymeric materials 1. Introduction Definition General characteristics Historic introduction Polymers: Examples 2.
More informationCyclo Dehydration Reaction of Polyhydrazides. 11. Kinetic Parameters Obtained from Isothermal Thermogravimetry
Cyclo Dehydration Reaction of Polyhydrazides. 11. Kinetic Parameters Obtained from Isothermal Thermogravimetry B. GEBBEN, M. H. V. MULDER, and C. A, SMOLDERS, University of Twente, Dept. of Chemical Technology,
More information3.091 Introduction to Solid State Chemistry. Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS
3.091 Introduction to Solid State Chemistry Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS 1. INTRODUCTION Crystals are held together by interatomic or intermolecular bonds. The bonds can be covalent,
More informationUB association bias algorithm applied to the simulation of hydrogen fluoride
Fluid Phase Equilibria 194 197 (2002) 249 256 UB association bias algorithm applied to the simulation of hydrogen fluoride Scott Wierzchowski, David A. Kofke Department of Chemical Engineering, University
More informationIAP 2006: From nano to macro: Introduction to atomistic modeling techniques and application in a case study of modeling fracture of copper (1.
IAP 2006: From nano to macro: Introduction to atomistic modeling techniques and application in a case study of modeling fracture of copper (1.978 PDF) http://web.mit.edu/mbuehler/www/teaching/iap2006/intro.htm
More informationFinal Project: Indentation Simulation Mohak Patel ENGN-2340 Fall 13
Final Project: Indentation Simulation Mohak Patel ENGN-2340 Fall 13 Aim The project requires a simulation of rigid spherical indenter indenting into a flat block of viscoelastic material. The results from
More informationStructural and Mechanical Properties of Nanostructures
Master s in nanoscience Nanostructural properties Mechanical properties Structural and Mechanical Properties of Nanostructures Prof. Angel Rubio Dr. Letizia Chiodo Dpto. Fisica de Materiales, Facultad
More informationMolecular Dynamics Simulation of Fracture of Graphene
Molecular Dynamics Simulation of Fracture of Graphene Dewapriya M. A. N. 1, Rajapakse R. K. N. D. 1,*, Srikantha Phani A. 2 1 School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada
More informationEffect Of Curing Method On Physical And Mechanical Properties Of Araldite DLS 772 / 4 4 DDS Epoxy System
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 2, ISSUE 2, FEBRUARY 213 ISSN 2277-8616 Effect Of Curing Method On Physical And Mechanical Properties Of Araldite DLS 772 / 4 4 DDS Epoxy
More informationImproved stress prediction in adhesive bonded optical components
Improved stress prediction in adhesive bonded optical components J. de Vreugd 1a, M.J.A. te Voert a, J.R. Nijenhuis a, J.A.C.M. Pijnenburg a, E. Tabak a a TNO optomechatronics, Stieltjesweg 1, 2628 CK,
More informationSupporting Information
Supporting Information Atomic Force Microscopy Nanomechanical Mapping Visualizes Interfacial Broadening between Networks Due to Chemical Exchange Reactions Changfei He, Shaowei Shi, *, Xuefei Wu, Thomas
More informationMechanical Properties of Silica Aerogel A Molecular Dynamics Study
Mechanical Properties of Silica Aerogel A Molecular Dynamics Study Jincheng Lei 1), Jianying Hu 2) and *Zishun Liu 3) 1), 2) Int. Center for Applied Mechanics; State Key Laboratory for Strength and Vibration
More informationProperty Prediction with Multiscale Simulations of Silicon Containing Polymer Composites
Silicon-Containing Polymers and Composites ACS Division of Polymer Chemistry Omni Hotel, San Diego, CA Property Prediction with Multiscale Simulations of Silicon Containing Polymer Composites Dr. Andreas
More informationMaterials and Structures
Journal of Mechanics of Materials and Structures BRITTLE FRACTURE BEYOND THE STRESS INTENSITY FACTOR C. T. Sun and Haiyang Qian Volume 4, Nº 4 April 2009 mathematical sciences publishers JOURNAL OF MECHANICS
More informationRheological and mechanical properties of epoxy composites modified with montmorillonite nanoparticles
Plasticheskie Massy, No. 3, 2011, pp. 56 60 Rheological and mechanical properties of epoxy composites modified with montmorillonite nanoparticles S.O. Il in, 1 I.Yu. Gorbunova, 2 E.P. Plotnikova, 1 and
More informationCellular solid structures with unbounded thermal expansion. Roderic Lakes. Journal of Materials Science Letters, 15, (1996).
1 Cellular solid structures with unbounded thermal expansion Roderic Lakes Journal of Materials Science Letters, 15, 475-477 (1996). Abstract Material microstructures are presented which can exhibit coefficients
More informationPOLYMER STRUCTURES ISSUES TO ADDRESS...
POLYMER STRUTURES ISSUES TO ADDRESS... What are the basic microstructural features? ow are polymer properties effected by molecular weight? ow do polymeric crystals accommodate the polymer chain? Melting
More informationDevelopment of a code to generate randomly distributed short fiber composites to estimate mechanical properties using FEM
International Journal of Theoretical and Applied Mechanics. ISSN 0973-6085 Volume 12, Number 4 (2017) pp. 863-872 Research India Publications http://www.ripublication.com Development of a code to generate
More informationIntroduction to Polymerization Processes
Introduction to Polymerization Processes Reference: Aspen Polymers: Unit Operations and Reaction Models, Aspen Technology, Inc., 2013. 1- Polymer Definition A polymer is a macromolecule made up of many
More informationCoarse-grained Models for Oligomer-grafted Silica Nanoparticles
Modeling So+ Ma-er: Linking Mul3ple Length and Time Scales KITP Conference, Santa Barbara, June 4-8, 2012 Coarse-grained Models for Oligomer-grafted Silica Nanoparticles Bingbing Hong Alexandros Chremos
More informationCationic Cure of Epoxy Resin by an Optimum Concentration of N-benzylpyrazinium Hexafluoroantimonate
Macromolecular Research, Vol. 10, No. 1, pp 34-39 (2002) Cationic Cure of Epoxy Resin by an Optimum Concentration of N-benzylpyrazinium Hexafluoroantimonate Jong Keun Lee* and Yusong Choi Department of
More informationMOLECULAR SIMULATION FOR PREDICTING MECHANICAL STRENGTH OF 3-D JUNCTIONED CARBON NANOSTRUCTURES
ECCM16-16 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 214 MOLECULAR SIMULATION FOR PREDICTING MECHANICAL STRENGTH OF 3-D JUNCTIONED CARBON NANOSTRUCTURES S. Sihn a,b*, V.
More informationMolecular Simulations of Carbon- Polymer Interfaces: Potential for Multiscale Composite Design
ICME, Melbourne, Feb 2018. Molecular Simulations of Carbon- Polymer Interfaces: Potential for Multiscale Composite Design Prof. Tiff Walsh and Dr. Baris Demir Institute for Frontier Materials Deakin University
More informationMACROSCALE EXPERIMENTAL EVIDENCE OF A REDUCED- MOBILITY NON-BULK POLYMER PHASE IN NANOTUBE- REINFORCED POLYMERS
MACROSCALE EXPERIMETAL EVIDECE OF A REDUCED- MOBILITY O-BULK POLYMER PHASE I AOTUBE- REIFORCED POLYMERS F.T. Fisher and L.C. Brinson Department of Mechanical Engineering orthwestern University Evanston,
More information