Molecular dynamics simulations of realistic, united atom models of polyethylene undergoing uniaxial extension are described. Systems composed of chains ranging from 25 to 400 carbons have been ...studied, under a variety of processing histories, including isothermal deformation at constant applied stress below the melt temperature Tm, isothermal deformation below Tm followed by annealing, isothermal deformation above Tm followed by crystallization at a quench temperature below Tm, and non-isothermal crystallization during simultaneous deformation and cooling through Tm. Extension and orientation of large segments of flexible chains by uniaxial deformation accelerates the primary nucleation rate to a time scale accessible by molecular dynamics simulation. Entanglements operative during active deformation promote extension and orientation without nucleation of a crystal phase, while relaxation of stress at constant strain is sufficient to allow slippage of chains past pinning points and rapid nucleation and growth of crystallites as neighboring oriented chains come into registry. Isothermal crystallization of pre-oriented systems shows an apparent increase in nucleation density at lower temperatures; the resulting ordered regions are smaller and more closely aligned in the direction of orientation. During non-isothermal deformation, where stretching and cooling occur simultaneously, a first order transition is observed, with discontinuities in the volume and global order parameter, when the system crystallizes.
We have performed dynamic Monte Carlo (MC) simulations and pulsed-gradient diffusion (D) experiments to study the effect of stereochemical composition on diffusion in linear polypropylene (PP) melts. ...The coarse-grained simulations were based on the rotational isomeric state model and Lennard-Jones potentials. For the proton NMR diffusion measurements we obtained three PP specimens of differing molecular weight M and dispersity, with the probability of a meso diad P m = 0.02 (syndiotactic), 0.23 (atactic), and 0.89 (nearly isotactic). The experiment supplied the conversion factor K between MC steps and real time. Both simulation and M-scaled experiment found D at high P m several times faster than at low P m. The constant-M simulation also showed a maximum near P m = 0.8 due to quenched randomness. To permit a more precise comparison with experiment, new simulations tracked the samples’ P m, mean M, and polydispersity, but K was found to vary significantly between samples. The GPC determination of M and its distribution, based on linear polyethylene calibration, may be dependent on PP stereochemistry (via D), generating misleading results. However, dilute PP diffusion measurements in a chlorinated solvent, consistent with classical dilute diffusion theory, suggest that the observed P m-dependence of K may instead be an intrinsic feature of this MC methodology, implying that MC cannot be relied upon to provide microstructure-independent results for self-diffusion.
We conduct a comprehensive study of the effect of stereochemistry on the diffusion of isotactic, atactic, and syndiotactic polypropylene (PP), with dynamical Monte Carlo. We simulate realistic ...two-bead Monte Carlo moves on a stereochemistry-dependent, coarse-grained model of PP based on the rotational isomeric state (RIS) model and repulsive Lennard-Jones interactions. We find that isotactic PP (iPP) diffuses faster than syndiotactic PP (sPP) as expected, but a maximum in the diffusion rate at an intermediate stereochemical composition (aPP) is also found. To determine the origin of this effect, we compare pair correlation functions of the slowest-moving beads to those of all beads, identifying conformations that limit mobility. We find a few small, long-lived clusters with chain conformations reminiscent of those in crystals in iPP and sPP; although slow-moving beads also cluster in aPP, they are short-lived with no dominant conformations. We look at the effects of local stereochemistry through Monte Carlo acceptance rates, categorized by the stereochemistry of the local tetrad and overall stereochemical composition. Sequences of meso and racemo diads diffuse faster in aPP due to quenched randomness of stereochemical sequences than in iPP and sPP. Comparison to isolated chain acceptance rates suggests that intermolecular cohesiveness of stereochemically pure sequences lowers mobility but can be overcome by the randomness of atactic stereochemistry. The mechanisms described here for PP may affect the mobility of other polymers in which stereochemical composition is an issue.
The influence of the quenched randomness in the stereochemical sequences of atactic chains on the mean-square unperturbed end-to-end distance, 〈r 2〉0, is assessed. The method uses a rotational ...isomeric state (RIS) model based on virtual bonds between the centers of mass of the C6 rings in polystyrene. This virtual bond model is derived from a conventional RIS model expressed in terms of the C−C bonds in the main chain. The zeroth-approximation virtual bond model, which retains only the most probable conformations of each tetrad, correctly finds 〈r 2〉0 ∼ n in the limit as n → ∞ if the probability for a meso diad, p m, is 0 < p m < 1, although the same zeroth-approximation model yields 〈r 2〉0 ∼ n 2 if p m is either 0 or 1. The values of 〈r 2〉0 at intermediate p m are surprisingly close to the ones deduced from a full, C−C bond based RIS model. This achievement of the zeroth-approximation model demonstrates the important role of the quenched randomness of the stereochemical sequences in determining the unperturbed dimensions of atactic chains. Excellent agreement with the 〈r 2〉0 from the full RIS model based on C−C bonds over the entire range of stereochemical composition, 0 ≤ p m ≤ 1, can be achieved in a first-approximation virtual bond model, which includes the next most probable conformations at each tetrad and refines slightly some of the conformations by minor adjustments in soft degrees of freedom.
Nonrandomness in the distribution of rotational isomeric states along a flexible unperturbed chain reduces its conformational entropy. Pairwise interdependence of the bonds is a necessary, but not ...sufficient, condition for a significant reduction. The reduction in conformational entropy from this source can be as severe as a factor of three. It is generally more severe for isotactic chains than for the syndiotactic chains constructed from the same monomer. Surprising effects are sometimes seen, such as the nearly identical reductions in conformational entropy for polydimethylsiloxane, a very flexible chain, and for poly(methyl methacrylate), a much stiffer chain.
Fractional difference in conformational entropy due to nonrandomness versus probability of helix in helix‐coil transition.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2005.
Includes bibliographical references (p. 195-207).
Molecular simulation has become a very powerful tool for ...understanding the process of polymer crystallization. By using carefully constructed simulations, one can independently observe the two phenomena responsible for melt crystallization: nucleation and growth. This research focuses on modeling the growth process using potentials that are well-parameterized for alkanes and polyethylene. In experiment and modeling of the kinetics of alkane crystallization, focus has been concentrated on growth rates very near the melting temperature, where the growth of these systems is optically observable. In this temperature range near .., diffusion is not a limiting factor, which has led to theory that models the thermodynamic driving force and its effect on kinetics. Phenomenologically, one observes a maximum growth rate at a temperature intermediate between the glass transition temperature ... and the melt temperature ... This arises as a competition between a thermodynamic driving force towards crystal growth, associated with locking chains into crystallographic registry and the ability of chains to diffuse to the new layer and rearrange themselves conformationally to satisfy the restrictions of crystal symmetry. The thermodynamic driving force is rate limiting at high temperatures, while melt mobility is rate limiting at low temperatures. Growth rates are of interest to the polymer processing community, who require accurate crystallization kinetic data over the entire temperature range, in order to predict solidification under process conditions and thus final fiber properties.
(cont.) A model which retains its connection to molecular structure would certainly be of benefit for purposes of product design; such connection is possible using molecular simulations. Nonequilibrium molecular dynamics enables us to observe growth for a range of temperatures around the temperature at which the maximum growth rate occurs. We present a molecular dynamics (MD) framework for measuring crystal growth rates for n-eicosane (C₂₀H₄₂, denoted C20), by simulating growth on a pre-existing crystal surface. We show that growth rates for short alkanes such as C20 are directly observable over a range of quench temperatures, for the case where the crystallization front is preceded by a supercooled amorphous region, and heat transfer occurs faster than the characteristic time for crystallization. We present data that we have acquired from these simulations through analysis of the propagation of orientational order, using the bond order parameter, and density changes, using Voronoi volumes. To determine molecular weight effects, we use the same technique to look at systems of C₅₀H₁₀₂ and C₁₀₀H₂₀₂ (denoted C50 and C100). With these higher molecular weight n-alkanes, we can also measure the occurrence of folds during crystal growth. From these MD simulations, we obtain data for the growth rate of n-alkane crystals over a range of temperatures and molecular weights. Qualitatively, we see frequent adsorption and desorption of chain segments on the surface in both C50 and C100 systems. We find evidence for a surface nucleus involving 4-5 chain segments, from multiple chains, that are approximately 20 beads long, shorter than the ultimate thickness of the chain stem in the crystal.
(cont.) We construct a general crystal growth model that can be parameterized entirely in terms of universal properties of polymer chains, described by polymer physics and chemically specific quantities that can be estimated polymer by polymer using molecular dynamics simulations. The model is an extension to polymer crystallization models to incorporate molecular weight effects, using a small number of chemically specific quantities that can be estimated from molecular dynamics simulations. It accounts for the thermodynamic driving force, using classical nucleation theory, and melt relaxation time, using WLF theory. Our model can predict rates as a function of temperature and molecular weight, up to the entanglement molecular weight. Past the entanglement molecular weight, the analysis reveals that the growth rate of alkanes and polyethylene can both be described by the same relationship. The appropriate relaxation time is used to describe the kinetic barrier to crystallization. For chains shorter than the entanglement length, this is the Rouse time. For chains longer than the entanglement molecular weight, kinetic limitations are modeled by the local relaxation of an entangled segment at the interface. Use of the model is illustrated for polyethylene crystallizing in a fiber spin line under conditions of slow cooling and fast cooling. Finally, we present a simplified framework for the study of polymer crystallization using Kinetic Monte Carlo (KMC). We have developed a general KMC algorithm for measuring growth of a polymer crystal phase during melt crystallization, based on the algorithm of Bortz et al.
(cont.) We have incorporated new moves into a general framework to allow multi-chain, three-dimensional growth and the escape of chains from the crystal to the melt, through the fold surface. We performed parametric studies on the melt-crystallization of C20 to study the effects of each energy barrier. In addition, the KMC algorithm allows us to consider the importance of individual moves in contributing to growth. We have shown, as a proof-of-concept, that this algorithm is capable of generating morphologies characteristic of several theories of secondary nucleation in polymer melts.
by Numan Waheed.
Ph.D.
We review the use of molecular dynamics (MD) simulation at MIT to gain insight into the molecular level mechanisms of polymer crystallization from the melt. Simulations are constructed to observe ...nucleation and growth processes separately. For nucleation, we induce elongation under constant load before quenching, to accelerate the process in accord with experimental observations. We observe multiple nucleation events, increased perfection of crystalline lamella on the 5nm length scale, and lamellar thickening. Nucleation is characterized by a competition of rates. The rate of spontaneous ordering competes with the rate of conformational relaxation to determine the number, size and chain tilt of the crystallites. To measure lamellar growth, we perform simulations for C20H42, C50H102 and C100H202 melts. From these simulations, we obtain data for the growth rate of n-alkane crystals over a range of temperatures and molecular weights. We construct a general crystal growth model that can be parameterized in terms of chemical properties of polymer chains and constants derived from polymer physics. Analysis reveals that the crystal growth rates of alkanes and polyethylene can both be described by the same relationship when the appropriate relaxation time is used to describe the transport barrier to crystallization. For chains shorter than the entanglement length, this is the Rouse time. For chains longer than the entanglement molecular weight, transport limitations are modeled by the local relaxation of an entangled segment at the interface.
In developing countries like Pakistan, cleft surgery is expensive for families, and the child also experiences much pain. In this article, we propose a machine learning–based solution to avoid cleft ...in the mother’s womb. The possibility of cleft lip and palate in embryos can be predicted before birth by using the proposed solution. We collected 1000 pregnant female samples from three different hospitals in Lahore, Punjab. A questionnaire has been designed to obtain a variety of data, such as gender, parenting, family history of cleft, the order of birth, the number of children, midwives counseling, miscarriage history, parent smoking, and physician visits. Different cleaning, scaling, and feature selection methods have been applied to the data collected. After selecting the best features from the cleft data, various machine learning algorithms were used, including random forest, k-nearest neighbor, decision tree, support vector machine, and multilayer perceptron. In our implementation, multilayer perceptron is a deep neural network, which yields excellent results for the cleft dataset compared to the other methods. We achieved 92.6% accuracy on test data based on the multilayer perceptron model. Our promising results of predictions would help to fight future clefts for children who would have cleft.
Microservices are containerized, loosely coupled, interactive smaller units of the application that can be deployed, reused, and maintained independently. In a microservices-based application, ...allocating the right computing resources for each containerized microservice is important to meet the specific performance requirements while minimizing the infrastructure cost. Microservices-based applications are easy to scale automatically based on incoming workload and resource demand automatically. However, it is challenging to identify the right amount of resources for containers hosting microservices and then allocate them dynamically during the auto-scaling. Existing auto-scaling solutions for microservices focus on identifying the appropriate time and number of containers to be added/removed dynamically for an application. However, they do not address the issue of selecting the right amount of resources, such as CPU cores, for individual containers during each scaling event. This paper presents a novel approach to dynamically allocate the CPU resources to the containerized microservice during the autoscaling events. Our proposed approach is based on the machine learning method, which can identify the right amount of CPU resources for each container, dynamically spawning for the microservices over time to satisfy the application’s response time requirements. The proposed solution is evaluated using a benchmark microservices-based application based on real-world workloads on the Kubernetes cluster. The experimental results show that the proposed solution outperforms by yielding a 40% to 60% reduction in violating the response time requirements with 0.5
×
to 1.5
×
less cost compared to the state-of-art baseline methods.
