This document is a summer internship report submitted by Prafull Kumar Sharma studying the depletion attraction between branched polymers using computer simulations. The report introduces the concepts of polymers, depletion attraction between colloids, dendrimer structure, and the bond fluctuation method used in the simulations. The goal is to understand depletion attraction between dendrimers with and without solvent using umbrella sampling to calculate free energy. Simulation results and their discussion are presented in section 3.
Surface Plasmon Modes of Dielectric-Metal-Dielectric Waveguides and ApplicationsIOSRJECE
The dielectric-metal-dielectric plasmonic waveguide structures find applications in integrated optics and fiber polarizers and sensors. Surface plasmon waves guided by thin metal film have been intensively studied over the last two decades. However, most studies have been confined to relatively low index dielectrics. With growing interest in silicon photonics and other semiconductors dielectric of relatively higher dielectric constant we carried out a detailed study of the modes supported by a metal filmbetween dielectrics of relatively higher dielectric constant. The study clearly shows that both modes, the“antisymmetric” (푎푏 ) short range and “symmetric” (푠푏 ) long range bound modes can exist only when the contrast between the indices is low. For high contrast the symmetric mode transforms into a leaky mode.For completeness we also includethe antisymmetric leaky (푎푙 ) mode and symmetric leaky (푠푙 ) mode in our study, although they are not important for guided wave structures. We have also included “leaky modes” in the bound mode domain as solution of the boundary value problem as reported in some early studies. We have also considered some applications of the DMD waveguides with an emphasis on identifying the participating mode in each application
The document discusses polymer brushes and methods for their synthesis. It provides an overview of polymer brushes, including their general features and how their properties depend on grafting density. It also describes various types of polymer brushes and common methods for synthesizing them, including grafting onto, grafting from, and grafting through approaches. Finally, it discusses uses of responsive polymer brushes and their potential applications in areas like drug delivery and microfluidic devices.
The document discusses using polymers to functionalize surfaces for applications such as drug delivery. It describes modeling polymers using techniques like self-consistent field theory and numerical methods. The summary concludes that the modeling could help experimentalists design random copolymer brush systems to achieve perpendicular lamellae for high-value semiconductor devices.
Theoretical study of metal clad optical waveguide polarizerijsrd.com
In this paper, the metal clad optical waveguide polarizer have been analysed and presented. The metal's that were used are Gallium Arsenide and Aluminium for the cladding purpose of comparison and analysis. It was found that the variation between TE mode and TM mode when Gallium Arsenide is used as the cladding is less as compared to Aluminium. This is due to the metal cladding itself will cause a cut-off region in the polarizer. Gallium arsenide may have fewer modes compared to aluminium and which resulted in the variation of the graphs between the two metals used. We have also shown that there is a slight drop of the TM to TE loss ratio when the buffer layer thickness is increased. It was also found that the high extinction ratio results in the high and linear attenuation in the fiber.
The document discusses the molecular weight of polymers. It defines molecular weight as the sum of the atomic weights of all the atoms in a polymer molecule. There are two types of average molecular weights - number average molecular weight (Mn) and weight average molecular weight (Mw). Mn is calculated by dividing the total weight of polymer molecules by the total number of molecules, while Mw takes into account that larger molecules contribute more to the total mass. Mw is always higher than Mn. Molecular weight affects various properties - higher molecular weight increases mechanical properties but lowers thermal properties. Various techniques can be used to determine molecular weight and its distribution.
This summary provides the key points in 3 sentences:
The document discusses polarization errors in fiber optic gyroscopes that use fiber ring interferometers. It shows that applying polarizing fibers at the input and in the sensing coil can significantly suppress polarization errors. Using polarizing fibers at both locations can radically reduce errors by suppressing interfering polarization modes before they propagate through the sensing coil.
- Polymer molecular weight determines many physical properties like transition temperatures and mechanical properties.
- Molecular weight distributions are described using average values like number average (MN), weight average (MW), and viscosity average (MV).
- For condensation polymers formed from bifunctional monomers, the most probable molecular weight distribution was derived by Flory. It results in a monotonically decreasing function with the monomer being the most probable species even at high conversion.
New optical w fiber panda for fiber optic gyroscope sensitive coilKurbatov Roman
This document proposes a new type of optical fiber called a W-fiber Panda that could improve fiber optic gyroscopes. The fiber has a core with nitrogen doping surrounded by stress-applying rods that create birefringence. Testing showed a polarizing version had 3 dB/km x-mode losses and 30 dB/km dichroism, while a polarization-maintaining version had ultra-low losses of 0.35 dB/km. This new fiber combines advantages of existing fibers by allowing a wide single-polarization spectral window as well as a desired mode field diameter. Its low losses could enable longer or more sensitive fiber optic gyroscope coils.
Surface Plasmon Modes of Dielectric-Metal-Dielectric Waveguides and ApplicationsIOSRJECE
The dielectric-metal-dielectric plasmonic waveguide structures find applications in integrated optics and fiber polarizers and sensors. Surface plasmon waves guided by thin metal film have been intensively studied over the last two decades. However, most studies have been confined to relatively low index dielectrics. With growing interest in silicon photonics and other semiconductors dielectric of relatively higher dielectric constant we carried out a detailed study of the modes supported by a metal filmbetween dielectrics of relatively higher dielectric constant. The study clearly shows that both modes, the“antisymmetric” (푎푏 ) short range and “symmetric” (푠푏 ) long range bound modes can exist only when the contrast between the indices is low. For high contrast the symmetric mode transforms into a leaky mode.For completeness we also includethe antisymmetric leaky (푎푙 ) mode and symmetric leaky (푠푙 ) mode in our study, although they are not important for guided wave structures. We have also included “leaky modes” in the bound mode domain as solution of the boundary value problem as reported in some early studies. We have also considered some applications of the DMD waveguides with an emphasis on identifying the participating mode in each application
The document discusses polymer brushes and methods for their synthesis. It provides an overview of polymer brushes, including their general features and how their properties depend on grafting density. It also describes various types of polymer brushes and common methods for synthesizing them, including grafting onto, grafting from, and grafting through approaches. Finally, it discusses uses of responsive polymer brushes and their potential applications in areas like drug delivery and microfluidic devices.
The document discusses using polymers to functionalize surfaces for applications such as drug delivery. It describes modeling polymers using techniques like self-consistent field theory and numerical methods. The summary concludes that the modeling could help experimentalists design random copolymer brush systems to achieve perpendicular lamellae for high-value semiconductor devices.
Theoretical study of metal clad optical waveguide polarizerijsrd.com
In this paper, the metal clad optical waveguide polarizer have been analysed and presented. The metal's that were used are Gallium Arsenide and Aluminium for the cladding purpose of comparison and analysis. It was found that the variation between TE mode and TM mode when Gallium Arsenide is used as the cladding is less as compared to Aluminium. This is due to the metal cladding itself will cause a cut-off region in the polarizer. Gallium arsenide may have fewer modes compared to aluminium and which resulted in the variation of the graphs between the two metals used. We have also shown that there is a slight drop of the TM to TE loss ratio when the buffer layer thickness is increased. It was also found that the high extinction ratio results in the high and linear attenuation in the fiber.
The document discusses the molecular weight of polymers. It defines molecular weight as the sum of the atomic weights of all the atoms in a polymer molecule. There are two types of average molecular weights - number average molecular weight (Mn) and weight average molecular weight (Mw). Mn is calculated by dividing the total weight of polymer molecules by the total number of molecules, while Mw takes into account that larger molecules contribute more to the total mass. Mw is always higher than Mn. Molecular weight affects various properties - higher molecular weight increases mechanical properties but lowers thermal properties. Various techniques can be used to determine molecular weight and its distribution.
This summary provides the key points in 3 sentences:
The document discusses polarization errors in fiber optic gyroscopes that use fiber ring interferometers. It shows that applying polarizing fibers at the input and in the sensing coil can significantly suppress polarization errors. Using polarizing fibers at both locations can radically reduce errors by suppressing interfering polarization modes before they propagate through the sensing coil.
- Polymer molecular weight determines many physical properties like transition temperatures and mechanical properties.
- Molecular weight distributions are described using average values like number average (MN), weight average (MW), and viscosity average (MV).
- For condensation polymers formed from bifunctional monomers, the most probable molecular weight distribution was derived by Flory. It results in a monotonically decreasing function with the monomer being the most probable species even at high conversion.
New optical w fiber panda for fiber optic gyroscope sensitive coilKurbatov Roman
This document proposes a new type of optical fiber called a W-fiber Panda that could improve fiber optic gyroscopes. The fiber has a core with nitrogen doping surrounded by stress-applying rods that create birefringence. Testing showed a polarizing version had 3 dB/km x-mode losses and 30 dB/km dichroism, while a polarization-maintaining version had ultra-low losses of 0.35 dB/km. This new fiber combines advantages of existing fibers by allowing a wide single-polarization spectral window as well as a desired mode field diameter. Its low losses could enable longer or more sensitive fiber optic gyroscope coils.
The document discusses modelling polymers under tension. It introduces various polymer models including freely jointed chain, freely rotating chain, Gaussian chain and worm like chain models. It then describes the Lagowski Noolandi model in more detail. The document also discusses force-extension curves and how they can provide insight into polymer unfolding under tension. Finally, it presents results comparing force-extension curves for homopolymers and random block copolymers under varying parameters such as stiffness and composition.
MAGNETIZED PLASMA WITH FERROMAGNETIC GRAINS AS A VIABLE NEGATIVE REFRACTIVE I...ijrap
This document discusses magnetized plasma with ferromagnetic grains (MPFG) as a potential negative refractive index medium. It is shown that:
1) MPFG has permittivity and permeability tensors that are controlled by the magnetized plasma and ferromagnetic grains.
2) For extraordinary waves propagating parallel to an external magnetic field, the refractive index of MPFG can be negative, indicating left-handed behavior, in certain frequency domains near resonance.
3) Numerical calculations demonstrate that both the effective permittivity and permeability of MPFG can be simultaneously negative for some frequencies, allowing for negative refractive index and transparent propagation of electromagnetic waves.
This document discusses molecular weight of polymers. It defines molecular weight as the sum of atomic weights of atoms in a molecule. Polymers have extremely high molecular weights due to their long molecular chains. There are different types of average molecular weights including number average, weight average, viscosity average, and z-average. Molecular weight distribution is also discussed. Higher molecular weight increases properties like ductility, impact resistance, weather resistance but also increases viscosity making processing more difficult.
Osmotic pressure and light scattering methods are used to determine the number-average and weight-average molecular weights of polymers in solution. Polymers can be characterized as amorphous, semicrystalline, or crystalline depending on their chain structure and interactions. Thermoplastics exhibit glass transitions and/or melting points while thermosets only exhibit glass transitions.
Determination of molecular weight of polymers by visometryudhay roopavath
This document discusses methods for determining the molecular weight of polymers using viscometry. It defines various types of average molecular weights and explains how intrinsic viscosity is measured through polymer solution viscosity. Viscosity measurements are used to calculate intrinsic viscosity and relate it to molecular weight through the Mark-Houwink-Sakurada equation. Double extrapolation plots of reduced viscosity and inherent viscosity versus concentration are used to determine intrinsic viscosity.
Average molecular weight of polymer
-Number average molecular weight
-Weight average molecular weight
Properties of Polymer
Uses/Application of Polymer
The document discusses two finite element models of low density thermally bonded monocomponent fibre nonwovens: (1) a machine direction model and (2) a cross direction model. The models are used to determine the deformation response of the nonwovens under tensile loads. The results of the FE simulations are compared to experimental tensile tests. Parameters like material properties, fibre cross-sectional area, and bond point thickness are varied to analyze their effects.
This document discusses modeling the elastic properties of laminated composites. It first defines composites as materials made of two or more distinct constituent materials. It then discusses various properties of composites like strength and corrosion resistance. It classifies composites based on their matrix material and reinforcement type. It also discusses volume and weight fractions. Rules of mixture are presented for calculating longitudinal and transverse modulus. Stress-strain relationships and analysis methods for orthotropic laminates are described. Forces, moments, and the inverse of the stiffness matrix for laminated composites are defined. Computer simulation of composite modeling allows for virtual testing of multiple design scenarios.
IRJET- Computation of Failure Index Strength of FML and FRB CompositesIRJET Journal
This document discusses the computation of failure indices of fiber metal laminate (FML) and fiber reinforced polymer (FRP) composites with different fiber orientations. It first provides background on FRP, FML, and different types of laminate configurations. It then outlines the methodology used, which involves using classical lamination theory (CLT) and the ANSYS software to predict stresses in FML and FRP laminates under in-plane tensile loading. Specific laminate stacking sequences of [Al/45/-45/Al] and [00/45/-45/00] are analyzed. Stresses are calculated in the layers and failure indices are determined using Tsai-Wu criterion for the FRP layers and
This document introduces concepts of stiffness and strength in fiber-reinforced composite materials. It discusses:
1) Composites consist of a matrix reinforced with fibers, such as glass or carbon fibers in a polymer matrix. The fibers have much higher strength and stiffness than traditional materials.
2) The stiffness of a unidirectional composite in the fiber direction can be estimated using a rule of mixtures, based on the fiber and matrix properties and volume fractions. Transverse stiffness is estimated using a series model.
3) Fiber volume fraction, fiber and matrix properties, and fiber orientation determine the composite's anisotropic mechanical properties. Empirical models are used for more complex fiber arrangements.
4) Strength
Paper theoretical and experimental studies of lamb wave propagation in attenu...Vinh Nguyen Thanh
This document presents a theoretical model for predicting Lamb wave dispersion and attenuation in composite materials. The model accounts for anisotropic wave attenuation in composites by using a complex stiffness matrix for each unidirectional ply. Experimental validation was performed by measuring the complex stiffness of a CFRP laminate using laser interferometry and comparing predicted and measured group velocities and attenuations. The model was implemented in a software called FIBREWAVE that can predict Lamb wave behavior for composites with arbitrary layups given the complex stiffness matrix of the plies.
The document discusses the molecular weight of polymers and methods to determine it, focusing on membrane osmometry.
[1] Membrane osmometry uses a semipermeable membrane to separate a dilute polymer solution from pure solvent. The osmotic pressure across the membrane is measured and used to calculate the number average molecular weight of the polymer.
[2] Factors that affect molecular weight determination include concentration, temperature, and interactions between polymer and solvent. The van't Hoff equation relates osmotic pressure and concentration for ideal solutions, while real solutions require additional terms.
[3] A worked example demonstrates using osmotic pressure measurements at different concentrations to calculate the molecular weight and second vi
This document discusses simulating fatigue damage in solder joints using cohesive zone modeling. It introduces cohesive zone modeling as a numerical method to describe interface mechanics and model crack initiation and propagation. The document proposes using a cohesive zone model with a damage variable to simulate fatigue damage accumulation over successive loading cycles at solder interfaces. The model represents interfaces with cohesive elements having traction-separation laws that degrade nonlinearly based on a damage evolution law to capture fatigue failure below static strength limits.
11.modeling power losses in electric vehicle bldc motorAlexander Decker
This document analyzes and summarizes the power losses in an electric vehicle brushless direct current (BLDC) motor. It presents analytical methods to estimate bearing frictional losses and finite element analysis to estimate electromagnetic losses. The results show that electromagnetic losses contribute over 80% of total losses, while bearing losses contribute about 12%. Bearing losses increase significantly with increasing speed or load. Accurately accounting for both electromagnetic and mechanical losses is important for determining motor efficiency and designing efficient cooling systems.
Modeling power losses in electric vehicle bldc motorAlexander Decker
This document presents models for estimating the power losses in a brushless direct current (BLDC) electric vehicle motor. It summarizes:
1) Mechanical bearing losses are estimated using analytical models of bearing friction forces and torques. Bearing losses contribute around 12% of total motor losses.
2) Electromagnetic losses, including copper losses from winding resistance and core losses from eddy currents and hysteresis, are the dominant source of losses, contributing over 80% of total losses.
3) Both bearing and electromagnetic losses increase with increasing motor speed or load. Accurately modeling losses is important for evaluating motor efficiency and designing an effective cooling system.
Multi-Objective Genetic Topological Optimization for Design of composite wall...Sardasht S. Weli
The aim of this presentation is to show the utilization of Topology Optimization to optimize a wall barrier thickness and its resistance under the extreme environment which is blast loading.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The Discrete Element Method (DEM) involves numerically calculating the motion of discrete particles by applying Newton's laws of motion and integrating the equations of motion over small time steps. DEM uses a soft-sphere approach where small overlaps between particles are allowed to model deformations during contact and calculate interaction forces. Particle motion is computed by integrating translational and rotational accelerations determined from contact and body forces. Contact detection algorithms efficiently detect collisions between large numbers of particles by discretizing the computational domain into cells.
Study on Low Velocity Impact on Composite MaterialsJakir Hossen
An investigation was performed on impact damage in laminated composites caused by low-velocity impact. The major objective of the study was to fundamentally understand the failure mechanisms and mechanics of fiber-reinforced composites resulting from impact and to identify the essential parameters governing the impact damage.
Computational Chemistry aspects of Molecular Mechanics and Dynamics have been discussed in this presentation. Useful for the Undergraduate and Postgraduate students of Pharmacy, Drug Design and Computational Chemistry
The document summarizes Travis Hilbig's masters thesis defense on using molecular dynamics (MD) simulations to model the scratching of polymeric materials. The study aims to (1) create a model of high density polyethylene (HDPE), (2) simulate scratching on the material, (3) analyze penetration depth and recovery, and (4) determine factors influencing scratch behavior. MD simulations represent interactions using Lennard-Jones potentials parameterized for HDPE's intramolecular and intermolecular interactions. The results will provide insight into scratch resistance of polymers to optimize structures for applications.
The document discusses modelling polymers under tension. It introduces various polymer models including freely jointed chain, freely rotating chain, Gaussian chain and worm like chain models. It then describes the Lagowski Noolandi model in more detail. The document also discusses force-extension curves and how they can provide insight into polymer unfolding under tension. Finally, it presents results comparing force-extension curves for homopolymers and random block copolymers under varying parameters such as stiffness and composition.
MAGNETIZED PLASMA WITH FERROMAGNETIC GRAINS AS A VIABLE NEGATIVE REFRACTIVE I...ijrap
This document discusses magnetized plasma with ferromagnetic grains (MPFG) as a potential negative refractive index medium. It is shown that:
1) MPFG has permittivity and permeability tensors that are controlled by the magnetized plasma and ferromagnetic grains.
2) For extraordinary waves propagating parallel to an external magnetic field, the refractive index of MPFG can be negative, indicating left-handed behavior, in certain frequency domains near resonance.
3) Numerical calculations demonstrate that both the effective permittivity and permeability of MPFG can be simultaneously negative for some frequencies, allowing for negative refractive index and transparent propagation of electromagnetic waves.
This document discusses molecular weight of polymers. It defines molecular weight as the sum of atomic weights of atoms in a molecule. Polymers have extremely high molecular weights due to their long molecular chains. There are different types of average molecular weights including number average, weight average, viscosity average, and z-average. Molecular weight distribution is also discussed. Higher molecular weight increases properties like ductility, impact resistance, weather resistance but also increases viscosity making processing more difficult.
Osmotic pressure and light scattering methods are used to determine the number-average and weight-average molecular weights of polymers in solution. Polymers can be characterized as amorphous, semicrystalline, or crystalline depending on their chain structure and interactions. Thermoplastics exhibit glass transitions and/or melting points while thermosets only exhibit glass transitions.
Determination of molecular weight of polymers by visometryudhay roopavath
This document discusses methods for determining the molecular weight of polymers using viscometry. It defines various types of average molecular weights and explains how intrinsic viscosity is measured through polymer solution viscosity. Viscosity measurements are used to calculate intrinsic viscosity and relate it to molecular weight through the Mark-Houwink-Sakurada equation. Double extrapolation plots of reduced viscosity and inherent viscosity versus concentration are used to determine intrinsic viscosity.
Average molecular weight of polymer
-Number average molecular weight
-Weight average molecular weight
Properties of Polymer
Uses/Application of Polymer
The document discusses two finite element models of low density thermally bonded monocomponent fibre nonwovens: (1) a machine direction model and (2) a cross direction model. The models are used to determine the deformation response of the nonwovens under tensile loads. The results of the FE simulations are compared to experimental tensile tests. Parameters like material properties, fibre cross-sectional area, and bond point thickness are varied to analyze their effects.
This document discusses modeling the elastic properties of laminated composites. It first defines composites as materials made of two or more distinct constituent materials. It then discusses various properties of composites like strength and corrosion resistance. It classifies composites based on their matrix material and reinforcement type. It also discusses volume and weight fractions. Rules of mixture are presented for calculating longitudinal and transverse modulus. Stress-strain relationships and analysis methods for orthotropic laminates are described. Forces, moments, and the inverse of the stiffness matrix for laminated composites are defined. Computer simulation of composite modeling allows for virtual testing of multiple design scenarios.
IRJET- Computation of Failure Index Strength of FML and FRB CompositesIRJET Journal
This document discusses the computation of failure indices of fiber metal laminate (FML) and fiber reinforced polymer (FRP) composites with different fiber orientations. It first provides background on FRP, FML, and different types of laminate configurations. It then outlines the methodology used, which involves using classical lamination theory (CLT) and the ANSYS software to predict stresses in FML and FRP laminates under in-plane tensile loading. Specific laminate stacking sequences of [Al/45/-45/Al] and [00/45/-45/00] are analyzed. Stresses are calculated in the layers and failure indices are determined using Tsai-Wu criterion for the FRP layers and
This document introduces concepts of stiffness and strength in fiber-reinforced composite materials. It discusses:
1) Composites consist of a matrix reinforced with fibers, such as glass or carbon fibers in a polymer matrix. The fibers have much higher strength and stiffness than traditional materials.
2) The stiffness of a unidirectional composite in the fiber direction can be estimated using a rule of mixtures, based on the fiber and matrix properties and volume fractions. Transverse stiffness is estimated using a series model.
3) Fiber volume fraction, fiber and matrix properties, and fiber orientation determine the composite's anisotropic mechanical properties. Empirical models are used for more complex fiber arrangements.
4) Strength
Paper theoretical and experimental studies of lamb wave propagation in attenu...Vinh Nguyen Thanh
This document presents a theoretical model for predicting Lamb wave dispersion and attenuation in composite materials. The model accounts for anisotropic wave attenuation in composites by using a complex stiffness matrix for each unidirectional ply. Experimental validation was performed by measuring the complex stiffness of a CFRP laminate using laser interferometry and comparing predicted and measured group velocities and attenuations. The model was implemented in a software called FIBREWAVE that can predict Lamb wave behavior for composites with arbitrary layups given the complex stiffness matrix of the plies.
The document discusses the molecular weight of polymers and methods to determine it, focusing on membrane osmometry.
[1] Membrane osmometry uses a semipermeable membrane to separate a dilute polymer solution from pure solvent. The osmotic pressure across the membrane is measured and used to calculate the number average molecular weight of the polymer.
[2] Factors that affect molecular weight determination include concentration, temperature, and interactions between polymer and solvent. The van't Hoff equation relates osmotic pressure and concentration for ideal solutions, while real solutions require additional terms.
[3] A worked example demonstrates using osmotic pressure measurements at different concentrations to calculate the molecular weight and second vi
This document discusses simulating fatigue damage in solder joints using cohesive zone modeling. It introduces cohesive zone modeling as a numerical method to describe interface mechanics and model crack initiation and propagation. The document proposes using a cohesive zone model with a damage variable to simulate fatigue damage accumulation over successive loading cycles at solder interfaces. The model represents interfaces with cohesive elements having traction-separation laws that degrade nonlinearly based on a damage evolution law to capture fatigue failure below static strength limits.
11.modeling power losses in electric vehicle bldc motorAlexander Decker
This document analyzes and summarizes the power losses in an electric vehicle brushless direct current (BLDC) motor. It presents analytical methods to estimate bearing frictional losses and finite element analysis to estimate electromagnetic losses. The results show that electromagnetic losses contribute over 80% of total losses, while bearing losses contribute about 12%. Bearing losses increase significantly with increasing speed or load. Accurately accounting for both electromagnetic and mechanical losses is important for determining motor efficiency and designing efficient cooling systems.
Modeling power losses in electric vehicle bldc motorAlexander Decker
This document presents models for estimating the power losses in a brushless direct current (BLDC) electric vehicle motor. It summarizes:
1) Mechanical bearing losses are estimated using analytical models of bearing friction forces and torques. Bearing losses contribute around 12% of total motor losses.
2) Electromagnetic losses, including copper losses from winding resistance and core losses from eddy currents and hysteresis, are the dominant source of losses, contributing over 80% of total losses.
3) Both bearing and electromagnetic losses increase with increasing motor speed or load. Accurately modeling losses is important for evaluating motor efficiency and designing an effective cooling system.
Multi-Objective Genetic Topological Optimization for Design of composite wall...Sardasht S. Weli
The aim of this presentation is to show the utilization of Topology Optimization to optimize a wall barrier thickness and its resistance under the extreme environment which is blast loading.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The Discrete Element Method (DEM) involves numerically calculating the motion of discrete particles by applying Newton's laws of motion and integrating the equations of motion over small time steps. DEM uses a soft-sphere approach where small overlaps between particles are allowed to model deformations during contact and calculate interaction forces. Particle motion is computed by integrating translational and rotational accelerations determined from contact and body forces. Contact detection algorithms efficiently detect collisions between large numbers of particles by discretizing the computational domain into cells.
Study on Low Velocity Impact on Composite MaterialsJakir Hossen
An investigation was performed on impact damage in laminated composites caused by low-velocity impact. The major objective of the study was to fundamentally understand the failure mechanisms and mechanics of fiber-reinforced composites resulting from impact and to identify the essential parameters governing the impact damage.
Computational Chemistry aspects of Molecular Mechanics and Dynamics have been discussed in this presentation. Useful for the Undergraduate and Postgraduate students of Pharmacy, Drug Design and Computational Chemistry
The document summarizes Travis Hilbig's masters thesis defense on using molecular dynamics (MD) simulations to model the scratching of polymeric materials. The study aims to (1) create a model of high density polyethylene (HDPE), (2) simulate scratching on the material, (3) analyze penetration depth and recovery, and (4) determine factors influencing scratch behavior. MD simulations represent interactions using Lennard-Jones potentials parameterized for HDPE's intramolecular and intermolecular interactions. The results will provide insight into scratch resistance of polymers to optimize structures for applications.
This document discusses various techniques used to investigate fiber structure, including X-ray diffraction, infrared spectroscopy, thermal analysis, electron microscopy, optical microscopy, nuclear magnetic resonance, scanning electron microscopy, and methods to determine glass transition temperature. X-ray diffraction and nuclear magnetic resonance are useful for analyzing fiber crystallinity and structure. Infrared spectroscopy provides information on chemical groups and molecular configuration. Thermal analysis measures properties as a function of temperature. Microscopy techniques examine fiber surfaces at different magnifications.
Paper theoretical and experimental studies of lamb wave propagation in attenu...Vinh Nguyen Thanh
This document presents a theoretical model for predicting Lamb wave dispersion and attenuation in composite materials. The model accounts for anisotropic wave attenuation in composites by using a complex stiffness matrix for each unidirectional ply. Experimental validation was performed by measuring the complex stiffness of a CFRP laminate using laser interferometry and comparing predicted and measured group velocities and attenuations. The model was implemented in a software called FIBREWAVE that can predict Lamb wave behavior for composites with arbitrary layups given the complex stiffness matrix of the plies.
This research article describes a study using multi-angle laser light scattering to determine the molecular weights of two polystyrene polymer solutions. The molecular weights measured were 388,300±16,500 g/mol and 915,300±44,800 g/mol, which were within 2.7% of the known values for the solutions. The article provides background on static light scattering analysis and the Zimm plot method used to calculate molecular weight and radius of gyration from light scattering intensity measurements taken at varying angles.
Performance Investigation and Enhancement of Fiber Bragg Gratingfor Efficient...IOSRJECE
In this paper, the performance of various windowfunctions for Fiber Bragg Grating Sensor (FBGS)is investigated and evaluated in order to get optimized reflection spectrum with high reflectivity and an efficient side lobe suppression for efficient sensing measurement applications.For this purpose, a wide range of design parameters which include grating length and refractive index modulation amplitudehas been chosen to evaluate the sensor design. The performances of the different windowfunctions have been then compared in terms of reflectivity, full width half maximum bandwidth (FWHM), and sidelobe level(SLL) so as to get the most suitable design parametersto be used for sensing measurement.The simulation results presented in this paper show the effectiveness of the optimizedFBG sensor, which can be further implemented for high performance sensing applications.
This document discusses the use of positron annihilation spectroscopy to analyze the free volume nanohole distribution in polymers and its correlation to the physico-chemical properties of polymers. It provides background on positron annihilation spectroscopy and how it can be used to measure free volume in polymers. The document then describes several studies that use this technique to analyze the influence of free volume properties on the swelling of polymer hydrogels, structure-property relationships in modified epoxy resins, and free volume and interfacial interactions in epoxy clay composites.
This document discusses different types of materials including atoms, small molecules, and macromolecules. It describes how macromolecules are classified into natural and synthetic types, with examples of each. The document focuses on polymers as synthetic macromolecules, discussing their nomenclature, models of polymer chains, and various types of copolymers. It also examines the structures, configurations, and dynamics of macromolecules including random coil models.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes research on developing a multi-scale modeling approach to predict the structural behavior of carbon fiber reinforced composite pipes used for offshore oil and gas risers. The approach models the pipe behavior at the micro, meso, and macro scales and links the scales together. Experiments were conducted to validate the modeling approach and determine material properties at each scale. Results showed good agreement between predicted and experimental properties and structural response at different loading conditions. The multi-scale modeling approach shows promise for designing composite risers while addressing current limitations in experience, standards, and design methodologies.
Role of αc–relaxation in high-temperature polymer deformation.
Proceedings of the American Society for Composites 2009-Twenty-Fourth Technical ConferenceWith the Canadian Association for Composite Structures and Materials (Joint Canadian-American International Conference), September 15-17, Newark, DE
This document summarizes a numerical study of the structure and thermodynamics of colloidal suspensions using the variational method and integral equation theory. The interactions between colloid particles are modeled using either a Yukawa or Sogami potential. Results from the integral equation theory using a Sogami potential are found to be in good agreement with Monte Carlo simulation results and experimental data. The variational method and integral equation theory are used to calculate structural properties like the pair correlation function and thermodynamic properties.
Effect of Material Thickness on Attenuation (dB) of PTFE Using Finite Element...Abubakar Yakubu
This research article examines how the thickness of polytetrafluoroethylene (PTFE) samples affects the attenuation of electromagnetic waves at X-band frequency using finite element method (FEM) simulations. The results show that as the thickness of the PTFE samples increases, the attenuation also increases. Specifically, the 15 mm thick PTFE sample has an attenuation of -3.32 dB, the 30 mm sample has an attenuation of 0.64 dB, and the 50 mm sample has an attenuation of 1.97 dB. The study finds that increasing sample thickness leads to a decrease in electromagnetic wave transmission and an increase in attenuation.
Characterizing Luminescent Properties of Thin Films by Farisch HanoemanFarisch Hanoeman
Thesis at Delft University of Technology. Fundamental Aspects of Materials and Energy (FAME), Radiation Science and Technology department, Faculty of Applied Sciences. Supervisor: dr. E. van der Kolk, co-reader: prof. dr. P. Dorenbos.
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Depletion attraction between dendrimers
1. Depletion attraction between branched polymers
Summer Internship Project
Submitted By
Prafull Kumar Sharma
IIT Delhi
Supervised By
MSc. Martin Wengemeyer Prof. Dr. Jens-Uwe Sommer
(Phd Student) (Group Leader)
Student: Prafull Kumar Sharma
Studies: Engineering Physics
Project Type: Summer Internship Project
Student ID: 2013PH10861 (IIT Delhi)
Address: SC-11,Satpura Hostel,IIT
Campus,New Delhi,110016
Phone-No.: +91-7530831251
E-Mail: ph1130861@iitd.ac.in
New Delhi, 12/10/2016
2. Table of Contents
1MOTIVATION............................................................................................................1
2INTRODUCTION......................................................................................................1
2.1THEORY OF POLYMERS........................................................................................................1
2.2DEPLETION ATTRACTION BETWEEN TWO COLLOIDS...........................................................2
2.3THEORY OF DENDRIMERS....................................................................................................3
2.4BOND-FLUCTUATION-METHOD...........................................................................................4
2.5 UMBRELLA SAMPLING.......................................................................................................6
3 RESULTS AND DISCUSSION................................................................................7
4 REFERENCES........................................................................................................11
3. List of Abbreviations and Symbols
MCS Monte Carlo Steps
MC Monte Carlo
LeMonADE Lattice Based extensible Monte-Carlo Algorithm and Development
Environment
PMF Potential of mean force
BFM Bond Fluctuation Model
WHAM Weighted Histogram Analysis Method
c Density of solvent
g1 Generation of dendrimer 1
g2 Generation of dendrimer 2
4. Prafull Kumar Sharma (IPF,Dresden)
1 MOTIVATION
One of the major challenges for scientists is to design and modify molecules such as
polymers, to give them functionality suitable for purposes such as drug delivery, cata-
lysis, fluorescent sensors etc. For developing such kind of understanding, simulations
are one of the important way to understand and predict the effect of molecular design
on it's various physical properties.[1]
Dendrimers are basically synthetic polymers having treelike structure with branching.
These kind of polymers have their applications in bioengineering, material science and
chemical industry. Dendrimers are used as drug delivery agents due to large number of
sites having possibility to couple to an active species. These kind of molecules are
used in chemical reactions as catalysts. Dendrimers can also be used in sensor applica-
tions. However there is still a lot of need to increase our understanding about these
molecules in order to have more optimized designs and possibilities of new applica-
tions.[2]
The main aim of this project is to understand “depletion attraction between
dendrimers” with or without solvent. In this project, we used Bond fluctuation model
(BFM) for simulation method along with umbrella sampling for free energy calcula-
tion. I would like to thank MSc Martin Wengemayer and MSc Ron Dockhorn for their
constant guidance throughout the project. I would like to thank IPF for their scholar-
ship. I would also like to acknowledge warm support of Prof. Sommer and the group
during the stay.
2 INTRODUCTION
2.1 Theory of Polymers
A polymer molecule consists of several identical repetitive units,called as
'monomers'.Every polymer can be thought of as linear chain of N connected segments
(first proposed by Werner Kuhn) ,now called Kuhn Segments. Each segment in a freely
jointed chain can randomly orient in any direction without the influence of any forces,
independent of the directions taken by other segments. While considering a real chain
consisting of bonds and with variable/fixed bond angles, dihedral angles, and bond
lengths, Polymers can be characterized in terms of bond length l, dihedral angle φ and
bond angle θ . In this simulation one bond vector represents one Kuhn segment, for
1
5. Prafull Kumar Sharma (IPF,Dresden)
this reason the distance between two connected monomers will be b. The dihedral
angle φ is defined as the rotation of the subsequent bond vector around the axis which
conforms to the direction of the previous bond vector.
The end to end vector Re-e for a polymer of N monomer can be written as,
Re-e = ∑
i=1
i=N −1
ri+1−ri= ∑
i=1
i=N −1
bi where ri is the position vector of ith
monomer.
However if we calculate expectation value of above quantity for an ideal chain, it
would turn out to be zero. So for characterizing size/length/scaling of polymers, we
should calculate mean square end-to-end distance.
<Re-e
2`
> = b (N-1)2γ
where γ is flory exponent. For freely jointed real polymer chain,
theoretical value of γFlory is found to be equal to 3/5 which is indeed quite close to
value of 0.588 ,obtained in simulation. The radius of gyration Rg is used to character-
ize the span of polymeric chain i.e. span of largest dimension. It is defined similarly to
the moment of inertia by the average square distance between the monomers of the
chain to the chain’s centre of mass.[3]
2.2 Depletion Attraction between Two colloids
The Depletion Force is an attractive, short-range, entropic force which is a force res-
ulting from the system's thermodynamic tendency to increase its entropy rather than
from a particular underlying microscopic force.[4][5]
Suppose colloidal spheres are mixed with non-adsorbing depletants. Negative adsorp-
tion then results in an effective depletion layer near the surface. Presence of depletion
layer explains the presence of such attractive short range force. When the depletion
layer of two spheres overlap, free volume available for the depletants increases. Thus
free energy of the depletants is minimized by the states in which these colloidal
spheres are close together. Significance of this force can be realized in such way that
even though direct colloid-depletant interaction and colloid-colloid interactions are
both repulsive, there exists an attractive short range depletion force. For small de-
pletant concentration, the attraction equals the product of osmotic pressure and the
overlap volume.[6]
Also due to overlapping of depletion layers, ΔS i.e. change in en-
tropy S, is positive which yields out loss of energy ΔF = -TΔS.
2
6. Prafull Kumar Sharma (IPF,Dresden)
(a) (b)
Figure 1: The depletion layers are indicated by short dashes (a).When there is no overlap of deple-
tion layers, osmotic pressure on the colloids due to depletants (in this case, polymer chains) is isotropic,
thus no entropic (depletion) force. (b) For overlapping depletion layers, the osmotic pressure on the
spheres is unbalanced, the excess pressure is indicated by arrows. Taken from “Phase Behaviour in Dis-
persions of Spheres and Stiff Chains”, R.Tuiner and Schmidit
2.3 Theory of Dendrimers
Dendrimers represent monodisperse macromolecules with regular and strongly
branched architecture. Dendrimers can be characterized by three parameters which are
g, s and f .The generation g, shows which cell number we are at. The functionality, f ,
is the number of chains branching out from each branching point (monomer).The
spacer length s indicates length of linear chain which composes dendrimer and acts a
basic component. Part of the interest in dendrimers is that one can vary g, s and f
along with the kinds of monomers used to produce a very rich variety of structures
with very different material properties.[7][8]
Figure 2: A schematic of a dendrimer
with functionality f = 3, showing the
generation number g, and the spacer
length s. The terminal groups are shown
darker than the other monomers. Taken
from Macromolecules, 37, page 3049,
2004.
Dendrimers with lower s and g
and high density can be modelled
as a soft sphere which imitates
3
7. Prafull Kumar Sharma (IPF,Dresden)
same as hard sphere and shows depletion attraction in presence of depletants. However
dendrimers show diffusion of each other and presence of hollow core makes it feasible
to work as a drug delivery agent, in addition to depletion. However these two effects
can only be effectively viewed only in higher s and g because for lower s and g ,these
soft spherical dendrimers would almost act like a hard sphere. Also one interesting
case is diffusion of a big generation dendrimer (say g=7) in to a small generation
dendrimer (say g=2) in a solvent because such diffusion creates a metastable state
(highly attractive force) which is of very huge significance in terms of dendrimer as a
drug delivery agent (with drug being small generation dendrimer in this case).
Figure 3: Dendrimers used in simulation for PMF calculation between these two, where spacer length
s=2,g1=g2=4.colour is marked for distinction between comformation of the two.
2.4 Bond-Fluctuation-Method
In 1988 I. Carmesin and K. Kremer introduced the Bond-Fluctuation-Model
(BFM) as a Monte Carlo algorithm for simulating conformation and dynamics of poly-
mer systems.[9][10]
This method uses coarse-grained model which neglects chemical
properties of polymeric structures. In this method, monomers occupy 8 lattice posi-
tions to form a cube of edge length two in each positive direction, on a regular cubic
lattice. Each lattice position can be occupied by only one monomer in order to ensure
“excluded volume” effect (as per discussion in previous sections, 'excluded volume' is
one of the factor affecting depletion interaction between two spheres) . To ensure cut-
avoidance (no explicit test of local topology) on the single cubic lattice the bond
4
8. Prafull Kumar Sharma (IPF,Dresden)
length is required to be smaller than 4. Monomers are connected by bond vector which
are generally taken from a given set of 108 bond vectors. In our simulations, allowed
bond vectors B are made up from permutations and sign-variations of six base vectors
in 3-D:
Thus, bond lengths corresponding to such combination of bond vectors are
{2,√ 5,√ 6,3,√ 10} .Above restrictions on monomers and bond vectors coupled
with shape and size of monomers fulfils criteria of self avoiding walk where one bond
unit is synonymous with Kuhn’s segment. The Monte Carlo step is performed in the
directions on the lattice’ axis, ΔB = P± (1, 0, 0) which means six possible directions
for monomers to move. Just like any other MC simulations, one direction in which a
monomer has to move, is selected randomly. Then firstly the new position is checked
for multiple lattice occupation and secondly whether the new bond vectors belong to
the allowed set B. If both condi-
tions are fulfilled, the move is
performed, otherwise rejected.
For a lattice with in total N
monomers one Monte Carlo Step
is defined as N attempts to move
a monomer as described above.
Thereby not every monomer
must be selected, but others can
be selected more than once.
Figure 4: Bond Fluctuation Model, as you can see one monomer occupies 8 lattice points on a regular
cube to form a cube and these monomers are connected by a bond vector from specific set of 108 bond
vectors. Taken from IPF theory polymer group applet
5
9. Prafull Kumar Sharma (IPF,Dresden)
For energetic interactions in MC simulations, we use metropolis algorithm. As in the
algorithm described above one monomer and one direction are selected randomly.
Then, the energetic contribution on the new position Enew is evaluated and compared to
the energy in the initial state Einit to get the energetic difference ΔE. If the new posi-
tion is more energetically favourable i.e. ΔE≤0, then the move is allowed. However if
new position is less energetically favourable i.e. ΔE>0, then the move is allowed with
probability, P =exp(- ΔE/kT) where k is Boltzmann constant and T is temperature.
In theoretical Polymer physics group at IPF, LeMonADE project has been developed
which implements BFM through a complex framework of C++ programs. In the pro-
gram, the boxsize, BS, is a magnitude of two (BSi= 2n
with i = x, y, z and n ϵ N).In this
model, we impose periodic boundary conditions on monomers i.e. those who are leav-
ing the box will re-enter the box.The program saves the configuration of the
monomers in the box after a given MCS interval. For each save, the simulated struc-
ture has a specific conformation.
2.5 Umbrella Sampling
The quantification of a pair interaction in computer simulations can be obtained by re-
stricting dendrimers implementing a known potential. Well known spring potential
Vspring, and morse potential, Vmorse which is implemented in C++ framework to couple
with Simulation setup for dendrimers. We have used Morse potential in addition to
spring potential to see whether overlap of tails (important for better overlap of probab-
ility density thus sampling) can be improved.[11][12]
Also (r,rƿ 0)sim is probability distribution for system which is superposition of VMF and
Vspring i.e. simulation setup and (r,rƿ 0)spring is probability distribution arising due to
spring potential with equilibrium position r0 only, which can be written as:
ƿ(r,r0)spring = ps exp(-Vspring(r,r0))
ƿ(r,r0)sim = psim exp(-Vspring(r,r0)).exp(-VMF(r))
With the aid of Umbrella sampling ,we can exratct out potential of mean force VMF and
write the equation in this form by solving above two equations,
where ps and psim are normalization constants for spring potential and simulation setup
respectively. Similarly in case of Morse potential,we replace Vspring with Vmorse and per-
6
10. Prafull Kumar Sharma (IPF,Dresden)
form umbrella sampling in similar fashion. As you can see there is an arbitrary term in
formula for PMF which depends on normalization constants. Thus we need to shift
values of PMF in each window for overlapping.
3 Results and Discussion
In this project, Umbrella sampling was used for calculating Potential of mean force by
overlapping windows and eliminating biased potential effect by means of 'manually
shifting with the help of histogram analysis and Excel sheet', and WHAM algorithm as
well. In this graph you can see, we have generated results for PMF value between two
symmetric dendrimers of generation 3 and spacer length 1 ,as a function of distance
between their centre of mass. Also you can see PMF remains same regardless of
biased potential ,method of overlapping windows and adjustment, which is as expec-
ted due to fact in the end we eliminate effect of biased potential. In this graph, we have
used spring constant K=.50 for sampling over Rc-c >10 and K=1.50 for sampling over
Rc--c <10. Also optimized value of morse parameters a =.05 and D=100 ,where D is
well depth, is used. We used biased potential because the forces like depletion force
are very short range and to sample them we need to keep the dendrimers together and
very close to each other. In case of interaction between unsymmetric dendrimers , due
to bigger size of other dendrimer compared to symmetric dendrimer , PMF in case of
unsymmetric dendrimers case will be higher due to more repulsive force which can be
seen in the figure above as well. We also simulated the two dendrimers with biased po-
tential, in presence of solvent (in our case,linear chain polymers) with maximum dens-
ity, c=0.50 expecting a depletion force which could not be observed, which was expec-
ted.Reasons behind no observation of such force is most probably due to statistical er-
ror i.e. MCS were not sufficient enough to encompass most of phase space. Here force
of attraction involves diffusion component (in case of hard spheres, excluded volume
effect was only reason behind such short range force) as well. However one interesting
simulation would be to calculate PMF among one big dendrimer and one very small
dendrimer in the dense solvent (say, c=0.5).
7
11. Prafull Kumar Sharma (IPF,Dresden)
(a)
Figure 5: It should be noted that PMF is in unit of KBT and spacer length of both dendrimers
is set to 1.There is no solvent in this case.
*Here KBT is put as unity and PMF is calculated in unit of KBT.
8
12. Prafull Kumar Sharma (IPF,Dresden)
Figure 6: In the left side of the figure, you can see dendrimer solution with very high solvent density
c=0.5 (maximum possible) with red and green dendrimers inside. On the right hand side, dendrimers are
shown with red being generation 3 and green being generation 5 dendrimers. In this system we have
taken spacer length as 1.
There was a need of optimization due to fact that in case of smaller potential,
dendrimers might get away from each other due to weak force and roam around freely
thus making it impossible for us to sample PMF. In general we need a potential with
medium well depth and medium broadness for overlap. In case of spring potential, we
have only one parameter ,k (spring constant) which if increased will increase well
depth and decrease broadness of potential. However force of attraction needed to re-
strict them over a range of distance, depends on only one parameter k and with in-
creasing distance between dendrimers ,spring force will increase and pull back these
dendrimers from getting away. While morse potential allows us to have variable well
depth (change parameter D) and variable broadness (morse parameter ,a) quite inde-
pendently,it has issues regarding force of attraction because as you increase, distance
force will go to zero. And changing morse parameter and well depth won't always
change maximum magnitude of force of attraction that depends on product of these
two parameters, i.e. for a range of morse parameters and well depths,maximum mag-
nitude of force of attraction would be same (D*a= constant,yields an hyperbola) thus
while morse potential has independent control on depth and broadness, it has little and
sensitive control on force of attraction.
9
13. Prafull Kumar Sharma (IPF,Dresden)
(a)
(b)
Figure 7: It should be noted that PMF is in unit of KBT .There is Linear polymer chain solvent
in this case. (a) I have done overlapping of windows using histogram analysis method. this one
in paricular is for symmetric dendrimers of generation 4 and spacer length 2. (b) PMF for both
symmetric and unsymmetric dendrimers in solvent case.
10
14. Prafull Kumar Sharma (IPF,Dresden)
4 References
[1] E. Abbasi. Dendrimers: synthesis, applications, and properties. Nanoscale Research
Letters (2014) 9:247
[2] JK Kassube et al. Stereoselctive dendrimer catalysis. Topics in organometallic
chemistry. Volume 20,page 61-96 (june,2006), Springer,Hiedelberg
[3] Iwao Teraoka. Polymer solutions: An introduction to Physical properties.
Wiley,New York,2002.
[4] T Biben, P Bladon, and D Frenkel. Depletion effects in binary hard-sphere fluids.
Journal of Physics: Condensed Matter, 10799, 1996.
[5] Sho Asakura and Fumio Oosawa. Interaction between particles suspended in solu-
tions of macromolecules. Journal of Polymer Science, 33(126):183–192, December
1958
[6] HNW Lekkerkerker and Remco Tuinier. Colloids and the Depletion Interaction.
Springer,Heidelberg, London, New York, 2011.
[7] S.V. Lyulin et al. Effect of Solvent Quality and Electrostatic Interactions on Size
and Structure of Dendrimers. Brownian Dynamics Simulation and Mean-Field Theory.
Macromolecules 2004, 37, 3049-3063
[8] http://iitbmonash.org/Resources/Research_Opps_PDFs/IMURA_0017.pdf
[9] H. P. Deutsch and K. Binder. Interdiffusion and self-diffusion in polymer mixtures:
A Monte Carlo study. The Journal of Chemical Physics, 94(3):2294, 1991.
[10] I Carmesin and K Kremer. The bond fluctuation method: a new effective algo-
rithm for the dynamics of polymers in all spatial dimensions. Macromolecules, pages
2819–2823,1988.
[11] B. Roux. The calculation of potential of mean force using computer simulations
Computer physics communications 91 (1995),page 275-282
[12] Daan Frenkel and Brend Smit. Understanding Molecular Simulation: From algo-
rithms to applications, page 192-196.
11