ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 20 May 2024 10:16:42 GMT2024-05-20T10:16:42Z50851- Effect of textile geometry on axisymmetric stretch forming of knitted fabric compositeshttps://scholarbank.nus.edu.sg/handle/10635/58201Title: Effect of textile geometry on axisymmetric stretch forming of knitted fabric composites
Authors: Lim, T.C.; Ramakrishna, S.; Shang, H.M.
Abstract: Plain weft-knitted fabrics are known for their excellent quality to stretch and drape around a convex surface without wrinkling. In recent years, sheet forming of knitted fabric composites has been investigated in view of promising future applications. In this paper a prediction of attainable shell height is proposed with reference to the textile geometry and the tool profile. Comparison between the measured and predicted shell heights shows reasonable agreement. The present analysis should provide a guideline for manufacturers in selecting the appropriate textile geometry for satisfactory stretch forming operations of knitted fabric composites.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/582012000-01-01T00:00:00Z
- Effect of fibre bundle structure on stretch forming properties of plain weft-knitted fabric compositeshttps://scholarbank.nus.edu.sg/handle/10635/58173Title: Effect of fibre bundle structure on stretch forming properties of plain weft-knitted fabric composites
Authors: Lim, T.C.; Ramakrishna, S.; Shang, H.M.
Abstract: Knitted fabrics are known for their excellent stretchability and their flat composites have recently been shown to be easily stretch-formed into thin shells of revolution. In this paper, the stretch-forming properties are being investigated with due attention given to the fibre bundle loop structure. The capability of a plain weft-knitted fabric composite sheet to be stretch-formed is elucidated with reference to the fibre bundle structure.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/581731999-01-01T00:00:00Z
- Geometrical non-linearity of textile composites in large deformationhttps://scholarbank.nus.edu.sg/handle/10635/58336Title: Geometrical non-linearity of textile composites in large deformation
Authors: Lim, T.C.; Zako, M.; Sakata, S.; Ramakrishna, S.
Abstract: In considering small deformation of solids, it is common to assume linear elasticity. Where large deformation is concerned, material non-linearity - whether hyper elasticity, strain hardening, etc - must be considered. In large deformation of textile composites, overall material non-linearity consists of (a) constituent material non-linearity, and (b) geometrical non-linearity due to strain-deformation relation. This paper firstly proposes a finite element procedure for obtaining the stiffness matrix of a representative volume element. The procedure involved is simple due to an effective decoupling methodology. Secondly, co-ordinate updating of the FE mesh is performed to allow readjustment to the fibre bundle elements in the RVE. This enables the process of fabric realignment to be theoretically mimicked to consider the influence of fibre bundle reorganisation on the overall stiffness of the textile composite - hence geometrical non-linearity.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/583362000-01-01T00:00:00Z
- Simplified model for the influence of inclusion aspect ratio on the stiffness of aligned reinforced compositeshttps://scholarbank.nus.edu.sg/handle/10635/84472Title: Simplified model for the influence of inclusion aspect ratio on the stiffness of aligned reinforced composites
Authors: Lim, T.C.
Abstract: A simplified model for the Young's Modulus of aligned composites possessing spheroidal inclusions, of any aspect ratio α, is developed herein based on a triply periodic array of parallelpiped inclusions. The Young's Modulus of continuous unidirectional fiber composites (α → ∞), particulate composites (α = 1) and periodically bilaminated composites (α = 0) are obtained as limiting cases based on the Parallel-Series and Series-Parallel schemes of analyses. A reinforcing parameter, R, of the inclusion is then identified from the limiting cases such that R ε [0, 11]. By curve-fitting for a relationship between the reinforcement parameter and the inclusion aspect ratio for α ε [0, ∞], the Young's Modulus for aligned short fiber composites (α > 1) and aligned flake composites (α lt; 1) are obtained. For verification, the present model at limiting cases (α = , 1, ∞) were reduced to other simple models and/or compared with experimental results. For non-limiting cases (α < 1, α > 1), comparison with other theoretical models show reasonable agreement.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844722003-01-01T00:00:00Z
- Simplified transverse Young's modulus of aligned ribbon-reinforced composites by the mechanics-of-materials approachhttps://scholarbank.nus.edu.sg/handle/10635/84473Title: Simplified transverse Young's modulus of aligned ribbon-reinforced composites by the mechanics-of-materials approach
Authors: Lim, T.C.
Abstract: A simplified transverse Young's Modulus of aligned, continuous ribbon-reinforced composites is developed herein within the framework of the mechanics-of-materials approach for the convenience of the designer. The chosen geometry is that of doubly periodic array of rectangular parallel-piped, akin to the method-of-cells approach. Results from the present model compare well with an exact model, which is a combination of Mori-Tanaka's average stress of the matrix and Eshelby's stress field for an ellipsoidal inclusion. Furthermore, results reveal that increasing ribbon width at constant ribbon volume fraction leads to significant stiffness enhancement in the ribbon width direction with marginal loss of stiffness in the ribbon thickness direction.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844732003-01-01T00:00:00Z
- Next-Generation Applications for Polymeric Nanofibreshttps://scholarbank.nus.edu.sg/handle/10635/68000Title: Next-Generation Applications for Polymeric Nanofibres
Authors: Lim, T.-C.; Ramakrishna, S.
Tue, 29 Nov 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/680002005-11-29T00:00:00Z
- Mathematical connections between bond-stretching potential functionshttps://scholarbank.nus.edu.sg/handle/10635/84455Title: Mathematical connections between bond-stretching potential functions
Authors: Lim, T.-C.
Abstract: Mathematical connections are useful in enabling a set of parametric data from a chemical bond-stretching potential function to be applied in a computational chemistry software that adopts a different potential function. This paper establishes connections between four potential energy functions in stretching and compression of covalent bonds. The potential functions that are mathematically connected are: (i) harmonic potential, (ii) polynomial series potential, (iii) Morse potential, and (iv) Murrell-Mottram potential. Two methods are employed in obtaining the relationships between the four potential functions. The expansion approach enables the relationships to be made at large bond-stretching, whilst the differential approach allows for the connections to be made only at infinitesimal bond-stretching. For verification, parametric data from the Murrell-Mottram potential is converted to parametric data of the harmonic, polynomial series and Morse potentials. For comparison, the bond-stretching energies for these functions are plotted. Discrepancy between the Morse and the Murrell-Mottram potentials at large bond-stretching is discussed in terms of the assumed infinitesimal deformation.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844552003-01-01T00:00:00Z
- Material structure for attaining pure Poisson-shearinghttps://scholarbank.nus.edu.sg/handle/10635/84454Title: Material structure for attaining pure Poisson-shearing
Authors: Lim, T.-C.
Abstract: A material structure is proposed to give pure in-plane (axis-1 and axis-2) shearing when loaded in the out-of-plane direction (axis-3). It is shown that it is possible to simultaneously attain v0 to give Poisson-shearing through the material structure. The Poison-shear ratio is defined, and demonstrated for the case of very large pure in-plane shearing for a prescribed out-of-plane loading.
Tue, 15 Oct 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844542002-10-15T00:00:00Z
- Influence of doubly periodic array aspect ratio on the transverse anisotropy of continuous unidirectional fiber reinforced compositeshttps://scholarbank.nus.edu.sg/handle/10635/84449Title: Influence of doubly periodic array aspect ratio on the transverse anisotropy of continuous unidirectional fiber reinforced composites
Authors: Lim, T.C.
Abstract: A modified mechanics-of-materials approach is developed for analyzing the influence of fiber arrangement in a rectangular array on the transverse anisotropy of transversely-isotropic unidirectional fiber reinforced-composites. The class of material under discussion is one of which is transversely isotropic only when the fiber array aspect ratio is unity. The method takes a one-dimensional approach akin to the slab analysis of metal forming studies-with the exception that the present material being considered is heterogeneous and that deformation is within linear elastic range. Compared to the conventional mechanics-of-materials approach, the present modified model, at unity array aspect ratio assumption for randomly arrayed fibers, gives agreement with experimental results. Theoretical curves for other array aspect ratios are further plotted and discussed in regard to the fiber array and its relation to transverse anisotropy.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844492001-01-01T00:00:00Z
- Functionally graded beam for attaining poisson-curvinghttps://scholarbank.nus.edu.sg/handle/10635/84445Title: Functionally graded beam for attaining poisson-curving
Authors: Lim, T.C.
Abstract: A material is generally thought to undergo transverse contraction (or expansion) when axially stretched (or compressed). Hence in the elastic property known as Poisson's ratio, a negative sign is introduced to give a positive value. In this paper, a quantitative definition for Poisson-curving is introduced and the amount of thickness change is detailed in the light of this definition.
Sun, 15 Dec 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844452002-12-15T00:00:00Z
- Mathematical relationships between bond-bending force fieldshttps://scholarbank.nus.edu.sg/handle/10635/84456Title: Mathematical relationships between bond-bending force fields
Authors: Lim, T.-C.
Abstract: Molecular mechanics softwares adopt various set of force field functions. In some cases, reliable data from one set of force field parameters cannot be used in a software that adopts another set of force field. Using mathematical approach, exact relationships between parameters from three bond-bending force fields, namely the (i) harmonic cosine angle, (ii) polynomial series, and (iii) Fourier series, are herein developed. Parameters from these three potential functions are further related to the approximate form, the harmonic angle function, which is valid for small change in chemical bond angle.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844562002-01-01T00:00:00Z
- Young's modulus of coated inclusion composites by the generalized mechanics-of-materials (GMM) approachhttps://scholarbank.nus.edu.sg/handle/10635/84480Title: Young's modulus of coated inclusion composites by the generalized mechanics-of-materials (GMM) approach
Authors: Lim, T.C.
Abstract: A micromechanical model of the Young's modulus for three special cases of composites - continuous unidirectional fiber composites, particulate composites and periodically bilaminate composites - has been developed within the framework of the mechanic-of-materials approach. Parallel-series (PS) and series-parallel (SP) schemes were adopted based upon opposing combination sequence of the parallel model (direct rule-of-mixture) and the series model (inverse rule-of-mixture). By expressing the inclusion's geometrical characteristics in terms of reinforcement volume fraction and interphase volume, a set of reinforcement parameters for the inclusion and its interphase are extracted. Based on reinforcement parameters for the special cases, those of more general cases, which are intermediates of the special cases, are obtained by curve-fitting approximation. Young's modulus of simple cases such as coated fiber composites in longitudinal direction and coated lamina composites are shown to be approximate to the parallel and series models respectively. Cases such as coated fiber composites in transverse direction and coated particulate composites are compared with other results and observed to be highly and moderately conservative by the PS and SP techniques respectively.
Mon, 01 Sep 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844802003-09-01T00:00:00Z
- Unified practical bounds for the thermal conductivity of composite materialshttps://scholarbank.nus.edu.sg/handle/10635/84479Title: Unified practical bounds for the thermal conductivity of composite materials
Authors: Lim, T.C.
Abstract: Two schemes for the thermal conductivity of three classes of composites - unidirectional continuous fibre composites, particulate composites and laminae sheets - are presented herein based on combination of parallel and series models. Comparison with experimental results reveals reasonable correlation even at extreme reinforcement-to-matrix thermal conductivity ratio. Results of the two sets of schemes further show that one is higher than the other. Hence, the two sets of solutions are named practical bounds due to their simplicity. By introducing a reinforcement parameter, the solutions for the three classes of composite materials are unified, and approximate solutions for another two classes of composite materials - unidirectional short fibre composites and aligned flake composites - are suggested based on the reinforcement parameter. © 2002 Elsevier Science B.V. All rights reserved.
Wed, 01 May 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844792002-05-01T00:00:00Z
- Scaling function between the Exponential-6 and the generalized Lennard-Jones potential functionshttps://scholarbank.nus.edu.sg/handle/10635/84471Title: Scaling function between the Exponential-6 and the generalized Lennard-Jones potential functions
Authors: Lim, T.-C.
Abstract: The van der Waals forces for non-bonded interaction can be expressed either by the Exponential-6 or by the Lennard-Jones(m-n) potential functions, whereby m > n. Hitherto a relationship exists between the Exponential-6 and the Lennard-Jones(12-6) potential functions, with a scaling factor ξ = 13. 772 at or near the equilibrium and ξ = 12.0 for long range interaction. This paper attempts to develop relationships between Exponential-6 and a more generalized Lennard-Jones(m-n). Analysis reveals that the relationship exists only when n = 6 and that two sets of scaling factors (as functions of index m) applies for the relationship between Exponential-6 and the Lennard-Jones(m-6), whereby m > 6.
Thu, 01 May 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844712003-05-01T00:00:00Z
- Spring constant analogy for estimating stiffness of a single polyethylene moleculehttps://scholarbank.nus.edu.sg/handle/10635/84474Title: Spring constant analogy for estimating stiffness of a single polyethylene molecule
Authors: Lim, T.-C.
Abstract: The stiffness of a simple planar polymeric chain is modeled using analogies of mechanical springs arranged in series and in parallel assemblies. The stiffness of chemical bonds is resolved into two perpendicular axes defined by the longitudinal and transverse axes in the molecular plane. Using Hooke's definition of spring stiffness, the molecular stiffness of polyethylene is obtained along the longitudinal and transverse directions. This paper demonstrates the use of physical analogies and mathematical approximations for obtaining an analytical form for the stiffness of a simple single-molecule.
Sat, 01 Nov 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844742003-11-01T00:00:00Z
- Modelling of composite sheet forming: A reviewhttps://scholarbank.nus.edu.sg/handle/10635/84495Title: Modelling of composite sheet forming: A review
Authors: Lim, T.-C.; Ramakrishna, S.
Abstract: The use of composite materials in sheet forming applications is gaining popularity with the rise of consumer demands and specific mechanical properties. In addition to unidirectional (UD) fibres, the use of textile reinforcements such as woven fabric and knitted fabric has been shown to be feasible in recent years. This paper gives a survey on the modelling of composite sheet forming for both UD fibre and textile composites. Two broad approaches are reviewed here - the mapping approach and the mechanics approach. Mapping approaches for UD fibre composites, woven fabric composites and knitted fabric composites are elucidated on the basis of their fibre geometry. For the mechanics approach both the viscous fluid models and elastic solid models, as a means of describing the constitutive properties, are reviewed. Various updating methods for modelling large deformation found in sheet forming are then described. Finally, a guideline for the choice of modelling techniques for various types of fibre/fabric reinforcements and suggestions for future work are given. © 2002 Elsevier Science Ltd. All rights reserved.
Mon, 01 Apr 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844952002-04-01T00:00:00Z
- Mathematical relationships for development of a molecular potential function converterhttps://scholarbank.nus.edu.sg/handle/10635/84494Title: Mathematical relationships for development of a molecular potential function converter
Authors: Lim, T.-C.
Abstract: This paper gives a short review on relating molecular potential functions within the same category of interatomic interactions. The bond-stretching potentials that were related include the harmonic, polynomial series and Morse functions. The bond-bending potentials that were connected involve the harmonic angle, polynomial angle series, harmonic cosine and Fourier series functions. The bond-twisting potentials that were related are the trigonometric series and the cosine power series functions. Finally, the non-bonded potentials that were connected include the Lennard-Jones type and the Exponential-6 functional forms. The above-mentioned relationships were previously obtained using mathematical methods such as Maclaurin's series expansions, trigonometric identities and elementary calculus. These relationships are tabulated in a concise manner in preparation for the development of a potential function converter software that enables a given molecular potential function to be converted to a different functional form. The software can be further utilized as an educational tool for displaying, in a graphical manner, the similarities and discrepancies in normalized molecular potential functions.
Mon, 01 Sep 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844942003-09-01T00:00:00Z
- The Relationship between Lennard-Jones (12-6) and Morse Potential Functionshttps://scholarbank.nus.edu.sg/handle/10635/84476Title: The Relationship between Lennard-Jones (12-6) and Morse Potential Functions
Authors: Lim, T.-C.
Abstract: The most commonly used potentials for van der Waals interactions are the Exponential-6 and the Lennard-Jones (12-6) potential. In this paper a correlation between them is described. The Morse function, which is normally applied for quantifying 2-body interactions, has been adopted in one software. This paper deals with the validity of the Morse function for non-bonded interactions by means of obtaining a relationship between the Morse and the Lennard-Jones (12-6) potential functions. An approximate and an exact mathematical relationship is demonstrated to exist between these two potentials.
Sat, 01 Nov 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/844762003-11-01T00:00:00Z
- Modelling of composite sheet forming: A reviewhttps://scholarbank.nus.edu.sg/handle/10635/68316Title: Modelling of composite sheet forming: A review
Authors: Lim, T.-C.; Ramakrishna, S.
Abstract: The use of composite materials in sheet forming applications is gaining popularity with the rise of consumer demands and specific mechanical properties. In addition to unidirectional (UD) fibres, the use of textile reinforcements such as woven fabric and knitted fabric has been shown to be feasible in recent years. This paper gives a survey on the modelling of composite sheet forming for both UD fibre and textile composites. Two broad approaches are reviewed here - the mapping approach and the mechanics approach. Mapping approaches for UD fibre composites, woven fabric composites and knitted fabric composites are elucidated on the basis of their fibre geometry. For the mechanics approach both the viscous fluid models and elastic solid models, as a means of describing the constitutive properties, are reviewed. Various updating methods for modelling large deformation found in sheet forming are then described. Finally, a guideline for the choice of modelling techniques for various types of fibre/fabric reinforcements and suggestions for future work are given. © 2002 Elsevier Science Ltd. All rights reserved.
Mon, 01 Apr 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/683162002-04-01T00:00:00Z
- Mathematical relationships for development of a molecular potential function converterhttps://scholarbank.nus.edu.sg/handle/10635/68297Title: Mathematical relationships for development of a molecular potential function converter
Authors: Lim, T.-C.
Abstract: This paper gives a short review on relating molecular potential functions within the same category of interatomic interactions. The bond-stretching potentials that were related include the harmonic, polynomial series and Morse functions. The bond-bending potentials that were connected involve the harmonic angle, polynomial angle series, harmonic cosine and Fourier series functions. The bond-twisting potentials that were related are the trigonometric series and the cosine power series functions. Finally, the non-bonded potentials that were connected include the Lennard-Jones type and the Exponential-6 functional forms. The above-mentioned relationships were previously obtained using mathematical methods such as Maclaurin's series expansions, trigonometric identities and elementary calculus. These relationships are tabulated in a concise manner in preparation for the development of a potential function converter software that enables a given molecular potential function to be converted to a different functional form. The software can be further utilized as an educational tool for displaying, in a graphical manner, the similarities and discrepancies in normalized molecular potential functions.
Mon, 01 Sep 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/682972003-09-01T00:00:00Z
- Modified Halpin-Tsai equation for Clay-Reinforced polymer nanofiberhttps://scholarbank.nus.edu.sg/handle/10635/60817Title: Modified Halpin-Tsai equation for Clay-Reinforced polymer nanofiber
Authors: Ramakrishna, S.; Lim, T.C.; Inai, R.; Fujihara, K.
Abstract: In this paper, two sets of electrospun fibers - nylon-6 and montmorillonite (MMT)-reinforced nylon-6 - are being investigated for their tensile modulus. Results show that a reduction of fiber diameter close to nano-scale range reveals increasing modulus due to greater alignment of polymeric molecules and increased influence of surface stresses as a result of increased surface-to-volume ratio. However, addition of MMT caused a reduction of modulus in spite its very high modulus. This anomalous phenomenon may well be attributed to the effect of small fiber radius for containing the MMT platelet's width. By expressing the matrix modulus as a function of fiber diameter and by introducing a proportionality constant, we obtained a semi-empirical micromechanical model within the framework of the Halpin-Tsai equation - hence the modified Halpin-Tsai model. The result suggests that the fibers be shrunk for increasing its modulus without reinforcement. However, for cases where fillers are required to fulfill non-mechanical purposes (such as medical purposes), the modified Halpin-Tsai model is useful for informing the designer of the threshold weight or volume fraction of the inclusion to maintain the modulus above the required level.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/608172006-01-01T00:00:00Z
- An integrated mechanics-of-materials model for the elastic stiffness of compositeshttps://scholarbank.nus.edu.sg/handle/10635/67743Title: An integrated mechanics-of-materials model for the elastic stiffness of composites
Authors: Lim, T.C.
Abstract: An integrated mechanics-of-materials model is developed herein for three classes of composites, namely continuous unidirectional fibre composites, particulate reinforced composites and periodically bilaminate composites. Through a judicious choice of expressing the model, a new parameter, which describes the effect of reinforcing geometry on the composite stiffness in the direction of interest, was extracted. The reinforcement parameter ranges from zero (for the lowest possible reinforcing efficiency) to unity (for the highest possible reinforcing efficiency). The reinforcement parametric values for all the three classes of composites, both parallel and transverse to the reinforcement axis-of-symmetry, are presented. Finally the possible reinforcement parameter range for unidirectional short fibre composites and aligned flake composites are suggested based upon the reinforcement parameter of the three presently considered special cases.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677432001-01-01T00:00:00Z
- Knitted fabric composite sheet forming simulation considering fabric realignmenthttps://scholarbank.nus.edu.sg/handle/10635/58423Title: Knitted fabric composite sheet forming simulation considering fabric realignment
Authors: Lim, T.C.; Fujihara, M.; Zako, M.; Ramakrishna, S.; Shang, H.M.
Abstract: In recent years, sheet forming of textile reinforced polymers have shown promising future applications. It is understood that the reorientation of fabric structure at the microscopic level alters the macroscopic constitutive relationship of the composite. In this paper, a new sheet forming simulation technique is proposed and being applied to knitted fabric composites.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/584231999-01-01T00:00:00Z
- Functionally graded beam for attaining poisson-curvinghttps://scholarbank.nus.edu.sg/handle/10635/67767Title: Functionally graded beam for attaining poisson-curving
Authors: Lim, T.C.
Abstract: A material is generally thought to undergo transverse contraction (or expansion) when axially stretched (or compressed). Hence in the elastic property known as Poisson's ratio, a negative sign is introduced to give a positive value. In this paper, a quantitative definition for Poisson-curving is introduced and the amount of thickness change is detailed in the light of this definition.
Sun, 15 Dec 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677672002-12-15T00:00:00Z
- Elastic stiffness of three-phase composites by the generalized Mechanics-of-Materials (GMM) approachhttps://scholarbank.nus.edu.sg/handle/10635/67761Title: Elastic stiffness of three-phase composites by the generalized Mechanics-of-Materials (GMM) approach
Authors: Lim, T.C.
Abstract: A Generalized Mechanics-of-Materials (GMM) model is developed herein for practical approximation to the stiffness of three-phase composites. The three classes of composites considered are unidirectional two-fiber composite system, two-particulate composite system and combined fiber and particulate system. The geometrical model for the representative volume element (RVE) adopted is that of alternating cubic array of two arbitrary cuboid reinforcements. Non-dimensionalized stiffness of the three classes of three-phase composites are addressed by altering the dimensions of the reinforcing cuboids. The reinforcements in the RVE are in parallel to the applied load while the displaced surface of the RVE is assumed uniform. Verification of the model was carried out by reducing the three-phase model to that of two-phase ones, as well as by comparison with previous experimental results. Generalization for the three classes of composite stiffness was attained through a judicious choice of expression, which resulted in the identification of a parameter that conveniently describes the effect of reinforcement geometry.
Fri, 01 Mar 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677612002-03-01T00:00:00Z
- Exact non-linear relationship between Exponential-6 and Lennard-Jones (12-6) potential functionshttps://scholarbank.nus.edu.sg/handle/10635/67764Title: Exact non-linear relationship between Exponential-6 and Lennard-Jones (12-6) potential functions
Authors: Lim, T.-C.
Abstract: The relationship between two of the most frequently adopted van der Waals potential functions - Exponential-6 and Lennard-Jones (12-6) - is shown to be faulty upon comparison of the repulsive terms. By using the Maclaurin's series expansions, an exact relationship between both the potential functions is obtained by means of a non-linear correction factor. A purely Exponential-6 form is recovered when the correction factor is taken at zeroth order, while a purely Lennard-Jones (12-6) form is attained as the order of the correction factor tends to infinity. For real van der Waals systems that are bounded by the Exponential-6 and Lennard-Jones (12-6) potential functions, a positive integer order of the correction factor may possibly provide good curve-fitting to experimental data.
Sat, 01 Nov 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677642003-11-01T00:00:00Z
- Mathematical connections between bond-stretching potential functionshttps://scholarbank.nus.edu.sg/handle/10635/67776Title: Mathematical connections between bond-stretching potential functions
Authors: Lim, T.-C.
Abstract: Mathematical connections are useful in enabling a set of parametric data from a chemical bond-stretching potential function to be applied in a computational chemistry software that adopts a different potential function. This paper establishes connections between four potential energy functions in stretching and compression of covalent bonds. The potential functions that are mathematically connected are: (i) harmonic potential, (ii) polynomial series potential, (iii) Morse potential, and (iv) Murrell-Mottram potential. Two methods are employed in obtaining the relationships between the four potential functions. The expansion approach enables the relationships to be made at large bond-stretching, whilst the differential approach allows for the connections to be made only at infinitesimal bond-stretching. For verification, parametric data from the Murrell-Mottram potential is converted to parametric data of the harmonic, polynomial series and Morse potentials. For comparison, the bond-stretching energies for these functions are plotted. Discrepancy between the Morse and the Murrell-Mottram potentials at large bond-stretching is discussed in terms of the assumed infinitesimal deformation.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677762003-01-01T00:00:00Z
- Material structure for attaining pure Poisson-shearinghttps://scholarbank.nus.edu.sg/handle/10635/67775Title: Material structure for attaining pure Poisson-shearing
Authors: Lim, T.-C.
Abstract: A material structure is proposed to give pure in-plane (axis-1 and axis-2) shearing when loaded in the out-of-plane direction (axis-3). It is shown that it is possible to simultaneously attain v<0 and v>0 to give Poisson-shearing through the material structure. The Poison-shear ratio is defined, and demonstrated for the case of very large pure in-plane shearing for a prescribed out-of-plane loading.
Tue, 15 Oct 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677752002-10-15T00:00:00Z
- Mathematical relationships between bond-bending force fieldshttps://scholarbank.nus.edu.sg/handle/10635/67777Title: Mathematical relationships between bond-bending force fields
Authors: Lim, T.-C.
Abstract: Molecular mechanics softwares adopt various set of force field functions. In some cases, reliable data from one set of force field parameters cannot be used in a software that adopts another set of force field. Using mathematical approach, exact relationships between parameters from three bond-bending force fields, namely the (i) harmonic cosine angle, (ii) polynomial series, and (iii) Fourier series, are herein developed. Parameters from these three potential functions are further related to the approximate form, the harmonic angle function, which is valid for small change in chemical bond angle.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677772002-01-01T00:00:00Z
- Scaling function between the Exponential-6 and the generalized Lennard-Jones potential functionshttps://scholarbank.nus.edu.sg/handle/10635/67798Title: Scaling function between the Exponential-6 and the generalized Lennard-Jones potential functions
Authors: Lim, T.-C.
Abstract: The van der Waals forces for non-bonded interaction can be expressed either by the Exponential-6 or by the Lennard-Jones(m-n) potential functions, whereby m > n. Hitherto a relationship exists between the Exponential-6 and the Lennard-Jones(12-6) potential functions, with a scaling factor ξ = 13. 772 at or near the equilibrium and ξ = 12.0 for long range interaction. This paper attempts to develop relationships between Exponential-6 and a more generalized Lennard-Jones(m-n). Analysis reveals that the relationship exists only when n = 6 and that two sets of scaling factors (as functions of index m) applies for the relationship between Exponential-6 and the Lennard-Jones(m-6), whereby m > 6.
Thu, 01 May 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677982003-05-01T00:00:00Z
- Simplified model for the influence of inclusion aspect ratio on the stiffness of aligned reinforced compositeshttps://scholarbank.nus.edu.sg/handle/10635/67800Title: Simplified model for the influence of inclusion aspect ratio on the stiffness of aligned reinforced composites
Authors: Lim, T.C.
Abstract: A simplified model for the Young's Modulus of aligned composites possessing spheroidal inclusions, of any aspect ratio α, is developed herein based on a triply periodic array of parallelpiped inclusions. The Young's Modulus of continuous unidirectional fiber composites (α → ∞), particulate composites (α = 1) and periodically bilaminated composites (α = 0) are obtained as limiting cases based on the Parallel-Series and Series-Parallel schemes of analyses. A reinforcing parameter, R, of the inclusion is then identified from the limiting cases such that R ε [0, 11]. By curve-fitting for a relationship between the reinforcement parameter and the inclusion aspect ratio for α ε [0, ∞], the Young's Modulus for aligned short fiber composites (α > 1) and aligned flake composites (α lt; 1) are obtained. For verification, the present model at limiting cases (α = , 1, ∞) were reduced to other simple models and/or compared with experimental results. For non-limiting cases (α < 1, α > 1), comparison with other theoretical models show reasonable agreement.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/678002003-01-01T00:00:00Z
- Simplified transverse Young's modulus of aligned ribbon-reinforced composites by the mechanics-of-materials approachhttps://scholarbank.nus.edu.sg/handle/10635/67801Title: Simplified transverse Young's modulus of aligned ribbon-reinforced composites by the mechanics-of-materials approach
Authors: Lim, T.C.
Abstract: A simplified transverse Young's Modulus of aligned, continuous ribbon-reinforced composites is developed herein within the framework of the mechanics-of-materials approach for the convenience of the designer. The chosen geometry is that of doubly periodic array of rectangular parallel-piped, akin to the method-of-cells approach. Results from the present model compare well with an exact model, which is a combination of Mori-Tanaka's average stress of the matrix and Eshelby's stress field for an ellipsoidal inclusion. Furthermore, results reveal that increasing ribbon width at constant ribbon volume fraction leads to significant stiffness enhancement in the ribbon width direction with marginal loss of stiffness in the ribbon thickness direction.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/678012003-01-01T00:00:00Z
- Deep-drawing analysis of knitted composite materials considering the geometrical non-linearity of knitted structureshttps://scholarbank.nus.edu.sg/handle/10635/67756Title: Deep-drawing analysis of knitted composite materials considering the geometrical non-linearity of knitted structures
Authors: Masaru, Z.; Makoto, F.; Cheng, L.T.; Seiichiro, S.
Abstract: A new methodology for FEM deep drawing simulation of textile composites sheets has been described. In deep drawing process of textile composites, the fabric structure changes in various ways with progress of deformation of blank. The deformation of fiber bundle of textile composites affects moldability in deep drawing process. The large deformation of fabric geometry for knitted fabric structure must be taken into consideration when the equivalent mechanical properties of blank obtained. The assumption that the blank is regarded as in-plane periodic fabric composite is applied and the equivalent mechanical properties are obtained. The effect of the reorientation of fabrics on the equivalent mechanical properties is adopted into deep drawing simulation of blank. The reoriented unit fabric structures are decided by deformation analysis of unit fabric structure according to macroscopic strain. In deep drawing analysis, it is assumed that the die and the punch are rigid bodies, and the deep drawing process can be presented by movement of the rigid punch. The relative inclined restraint condition is introduced into analysis. The computational results have a quality agreement with the experimental results.
Thu, 01 Feb 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677562001-02-01T00:00:00Z
- Influence of doubly periodic array aspect ratio on the transverse anisotropy of continuous unidirectional fiber reinforced compositeshttps://scholarbank.nus.edu.sg/handle/10635/67772Title: Influence of doubly periodic array aspect ratio on the transverse anisotropy of continuous unidirectional fiber reinforced composites
Authors: Lim, T.C.
Abstract: A modified mechanics-of-materials approach is developed for analyzing the influence of fiber arrangement in a rectangular array on the transverse anisotropy of transversely-isotropic unidirectional fiber reinforced-composites. The class of material under discussion is one of which is transversely isotropic only when the fiber array aspect ratio is unity. The method takes a one-dimensional approach akin to the slab analysis of metal forming studies-with the exception that the present material being considered is heterogeneous and that deformation is within linear elastic range. Compared to the conventional mechanics-of-materials approach, the present modified model, at unity array aspect ratio assumption for randomly arrayed fibers, gives agreement with experimental results. Theoretical curves for other array aspect ratios are further plotted and discussed in regard to the fiber array and its relation to transverse anisotropy.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677722001-01-01T00:00:00Z
- Young's modulus of coated inclusion composites by the generalized mechanics-of-materials (GMM) approachhttps://scholarbank.nus.edu.sg/handle/10635/67816Title: Young's modulus of coated inclusion composites by the generalized mechanics-of-materials (GMM) approach
Authors: Lim, T.C.
Abstract: A micromechanical model of the Young's modulus for three special cases of composites - continuous unidirectional fiber composites, particulate composites and periodically bilaminate composites - has been developed within the framework of the mechanic-of-materials approach. Parallel-series (PS) and series-parallel (SP) schemes were adopted based upon opposing combination sequence of the parallel model (direct rule-of-mixture) and the series model (inverse rule-of-mixture). By expressing the inclusion's geometrical characteristics in terms of reinforcement volume fraction and interphase volume, a set of reinforcement parameters for the inclusion and its interphase are extracted. Based on reinforcement parameters for the special cases, those of more general cases, which are intermediates of the special cases, are obtained by curve-fitting approximation. Young's modulus of simple cases such as coated fiber composites in longitudinal direction and coated lamina composites are shown to be approximate to the parallel and series models respectively. Cases such as coated fiber composites in transverse direction and coated particulate composites are compared with other results and observed to be highly and moderately conservative by the PS and SP techniques respectively.
Mon, 01 Sep 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/678162003-09-01T00:00:00Z
- The Relationship between Lennard-Jones (12-6) and Morse Potential Functionshttps://scholarbank.nus.edu.sg/handle/10635/67812Title: The Relationship between Lennard-Jones (12-6) and Morse Potential Functions
Authors: Lim, T.-C.
Abstract: The most commonly used potentials for van der Waals interactions are the Exponential-6 and the Lennard-Jones (12-6) potential. In this paper a correlation between them is described. The Morse function, which is normally applied for quantifying 2-body interactions, has been adopted in one software. This paper deals with the validity of the Morse function for non-bonded interactions by means of obtaining a relationship between the Morse and the Lennard-Jones (12-6) potential functions. An approximate and an exact mathematical relationship is demonstrated to exist between these two potentials.
Sat, 01 Nov 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/678122003-11-01T00:00:00Z
- Unified practical bounds for the thermal conductivity of composite materialshttps://scholarbank.nus.edu.sg/handle/10635/67814Title: Unified practical bounds for the thermal conductivity of composite materials
Authors: Lim, T.C.
Abstract: Two schemes for the thermal conductivity of three classes of composites - unidirectional continuous fibre composites, particulate composites and laminae sheets - are presented herein based on combination of parallel and series models. Comparison with experimental results reveals reasonable correlation even at extreme reinforcement-to-matrix thermal conductivity ratio. Results of the two sets of schemes further show that one is higher than the other. Hence, the two sets of solutions are named practical bounds due to their simplicity. By introducing a reinforcement parameter, the solutions for the three classes of composite materials are unified, and approximate solutions for another two classes of composite materials - unidirectional short fibre composites and aligned flake composites - are suggested based on the reinforcement parameter. © 2002 Elsevier Science B.V. All rights reserved.
Wed, 01 May 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/678142002-05-01T00:00:00Z
- Spring constant analogy for estimating stiffness of a single polyethylene moleculehttps://scholarbank.nus.edu.sg/handle/10635/67805Title: Spring constant analogy for estimating stiffness of a single polyethylene molecule
Authors: Lim, T.-C.
Abstract: The stiffness of a simple planar polymeric chain is modeled using analogies of mechanical springs arranged in series and in parallel assemblies. The stiffness of chemical bonds is resolved into two perpendicular axes defined by the longitudinal and transverse axes in the molecular plane. Using Hooke's definition of spring stiffness, the molecular stiffness of polyethylene is obtained along the longitudinal and transverse directions. This paper demonstrates the use of physical analogies and mathematical approximations for obtaining an analytical form for the stiffness of a simple single-molecule.
Sat, 01 Nov 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/678052003-11-01T00:00:00Z
- A three-level hierarchical approach in modeling sheet thermoforming of knitted-fabric compositeshttps://scholarbank.nus.edu.sg/handle/10635/67737Title: A three-level hierarchical approach in modeling sheet thermoforming of knitted-fabric composites
Authors: Lim, T.-C.
Abstract: A three-level hierarchical approach in modeling thermoforming process of curved-fabric-reinforced polymer sheet is presented in this paper. In the microscopic level, fiber bundle properties are analytically obtained from fiber filament and matrix material properties using simple rule-of-mixture approach. In the mesoscopic level, the representative volume element properties are obtained from the fiber bundle and matrix material properties using the mesoscopic mesh. Subsequent updating of mesoscopic nodal mesh coordinates and imposition of further strain gives the constitutive behavior of the composite material with due consideration to fabric reorientation, hence geometrical non-linearity. In the macroscopic level, the constitutive relationship, as a function of strain state, is applied to the macroscopic mesh whereby the material property of every macroscopic element is determined from the strain state resulting from the previous incremental plunger penetration and from the material database. Using the example of plain weft-knitted-fabric composites, both experimental and theoretical strain fields show reasonable agreement. © 2003 Elsevier Ltd. All rights reserved.
Sun, 01 Jun 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677372003-06-01T00:00:00Z
- Constitutive relationship of a material with unconventional Poisson's ratiohttps://scholarbank.nus.edu.sg/handle/10635/67752Title: Constitutive relationship of a material with unconventional Poisson's ratio
Authors: Lim, T.-C.
Abstract: A set of in-plane constitutive relationships for both positive and negative Poisson's ratio, even for magnitudes exceeding 1, was derived for a type of honeycomb microstructure. This derivation made no distinction between θ<90°C or θ>90°C, thus establishing a bridge between the two sets of material characteristics.
Mon, 15 Dec 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677522003-12-15T00:00:00Z
- Elastic properties of a polyethylene single-moleculehttps://scholarbank.nus.edu.sg/handle/10635/67760Title: Elastic properties of a polyethylene single-molecule
Authors: Lim, T.-C.
Abstract: Analytical closed-form solution of the elastic properties (such as longitudinal stiffness, shear stiffness and Poisson's ratio) of a taut polyethylene single-molecule is developed in this paper in terms of C-C and C-C-C bond parameters. The concepts considered herein include resolution of forces and of displacement, with due application of Hooke's law to determine the longitudinal stiffness and the in-plane Poisson's ratio. Adopting the solid mechanics theory as an analogy, the shear stiffness of a taut polyethylene chain is conveniently obtained. Results reveal unique Poisson's ratio property of a polyethylene single-molecule in comparison to usual bulk materials, thereby suggesting size-dependency of nano-scale materials in terms of the Poisson's ratio. Finally some frequently occurring terms in all three elastic property expressions are grouped to summarize and to reveal some form of uniformity in the analytical solutions.
Sat, 01 Nov 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/677602003-11-01T00:00:00Z
- A conceptual review of nanosensorshttps://scholarbank.nus.edu.sg/handle/10635/54016Title: A conceptual review of nanosensors
Authors: Lim, T.-C.; Ramakrishna, S.
Abstract: Nanosensors are gaining increasing attention due to the need to detect and measure chemical and physical properties in difficult to reach biological and industrial systems that are in the nano-scale region. This conceptual review surveys various nanosensors, which are categorized into three broad types: optical, electromagnetic and mechanical nanosensors. The sensing concepts and their corresponding advantages are discussed with reference to their applications. © 2006 Verlag der Zeitschrift für Naturforschung.
Sat, 01 Jul 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/540162006-07-01T00:00:00Z
- Optimization of the formability of knitted fabric composite sheet by means of combined deep drawing and stretch forminghttps://scholarbank.nus.edu.sg/handle/10635/58587Title: Optimization of the formability of knitted fabric composite sheet by means of combined deep drawing and stretch forming
Authors: Lim, T.C.; Ramakrishna, S.; Shang, H.M.
Abstract: The formability of sheet metals has been investigated widely in the last 5 decades. However, formability studies on polymer composite materials are very limited and relatively new. This paper describes the sheet formability of knitted Kevlar fiber reinforced polypropylene composite material. Previous studies have indicated that sheet formability is governed by the complex interplay between pure stretch forming and pure deep drawing. For this purpose, a new parameter, X, which describes the amount of stretching relative to drawing during forming has been introduced. The formability characteristics of knitted fabric composite are discussed with reference to X. The effects of forming conditions (such as blank-holding load, the blank size and the tool geometry) on the composite formability are also described.
Wed, 19 May 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/585871999-05-19T00:00:00Z
- Analytical modelling for sheet thermoforming of knitted fabric reinforced PMChttps://scholarbank.nus.edu.sg/handle/10635/59535Title: Analytical modelling for sheet thermoforming of knitted fabric reinforced PMC
Authors: Lim, T.C.; Ramakrishna, S.; Shang, H.M.
Abstract: Knitted fabrics are known for their excellent stretching and draping properties due to their curved fabric architecture. In recent years knitted fabrics have been used as reinforcement network for polymer sheet thermo-processing. This paper describes a method for evaluating the product height, product profile and strain distribution of a flat polymer matrix sheet, reinforced with knitted fabric, undergoing the sheet thermoforming process. The availability of a knitted fabric reinforced PMC to stretch is proposed to be equal to the least ratio of curved loop length to its projected length. The product profile is then obtained from the availability of the material to stretch and the tool geometry involved. Finally a mapping scheme is proposed to evaluate the severity of deformation in terms of strain distribution. A reasonably good agreement is observed between the model and experimental results. An understanding of the severity of deformation distribution would shed light on the location of highest degree of deformation as well as its magnitude and should therefore assist the product designer in dealing with the thermoforming process of this new material.
Fri, 15 Feb 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/595352002-02-15T00:00:00Z
- Correlation among parameters of the extended-Rydberg potential energy functionhttps://scholarbank.nus.edu.sg/handle/10635/112589Title: Correlation among parameters of the extended-Rydberg potential energy function
Authors: Lim, T.-C.
Abstract: This paper reports a remarkable correlation among parameters of extended-Rydberg potential function by recasting the Morse potential in the form of extended-Rydberg function via the application of infinite series expansion to the exponential terms of the Morse function. By using linear regression, a reasonable band that encompasses 90% of the diatomic combination given by Huxley and Murrell [J. Chem. Soc. Faraday Trans. II 79 (1983) 323] is furnished in a plotted characteristic map. © 2005 Springer Science+Business Media, Inc.
Mon, 01 Aug 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125892005-08-01T00:00:00Z
- On the applicability of mathematical constants and sequences in intermolecular potential energy functionshttps://scholarbank.nus.edu.sg/handle/10635/112624Title: On the applicability of mathematical constants and sequences in intermolecular potential energy functions
Authors: Lim, T.-C.
Abstract: Six intermolecular potential energy functions incorporating mathematical functions such as the Golden ratio, Euler number and Pi, and three consecutive numbers in the Half Square, Lucas and Fibonacci sequences are proposed herein. It is shown that the Lucas potential function exhibits reasonable agreement with the Lennard-Jones(12-10) function, whilst the Golden ratio potential function describes the argon gas potential energy and the Lennard-Jones(14-7) function excellently. Both the Euler and Pi potential functions agree well with the Lennard-Jones(12-6) function, whilst the Fibonacci potential function exhibits very good correlation with the Lennard-Jones(9-6) function. The relatedness of the mathematical constants and sequences examined in this paper with application to intermolecular potential functions suggests their additional significance in the field of chemistry. © Springer Science+Business Media, LLC 2007.
Tue, 01 May 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1126242007-05-01T00:00:00Z
- Application of binomial coefficients in representing central difference solution to a class of PDE arising in chemistryhttps://scholarbank.nus.edu.sg/handle/10635/112577Title: Application of binomial coefficients in representing central difference solution to a class of PDE arising in chemistry
Authors: Lim, T.-C.
Abstract: The use of differential equations for modeling chemical systems and solving by numerical approaches (e.g. finite difference methods) are prevalent in chemistry-related problems. As an extension to the direct use of Pascal's Triangle to obtain the forward and backward difference equations to partial differentials by Lim [Mathematical Medley 31 (2004) 2], this paper proposes the use of binomial coefficient to generate central difference equations to odd-ordered partial differentials in a single-step operation. All finite difference equations to partial differentials shown herein display finite series of palindromic coefficients with alternating signs. © 2005 Springer Science+Business Media, Inc.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125772006-01-01T00:00:00Z
- A relationship between the 2-body energy of Kaxiras-Pandey and Pearson-Takai-Halicioglu-Tiller Potential Functionshttps://scholarbank.nus.edu.sg/handle/10635/112575Title: A relationship between the 2-body energy of Kaxiras-Pandey and Pearson-Takai-Halicioglu-Tiller Potential Functions
Authors: Lim, T.-C.
Abstract: A parametric relationship between the Pearson-Takai-Halicioglu-Tiller (PTHT) and the Kaxiras-Pandey (KP) empirical potential energy functions is developed for the case of 2-body interaction. The need for such relationship arises when preferred parametric data and adopted software correspond to different potential functions. The analytical relationship was obtained by equating the potential functions derivatives at zeroth, first and second order with respect to the interatomic distance at the equilibrium bond length, followed by comparison of coefficients in the repulsive and attractive terms. Plots of non-dimensional 2-body energy versus the non-dimensional interatomic distance verified the analytical relationships developed herein. The discrepancy revealed in theoretical plots suggests that the 2-body PTHT and KP potentials are more suitable for curve-fitting "softer" and "harder" bonds respectively.
Wed, 01 Dec 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1125752004-12-01T00:00:00Z
- Mass-modified wiener indices and the boiling points for lower chloroalkaneshttps://scholarbank.nus.edu.sg/handle/10635/112613Title: Mass-modified wiener indices and the boiling points for lower chloroalkanes
Authors: Lim, T.-C.
Abstract: A criterion for obtaining the chemical graph of a chloroalkane has been proposed by replacing the edge vertex containing CH3 group with covalently bonded chlorine atom. By introducing α as the group mass ratio of Cl to CH3 as well as a molecular mass factor M = M(α,n,nC), a mass-modified Wiener index has been proposed as Wm = MPW where W is the Wiener index obtainable from the chemical graph, whilst n and nC correspond to the number of chlorine and carbon atoms respectively in the chloroalkane molecule. The mass factor is defined in such a manner that Wm = W for alkanes in order to maintain consistency. Numerical trials on the boiling point versus Wiener index plane reveal that when P = 2 the chloroalkane curve shifts such that it coincides with the alkane curve. In view of the highly established empirical equation for alkanes it is suggested herein that, instead of obtaining separate empirical curves for haloalkanes, there is a good potential for boiling points of haloalkanes be obtainable based on the philosophy of mass factor in order to take advantage of the highly established empirical models of alkanes.
Wed, 01 Dec 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1126132004-12-01T00:00:00Z
- Potential energy function based on the narcissus constant, its square and its cubehttps://scholarbank.nus.edu.sg/handle/10635/112633Title: Potential energy function based on the narcissus constant, its square and its cube
Authors: Lim, T.-C.
Abstract: The narcissus constant, N = 2.3983843828..., is defined as a number that fulfills the narcissistic infinite nested radical equation N√ N+N× N√N+N× N√N+...=N=N√N× N+N√N× N+ N√N×.... Incorporation of this constant, its square and its cube into the generalized version of the Lennard-Jones potential function gives the narcissus constant potential function UNLJ/D= 1/N-1(R/r) N3}-N/N-1 (R/r)N2 which (a) is suitable for modeling van der Waals interaction due to its agreement with the Lennard-Jones (12-6) potential energy curve over long range, and (b) forms simple generalized hybrid interatomic-intermolecular potential energy function due to its correlation with the averaged form of Lennard-Jones, Morse, Buckingham and Linnett potential energy curve near the minimum well-depth. © 2006 Springer Science+Business Media, LLC.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1126332008-01-01T00:00:00Z