index

Our research focuses on theoretical studies of two problems: (1) Materials under external fields and (2) Complex polymer liquids. We are interested in employing computer simulation, Statistical Mechanics theory and Quantum theory to elucidate the static and dynamic properties of these systems, and the influences of chemical structure on their properties.

Materials under External Fields

External fields have a broad sense in our work, ranging from confined boundaries to electric and magnetic fields. For confined boundaries, we are particularly interested in flexible boundaries, such as renal tubules and cellular membranes. As the first step, the simple harmonic potential is chosen to mimic flexible spherical and cylindrical pores. Meanwhile, materials under electric and magnetic fields display unique properties and are linked to numerous applications. Some synthetic electroactive polymers, containing strong polar bonds, exhibit appreciable strains under electric fields, which are ideal materials for actuators, sensors and artificial muscles. Moreover, electric fields deform polymer thin films, and induce morphological change and phase transition for polymer blends. In biologic systems, electroporation is a standard technique in drug delivery and in transport of gene materials through cellular membranes because electric fields deform membranes and force membrane channels to open. In addition, magnetic fields affect the electron transport properties of semiconductor materials, and useful applications, such as current sensors, have been developed. Also, an increase of interest has been devoted to nano-materials, such as carbon nanotubes, and their electronic properties in external fields possess potential applications for molecular devices. We are conducting theoretical studies for the above systems. In the following is the summary of our ongoing research.

I. Polymeric materials in external fields

(1) Chain conformation in harmonic potentials

We have conducted Monte Carlo simulations for single polymers confined to three-dimensional and two-dimensional harmonic potentials. In the former case, the chain molecule tends to collapse into globule, but under 2D harmonic potentials, the chain molecule undergoes anisotropic deformation. To better understand the simulation results, we have devised Flory-type type theories to search for the scaling relations between the mean chain size and field strength. In 3D harmonic potentials, we obtain a power law R² ~ (N/k)^2/5 where R² is the mean squared end-to-end distance, N is the chain length (molecular weight), and k is the strength of the spherically harmonic potential. For 2D harmonic potentials, we find that the power low for the z-component (free of external forces) of R² is z² ~ N²k^2/5, and the x-component (subject to external forces) has a power law x² ~ k^-3/5. Namely, R²is the sum of an increasing and a decreasing function of field strength k. As a result, R² displays a non-monotonic behavior, i.e., it decreases first and increases again after passing a minimum as k is increased. Note that such a behavior is also seen while a flexible chain is confined to a rigid or a semi-flexible tube. Meanwhile, the simulations show that these power laws are valid for strong enough fields. For weak fields, the first-order perturbation theory is utilized to compare with the simulation results. These results reveal the conformational behavior of a flexible chain polymer under spherical and non-spherical applied potentials.

(2) Conformation of polar polymers in the absence and presence of electric fields

Polar polymers, consisting of pronounced polar bonds on the chain backbone, have different properties from neutral and ionic polymers. We investigate an all-atom model of poly(vinylidene di-fluoride) (PVDF), an example of polar polymers, to examine the conformational transition induced by environmental factors, such as temperature and solvent dielectric constant. We obtain a phase diagram to summarize the conformational properties as a function of temperature and chain length. The phase diagram shows discrete conformational transition, similar to the first-order phase transition, and continuous transition for intermediate and long chain lengths, respectively. These results can be attributed to the competition between the effective local rigidity of a chain molecule and intramolecular attraction, and perhaps, some extent of cooperative interactions for longer chains. By adjusting these parameters, the role of dipolar interactions can also be systematically studied. We find that dipolar interactions are effectively attractive and enhance chain collapsing.

Since polar polymers can deform significantly in electric fields, elucidation of field-induced chain elongation is an important topic. However, simulations of all-atom models are quite expensive, and development of a simple coarse-grained level model is greatly needed. The inception of the project is to characterize the influence of each type of interactions for polar PVDF with alternating methylene and methylene fluoride group on the chain backbone. We first treat the methylene and methylene fluoride groups of PVDF molecules as united atoms, similar to neutral alternating polyampholytes containing both positive and negative charges. The second model is an all-atom model with explicit charges. In the weak coupling limit without intramolecular interactions, the chain elongation of the two models agrees well at weak fields. However, the two models display pronounced deviation at strong fields due to different local chemical structures. Nevertheless, with some modifications, polyampholyte models may be useful for constructing coarse-grained level models for polar polymers.

(3) Chain relaxation subject to harmonic potentials

We consider a polymer chain confined by a harmonic potential in theta-solvents using the Zimm and Rouse model to elucidate the chain relaxation behavior in weak and strong fields, respectively. We investigate a case in which the center of the field is tuned to match the center-of-mass of the polymer at the instant when the field is switched on. The closed-form expressions are obtained for these models. When the field strength is weak enough so that the chain conformation is close to ideal Gaussian, the Zimm model predicts that the chain molecule would fluctuate within the confined space induced by the applied field. Moreover, the molecular rotation relaxes faster than the translational motion of the center-of-mass of the polymer molecule. However, under a strong field, the polymer molecule contracts continuously from a random coil to a collapsed conformation after the field is switched on. The Rouse model makes predictions that the center-of-mass of the confined polymer molecule would achieve its equilibrium state first. After the relaxation of the center-of-mass, the polymer molecule reaches the equilibrium chain conformation, followed by the molecular rotation. Furthermore, the Rouse model also predicts that in the presence of a strong field, the Rouse time is predominated by the field strength only. This model can be extended to study the motion of a probe molecule in inhomogeneous gels.

(4) Chain dynamics in alternating fields

We investigate the dynamics of a copolymer molecule in a theta-solvent under an alternating field using the Zimm model. We first consider a diblock copolymer with two blocks of same force constant, where the monomers on the two different blocks interact with the applied field differently. The theory predicts that the center of mass of the molecule and the chain conformation oscillates in response to the sinusoidal field. Such oscillation is not observed for the homopolymer cases, but becomes more pronounced when the fraction of the two blocks becomes equal. The strength of the oscillation is weakened in highly viscous solutions, and the phase of oscillation is shifted. Moreover, the oscillatory behavior diminishes at higher frequencies. For comparison, we also study a special copolymer model where the two monomers alternate along the polymer backbone. Again the oscillation emerges for the molecular motion and conformation. These results are qualitatively consistent with the recent experiments of single DNA molecules, and imply that the investigated DNA molecules may be more like copolymers due to coexistent charged and neutral groups on a DNA molecule.

(5) Molecular alignment under harmonic potentials

In this project, we intend to study the liquid crystal ordering in polymer/liquid crystal composites, with liquid crystals confined between polymer layers. This work is also related to rhodopsin, a membrane protein containing seven helical coils, confined within the cellular membrane. Each helical coil can be viewed as a cylinder, and these cylinders align within the layers of a cellular membrane. Recently, we have conducted Monte Carlo simulations to elucidate the alignment of rigid rods confined by spherically harmonic potentials. The initial calculation is for two rods, and we find that they tend to align in the presence of fields. For intermediate field strengths, parallel alignment emerges more often for shorter chains. Under very strong fields, the rods containing even number of beads display pronounced perpendicular alignment, whereas non-perpendicular alignment becomes more probable for the rods of odd number beads. Such a difference can be attributed to the different spatial arrangement of rods between the two cases. However, as the number of rods is increased, the parallel alignment becomes more favorable and liquid crystal ordering emerges under strong enough fields.

II. Semiconductor materials in magnetic fields

Based on an expansion of the memory function, we employ an analytical approach to analyze the role played by temperature, electron effective mass and background dielectric constant on the diffusion constant of a two-dimensional electron gas (2DEG), for instance in the GaAs/GaAlAs single heterojunction, in a uniform perpendicular external magnetic field. Using a short-time expansion of the Kubo-Greenwood formula, we are able to calculate the two-body and three-body effects from the corresponding correlation functions which are obtained from the hypernetted-chain integral equation theory and the Kirkwood superposition approximation, respectively. When our results are compared with already published Molecular Dynamics and Monte Carlo simulation results, the agreement is excellent. At low temperature, the diffusion constant first increases and then decreases as the magnetic field is increased but decreases monotonically with increasing magnetic field at high temperature. Our calculations show that the Lorentz force induced by an applied uniform magnetic field is enhanced by increasing the dielectric constant and decreasing the electron effective mass. This work is done in collaboration with Professor Godfrey Gumbs at Hunter College.

III. Carbon nanotubes in electric fields and magnetic fields

In this project, we study the electron properties of carbon nanotubes under electric and magnetic fields, in collaboration with Professor Godfrey Gumbs at Hunter College. In the first part, we calculate the exact time-dependent single-particle eigenstates for electrons in an intense terahertz laser field applied along the axis of a cylindrical nanotube. Making use of these results and linear response theory, we obtain the charge density fluctuations for an interacting electron gas confined to the surface of the nanotube. The dispersion equation for the collective plasmon-polariton excitations is derived. We obtain numerical results for the dispersion relation as a function of the wave vector along the axis of the nanotube, which show that under a THz field, some of the characteristic excitation spectrum is altered due to the nonlocal coupling between energy bands.

Also, we carry out calculations of the collective plasmon excitations for an electron gas confined to the surface of a cylindrical nanotube in a magnetic field which is perpendicular to the axis of the cylinder. The eigenenergies of the single-particle states are first calculated. In a weak magnetic field, only a few of the lowest eigenstates show a coupling between the linear momentum along the axis of the nanotube and the angular momentum around its axis through numerical calculations. We then employ linear response theory to obtain the density fluctuations due to a weak external perturbation by using the single-particle eigenstates to calculate the polarization function in the dispersion equation. Numerical results for the magnetoplasmon dispersion for various magnetic field strengths show that the distortion of band structure under magnetic fields induces the extra excitation spectral bands of carbon nanotubes.

Complex polymer liquids

In this project, theoretical studies are carried out to explore three systems: (1) Grafted polymers, (2) Polymer blends and nanoparticle formation, and (3) Polyelectrolytes. We have studied polymers grafted onto convex and concave surfaces, to model the surface of nano-scaled probes and the interior surface of nano-scaled micelles, respectively. Also, we are interested in nanoparticle formations mediated by templated polymers, which can facilitate the control of the shape and size of nanoparticles, to understand the role of templated polymers. In addition, we have extended integral equation theory to study the conformation, fractional charge, and ion binding of polyelectrolytes. The research programs are summarized as follows.

I. Grafted polymers

Monte Carlo simulations are conducted to investigate a model composed of a fluctuating sphere labeled on one chain end of an isolated flexible chain polymer in good solvents. The labeled sphere is to model the instantaneous size of a bound flexible chain segment or a vibrating chromophore on a polymer chain. We assume the vibration of the sphere is governed by a harmonic-like potential, and the sphere size stays positive. We first adddress the issue regarding the confinement effect induced by a flexible chain on the fluctuating sphere. To rationalize the simulation results, we carry out a detailed analysis for a simple case containing a dimer grafted onto a fluctuating sphere. Using the sphere with a large size fluctuation, we find that the fluctuating sphere can be confined within the coiled polymer chain, and even trapped inside the grooves between neighboring monomers. The results imply the confinement effects may influence the properties of chromophores labeled on polymers or drugs bound to biopolymers. Moreover, in a separate study, we show the fluctuating sphere model can be used to fit a bound flexible chain segment, and provides a means to parameterize a polymer chain to an effective dumbbell, with possible applications in the dynamics of dilute polymer solutions. Furthermore, we find that the grafted polymer is slightly more elongated than a free chain due to the attached fluctuating sphere, but the Flory exponent is essentially not changed in the presence of a fluctuating sphere.

Moreover, we investigate the capacity of a spherical cavity with polymers grafted onto its interior surface, in hoping to model micelles as drug carriers. We are testing a recently developed algorithm in our laboratories to calculate the free energy as a function of the drug number in the cavity. This model can be extended to calculate the interior structure and thermodynamic properties of drug carriers containing grafted polymers.

II. Polymer blends and nanoparticle formation

(1) Effects of templated polymers on aggregation

We have conducted Monte Carlo simulations to investigate a greatly simplified model for a blend composed of templated materials (polymers or monomers), smaller reacting particles and solvents on a two-dimensional lattice. In the simulations, we compute the mean chain conformation of flexible templated polymers, and the distribution of the number of adjacent reacting particles aligned along the same axis to rationalize how templated materials affect the physical aggregation of smaller particles in a blend. We first examine the effects of the effective interactions between templated materials and smaller reacting particles. For repulsive interactions, flexible templated polymers tend to contract to reduce repulsions arising from smaller reacting particles, but for attractive interactions, chain dimension increases to maximize attraction. When templated material composition is increased, the conformational deformation of templated polymers becomes more pronounced. Moreover, for attractive interactions, reacting particles are more dispersed in the blend. In contrast, repulsive interactions increase the probability of aggregation of reacting particles. Also, our findings show that templated monomers (without chain connectivity) interact with reacting particles more effectively than with templated polymers due to the greater interacting area per monomer, which enhances the dispersion and segregation of reacting particles in the blend due to the attractive and repulsive interaction, respectively. In addition, as templated material composition is increased, the probability of forming a larger aggregate decreases. This simple model allows us to elucidate the role of templated materials on the physical aggregation of smaller particles in a blend. This project is done in collaboration with Profess Bahnu P. S. Chauhan in our department.

(2) Self-consistent calculations for nanoparticles coated with surfactants

A self-consistent calculation is devised to compute the geometry and spin density of magnetic iron (III) oxide nanoparticles coated with long chain acid surfactants. We assume the nanoparticle contains four iron and six oxygen atoms of a total spin S=2. The MM+ force field predicts the irons form a cyclic structure bridged by oxygen atoms, with bond lengths and angles close to a bulk crystal. In the calculation, geometry optimization is employed to obtain the structure of the surrounding surfactants around the nanoparticle, and the spin (or charge) density of the nanoparticle is calculated by using the ZINDO semiempirical method. We find surfactant anions tend to bind with the nanoparticle, and the nanoparticle spin density is sensitive to the surfactant number and charge. As the number of monoprotic surfactants is increased, the iron oxide particle is transformed from ferrimagnetism to ferromagnetism. In contrast to monoprotic acid surfactants, diprotic acid surfactants are more efficient to saturate the spin state of the uncompensated spins of nanoparticles.

III. Polyelectrolyte solutions

Polyelectrolytes are important industrial materials and ubiquitous in biological cells, such as polymethacrylic acid in superabsorbent polymers and DNA molecules. Despite tremendous research efforts, there remain many problems unresolved, such as conformation, the effects of short-range attraction and acid-equilibria of ionic polymers. We are in collaboration with Professor Arun Yethiraj at University of Wisconsin to advance theoretical development. Recently, we have devised a simple theoretical model to quantify the conformation and structure of flexible chain polyelectrolytes, and the results are in good agreement with simulations. Furthermore, we have incorporated the acid-base equilibria and short-range monomer interactions into the model of flexible chain polyelectrolyes. Our results show the discrete coil-helix conformational transition may occur depending on the dissociation constant and the strength of the attractive interaction of ionic polymers. Also, we have employed the integral equation theory to quantify the partial structure functions of a DNA solution, from the neutron scattering experiments. To fit these experimental data, we find a DNA molecule must comprise of three types of monomers: bared charged, protonated and counterion ion binding monomers. Our results suggest that DNA molecules are more like copolymers due to coexistent neutral and charged sites.

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Biographical Information

1. C.-Y. Shew and H. L. Chuang, “Introduction and applications of Beer's law,EScientific Monthly, March 1991 (in Chinese).

2. C.-Y. Shew and P. Mills, “A Monte Carlo method to simulate systems with barriers: Subspace Sampling,EJ. Phys. Chem. 97 (1993) 13824-13830.

3. C.-Y. Shew and P. Mills, “Monte Carlo simulations of the pair correlation function and the equilibrium association constant of the Sticky Electrolyte Model using the Subspace Sampling Method,EJ. Phys. Chem. 99 (1995) 12988-12997.

4. C.-Y. Shew and P. Mills, “The Subspace Sampling Method: A Monte Carlo approach for simulating the single particle density function and the equilibrium constant for systems described by multiple Hamiltonians,EJ. Phys. Chem. 99 (1995) 12980-12987.

5. C.-Y. Shew and A. Yethiraj, “Phase behavior of the Widom-Rowlinson mixture,E#060;i style='mso-bidi-font-style:normal'> J. Chem. Phys. 104 (1996) 7665-7670.

6. A. Yethiraj and C.-Y. Shew, “Structure of polyelectrolyte solutions,EPhys. Rev. Lett. 77 (1996) 3937-3940.

7. C.-Y. Shew and A. Yethiraj “Integral equation theory of solutions of rigid polyelectrolytes,EJ. Chem. Phys. 106 (1997) 5706-5719.

8. C.-Y. Shew and A. Yethiraj, “Ion binding of tobacco mosaic virus solutions,E#060;i style='mso-bidi-font-style:normal'> J. Chem. Phys. 109 (1998) 5162-5163.

9. C.-Y. Shew and A. Yethiraj, “Conformational properties of isolated polyelectrolytes in poor solvents,EJ. Chem. Phys. 110 (1999) 676-681.

10. C.-Y. Shew and A. Yethiraj, “Monte Carlo simulations and self-consistent integral equation theory for polyelectrolyte solutions,E#060;i style='mso-bidi-font-style:normal'> J. Chem. Phys. 110 (1999) 5437-5443.

11. C.-Y. Shew and A. Yethiraj, “Computer simulations and integral equation theory for the structure of salt-free rigid rod polyelectrolyte solutions: Explicit incorporation of counter ions,EJ. Chem. Phys. 110 (1999) 11599-11607.

12. C.-Y. Shew and A. Yethiraj, “Self-consistent integral equation theory for semi-flexible chain polyelectrolyte solutions,EJ. Chem. Phys. 113 (2000) 8841-8847.

13. R. Wenczel and C.-Y. Shew, “Confinement effects in polymers under an applied electric field,EAmerican Chemical Society Polymer Preprints 41 (2000) 1689-1690.

14. Y. Chen and C.-Y. Shew, “Conformational behavior of an isolated polymer chain labeled with an elastic ball,EAmerican Chemical Society Polymer Preprints 41 (2000) 1691-1692.

15. C.-Y. Shew and A. Yethiraj, “The effect of acid-base equilibria on the fractional charge and conformational properties of polyelectrolyte solutions,EJ. Chem. Phys. 114 (2001) 2830-2838.

16. A. Yethiraj, H. Fynewever, and C.-Y. Shew, “Density functional theory for pair correlation function in polymer liquids,EJ. Chem. Phys. 114 (2001) 4323-4330.

17. R. Wenczel and C.-Y. Shew, “Conformational behavior of isolated polymers under an external field in good solvents,EJ. Chem. Phys. 114 (2001) 4717-4723.

18. R. Wenczel and C.-Y. Shew, “Dynamics of a copolymer chain under an alternating electric field,EAmerican Chemical Society Polymer Preprints 42 (2001) 621-622.

19. Y. Chen and C.-Y. Shew, “Monte Carlo simulations for drug carrying capacity of micelles,EAmerican Chemical Society Polymer Preprints 42 (2001) 626-627.

20. Y. Chen and C.-Y. Shew, “Conformation and orientation of polymers in good solvents under external fields,EAmerican Chemical Society Polymer Preprints 42(2) (2001) 213-214.

21. A. Ajavon and C.-Y. Shew, “Monte Carlo simulations for the conformational behavior of a polymer chain in a flexible tube,EAmerican Chemical Society Polymer Preprints 42(2) (2001) 258-259.

22. Y. Chen and C.-Y. Shew, “Monte Carlo simulations for a fluctuating sphere labeled on a flexible polymer chain in good solvents,E#060;/span> J. Chem. Phys. 115 (2001) 9084-9091.

23. R. Wenczel and C.-Y. Shew, “Zimm model for a copolymer chain under an alternating field in q solvents,EJ. Chem. Phys. 115 (2001) 11325-11332.

24. C.-Y. Shew, G. Gumbs and G. Dubey, “Effect of two-body and three-body correlations on the diffusion constant of two-dimensional coulomb systems in a uniform magnetic field,ESolid State Communication 121 (2002) 187-191.

25. C.-Y. Shew and A. Yethiraj, “Integral equation theory for the structure of DNA solutions,E J. Chem. Phys. 116 (2002) 5308-5314.

26. R. Wenczel and C.-Y. Shew, “Extension of the Zimm and Rouse Model to polymers confined by a harmonic potential in q solvents,EJ. Chem. Phys. 116 (2002) 9537-9544.

27. M. B. Pomfret, C.-Y. Shew, N.-L. Yang and A. Ulman, “Self-consistent calculation of geometry and spin density of an iron oxide nanoparticle in acid surfactants,EAmerican Chemical Society Polymer Preprints 43(1) (2002) 461-462.

28. C.-Y. Shew, B. Chauhan and Y. Chen, “Lattice Monte Carlo simulations for the structure of precursors in polymer liquids,EAmerican Chemical Society Polymer Preprints 43(1) (2002) 1325-1326.

29. C.-Y. Shew and G. Gumbs, E#060;span style='mso-fareast-font-family:"Arial Unicode MS"'>Memory function approach to electronic diffusion in 2D electron systems,EPhys. Rev. B. 66 (2002) 245304-345309.

30. C.-Y. Shew, “Monte Carlo simulation for confinement induced molecular alignment,EAmerican Chemical Society Polymer Preprints 44(1) (2003) 1231-1232.

31. Y. Chen and C.-Y. Shew, “Monte Carl Simulations for the conformational behavior of a poly(vinylidene) molecule,EJ. Mol. Modeling in press (2003).

32. C.-Y. Shew, “Conformational behavior of a single polymer chain confined by a two-dimensional harmonic potential in good solvents,EJ. Chem. Phys. in revision.

33. G. Gumbs, A. Balassis, and C.-Y. Shew, “Plasmon-Polaritons for a nanotube in an intense Terahertz Field,E submitted to Phys. Lett.

34. Y. Chen, C.-Y. Shew, C. Gbemudu, and B. P. S. Chauhan, “Theoretical study of the effects of templated materials on aggregate formation,Esubmitted to Macromolecular Theory and Simulations.

35. Y. Chen and C.-Y. Shew, “Conformational behavior of polar polymer models under electric fields,Esubmitted to Chemical Physics Letters.

36. G. Gumbs, C.-Y. Shew and M. P. A. Fisher, “Nonlocal magnetoplasmons for cylindrical nanotubes in a perpendicular magnetic field,Esubmitted to Physical Review B.

37. C.-Y. Shew, A. Hall and A. Hall, “Theoretical studies of adsorbed particles on the surface of a cylinder,Esubmitted to American Chemical Society Polymer Preprints.

38. Y. Chen, A. Ajavon and C.-Y. Shew “Monte Carlo simulations of two rigid rods in a flexible cavity: Confinement induced spatial alignment,Ein preparation.

39. C.-Y. Shew, “A simple model for the motion of a probe molecule in polymer gels,Ein preparation.

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Opening Position in My Group

Title: Summer Research Assistant

Term: 10 weeks in summer

Description: Searching for an enthusiastic undergraduate student interested in interdisciplinary challenge, with background in Chemistry, Physics, Statistics, Mathematics or any other related areas.

Duties: Computer Simulation; Modeling; Development applications for polymers, materials science and bio-polymers.

Application requirements: The applicant requires at least one semester of General Chemistry

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Hot List

Professor Arun Yethiraj: http://www.chem.wisc.edu/~yethiraj

Professor Hyuk Yu: http://www.chem.wisc.edu/faculty/yu.html

Professor James L. Skinner: http://www.chem.wisc.edu/faculty/skinner.html

Professor James D. Batteas: http://www.chem.csi.cuny.edu/batteas.html

Professor Ruth E. Stark: http://www.csi.cuny.edu/divsci/stark.htm

Professor Pamela Mills: http://patsy.hunter.cuny.edu:8001/FandS/PM/mills.html

Professor Godfrey Gumbs: http://www.ph.hunter.cuny.edu/faculty/gumbs/

Professor John R. Lombardi: http://www.sci.ccny.cuny.edu/~lombardi/

The College of Staten Island: http://www.csi.cuny.edu

The City University of New York: http://www.cuny.edu

Mr. Yong Chen: homepage coming soon

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Last Revised: 6/20/03