- 나노구조고분자그룹
**연구**

# Research

I received my Ph. D in the Physics department, Columbia University, and my Ph. D advisor was Professor O'Shaughnessy in the Chemical Engineering Department; thus I have an interdisciplinary background, having worked on polymer physics, nanoscience and biophysics. From Sep. 2006 to Feb. 2009, I have worked as a postdoctoral researcher in Prof. Matsen’s group at the University of Reading. Professor Matsen has contributed enormously to the development and establishment of the numerical self-consistent mean field theory (SCFT) for polymer brushes and block copolymer systems.

# Current and Future Research

## 1. Brush Theory

Grafted polymers in solvent are naturally? stretched and form a brush. The earlier theoretical approach known as strong-stretching theory (SST) has been very successful in predicting fundamental properties such as the brush height L, parabolic density profile and broad chain end distribution. By using a more rigorous self-consistent-field theory (SCFT), I investigated finite-stretching corrections to the classical SST for polymer brushes in good solvent.

A polymer brush has a depletion layer next to the grafted substrate in which the polymer concentration linearly increases from zero to a maximum and I have shown that it is associated with a constant energy contribution and that it has a universal shape with a characteristic length scale of ~ 1/L. Furthermore, a systematic analysis of the exponentially decaying brush tail has shown that a simple theory can explain the shape and size of the tail

^{[1]}.## 2. Steric force between brush and nanoparticle

A common method of protecting a surface from external materials is to graft polymers densely enough to form a stretched brush. Then a particle
approaching the brush reduces the entropy of the polymers, and is thus repelled. Due to the non-trivial geometry involved, the previous theoretical predictions have generally involved the adoption of the Derjaguin approximation, in which the potential for a curved surface is estimated by an integral over uniform compressions.

For an accurate calculation of the energy penalty, we have developed numerical self-consistent field theory (SCFT) in a cylindrical-coordinate system, which can model a spherical particle of radius Rcompressing a brush of thickness L from above. By studying the free energy penalty F as a function of R, L and the compression depth D, we find that for brushes of experimentally realistic thickness the numerically calculated forces are an order of magnitude larger than the simple analytic estimation using SST. When our numerical SCFT data for uniform compression is combined with the Derjaguin approximation, the estimated energy penalty is in very good agreement with the full numerical calculation. This semi-analytical treatment provides an efficient and versatile tool for accurately predicting the repulsive force on particles of arbitrary shape

^{[2]}.## 3. Interaction between Polymer-Grafted Particles

For the purpose of stabilizing colloidalsuspensions, polymers are often grafted to the surface of the colloidal particle. Densely grafted polymers not only compatibilize particles with the solvent but also provide a steric repulsion when such particles are close enough for the polymer layers to be deformed. This effect provides an efficient method of preventing the agglomeration of particles by countering their van der Waals attractions.

However, there have been recent debates whether such a geometry can provide attraction of particles for a certain range of parameters, which may result in superstructured particle arrays. In this research, I examined the steric force between two polymer grafted particles by using SCFT in spherical coordinates. Due to the natural choice of the coordinate system and improvement in the algorithm, I was able to access to a wide range of parameters that have not been explored before. Our accurate calculation clearly shows that only a repulsive force is expected between the two particles regardless of the particle size, brush thickness and distance between the particles. I also compared the exact mean-field result to approximate solutions for those who want a quicker but still reliable method

^{[3]}.## 4. Nanoparticles in block copolymer templates

## 5. Block copolymer micelles

Block copolymers in solvent or in homopolymers self-assemble to form spherical or cylindrical micelles which mimic the structure formed by surfactants. Such micellar materials have great potential applications in various fields of nano- and bio-science. For example, the core-shell structured micelles have been suggested as carriers for drug delivery

^{[6]}. In this proposed work, the interaction between micelles or between a micelle and other materials, such as the cellular membrane, will be modeled and calculated. The previous projects involving block copolymer nanocomposites will be an effective preparation for this research and the SCFT method is an excellent tool for investigating this problem.## 6. Structured droplets on a surface

A simple liquid droplet on a flat surface is known to possess spherical cap geometry with a given contact angle, provided the surface interaction does not prefer complete wetting. However, complex liquids such as a block copolymer droplet have their own internal structure; hence the shape deviates from the classical spherical shape

^{[7]}. The experimentally reported terraced geometry is now theoretically tested, using SCFT of AB block copolymer droplet. Our ongoing research successfully provides the exact geometry of the layered droplet structure. At small A polymer-substrate attraction, LA, the droplet shows nearly spherical shape. Then, as LA increases, the droplets spread until complete spreading (0.5 periods) is reached. Most theoretical investigations of block copolymer phases have assumed an infinite size of periodic structure. In reality, a boundary must separate the periodic layer from the outside material. The exact shape of the boundary has never been fully understood before. Our work can also provide valuable information about how the block copolymer-outer material transition happens at the edge of the lamellar structure.

## 7. Amphiphilic bilayers and transmembrane proteins

The idea of quantitative mean-field calculations for more complicated systems are becoming realistic with the help of advances in computer hardware and the improvement of numerical algorithms such as the spectral method. For example, amphiphilic lipids self-assemble to form enclosed vesicles. Quantitative modeling of them will explain many interesting features such as phase separation between lipid species and fusion of membranes

^{[8]}. My basic interest is on the formation of the lipid bilayer vesicles and on how external constraints such as the surface tension of the system and chemical potential for the lipids affect their behavior. To study more complicated phenomena such as the fusion of vesicles and hemifusion process of membranes, dynamic mean-field theory can be employed. Ultimately, the quantitative SCFT method can be useful in modeling part of the cell membrane-cytoskeleton complex. For example, one transmembrane protein on a spherical vesicle can be modeled by the current two dimensional SCFT in cylindrical coordinates.## 8. Field-theoretical simulations (FTS) for polymeric systems

In the mesoscopic length scale, polymers are viewed as connected strings having attractive or repulsive interaction between different components. This nature makes it a reasonable attempt to directly model them using molecular dynamics (MD) or MC simulations. However, the computational demand of such methods, especially at melt densities, heavily restricts the size of the system and the length of polymers. Most modern simulations can only study short polymers of 100 monomers or less. The SCFT method is powerful in that it does not limit the size of the chain length. In fact, the Gaussian chain model makes the theory even more effective for longer chains.

However, the SCFT method has its own limitations; most notably, the saddle point method does not include any fluctuation around the mean-field solution. As a method to study the fluctuation effect, the idea of field-theoretical simulation (FTS) is now becoming widely popular and a few specific attempts for individual problems are already available (see Refs.

^{[9]}and references therein). The development of an FTS method will provide a useful tool for the understanding of various polymeric materials and their composite materials.# References

[1] J. U. Kim and M. W. Matsen, Eur. Phys. J. E 23, 135 (2007)

[2] J. U. Kim and M. W. Matsen, Macromolecules 41, 246 (2008)

[3] J. U. Kim and M. W. Matsen, Macromolecules 41, 4435 (2008)

[4] B. J. Kim et al., Langmuir 23, 12693 (2007)

[5] J. U. Kim and M. W. Matsen, Phys. Rev. Lett. 102, 078303 (2009)

[6] D. E. Discher and A. Eisenberg, Science 297, 967 (2002).

[7] A. B. Croll, M. V. Massa, M. W. Matsen and K. Dalnoki-Veress, Phys. Rev. Lett. 97, 204502 (2006)

[8] K. Katsov, M. Muller and M. Schick, Biophys. J. 87, 3277 (2004)

[9] G. H. Fredrickson, V. Ganesan and F. Drolet, Macrololecules 35, 16 (2002); A. Alexander-Katz, G. H. Fredrickson, Macromolecules 40, 4075 (2007)