We combine advanced theories and computer simulation techniques to study at nano to mesoscales (i.e., from subnanometers to micrometers) the behavior of nanostructured polymeric materials. We are currently working on self and directed assembly of block copolymers, stimuliresponsive polymer brushes, polyelectrolyte adsorption and layerbylayer assembly, and structure and properties of polymer nanocomposites. We are also working on fast Monte Carlo simulations and coarse graining of polymeric systems. All of these are at the forefront of nanoscale polymer science and engineering and have important technological applications in many fields.
A characteristic of complex fluids such as polymers is that they span over largely different time and length scales (e.g., 10^{12}~10^{0} s and 10^{10}~10^{0} m). We therefore use a suite of computational tools, ranging from particlebased molecular simulations (molecular dynamics, Monte Carlo simulations, dissipative particle dynamics) to molecularlevel theories (field theories, integralequation theories, densityfunctional theories) to mesoscopic simulations (e.g., phasefield modeling and cell dynamics simulations), to investigate both thermodynamic and dynamic behavior of polymeric systems. The overarching goal is to establish the interconnections between these results at different levels, thus enabling hierarchical modeling bridging various time and length scales.


Self and directed assembly of block copolymers


Block copolymers (BCPs) have great potential for applications in nanotechnology, due to their selfassembly into spatially periodic structures on the length scale of 10 to 100 nanometers, direct control of the size and shape of these nanostructures, and uniformity of these nanostructures.[1,2,3] Many applications (e.g., templates for nanolithography, nanowires, highdensity storage devices, and nanostructured membranes) envisage thin films of BCPs supported on a substrate, and wellordered nanostructures oriented perpendicular to the substrate are desirable. Unfortunately, due to defect formation and slow kinetics common in BCP systems, the order of their selfassembled nanostructures persists over only a few hundreds of nanometers. Control of both the perpendicular orientation and the inplane ordering to achieve wellordered nanostructures is therefore the key issue in many applications of BCPs. In our original DOE project, we have studied directing block copolymer assembly by external fields (including topographically and chemically patterned substrates, and electric field) to obtain wellordered nanostructures, using a highperformance, parallel FORTRAN 90 code (PolySCF) for 3D realspace selfconsistent field calculations developed in our group. This work allows knowledgebased rational design (instead of trialanderror experiments in a large parameter space) to obtain wellordered nanostructures of BCPs. 

Photovoltaic energy obtained using conjugated (semiconducting) polymers is very attractive due to its cheap materials, low processing cost, and ease of largescale manufacture. Control of the polymer morphology and structure on the nanoscale is critically important for optimizing the efficiency of polymer optoelectronic devices.[4,5,6,7] Such control can be achieved with magneticfield directed assembly in thin films of rodcoil (RC) BCPs containing conjugated rod blocks. In our renewed DOE project, we use both PolySCF extended to RC BCPs and the newly proposed fast offlattice Monte Carlo simulations with soft potentials that allow particle overlapping[8] to understand, predict, and ultimately control the selfassembled nanostructures of RC BCPs in bulk, under thinfilm confinement, and with applied magnetic field. This work will allow knowledgebased rational design of these nanomaterials, thus advancing their integration into a range of technologically important applications, including the fabrication of polymerbased photovoltaic cells, lightemitting diodes, fieldeffect transistors, and chemical and biological sensors. 



Stimuliresponsive polymer brushes


This NSF CAREER project is a computational study on the response of twocomponent polymer brushes, particularly the polyelectrolyte brushes, to various external stimuli (solvent selectivity, solution pH, ionic strength, and applied electric field) and the influence on such response by various design factors (chain architecture, polymer/block lengths and charges, grafting densities, and incompatibility between the two components). The seemingly simple twocomponent brushes (including both binary homopolymer brushes and block copolymer brushes) can exhibit a rich variety of interesting and novel behavior through selfassembly of the two components, and have diverse applications in many fields as "smart" surfaces.[9,10,11] The design of these responsive brushes for practical applications such as chemical gates, sensors, biomaterials, and drug delivery, however, requires detailed understanding of the physics of their stimuliresponse and knowledge of how various design factors affect their stimuliresponse, which are rather limited. 

Here we use coarsegrained models describing the generic features of twocomponent brushes, and two judiciously designed and complementary methods: 3D parallel selfconsistent field calculations and novel fast Monte Carlo simulations[8,12], which capture the physics of stimuliresponse of twocomponent brushes and can provide essential guidance to experimental design of such smart surfaces. This work provides us with fundamental understanding and predictive capability on the stimuliresponse of twocomponent polymer brushes and enables knowledgebased rational design of such smart surfaces best suited for targeted applications, while avoiding both labor and timeintensive trialanderror experiments.


Polyelectrolyte layerbylayer assembly


Polyelectrolyte layerbylayer (LbL) assembly has attracted exponentially growing interest due to its simplicity, versatility, and great potential for many applications.[13] Our understanding on the formation mechanism, internal structure, and molecular properties of polyelectrolyte multilayer (PEM), however, is still at an early stage. In great contrast to thousands of experimental papers on LbL assembly, very few theoretical and simulation studies have been reported. Although it is known that many parameters (e.g., nature and concentration of adsorbing species and added salt, solvent composition, pH of depositing solution, adsorption and washing time and temperature, etc.) affect the PEM structure and properties, to date there is no predictive tool for even the most basic quantities such as composition, layer thickness, and total charges in the multilayer.
In this ACSPRF project, we have creatively modeled the LbL assembly process as a series of kinetically trapped states using an equilibrium selfconsistent field theory. We have studied the internal structure and charge compensation of PEM formed on flat substrates, and the effects of various parameters affecting longrange electrostatic interactions (including the substrate charge density, polymer charge fractions, bulk salt concentrations) and shortrange interactions (including solvent qualities and repulsion between the two polymer species) in the system.[14] Our modeling of polyelectrolyte LbL assembly is in good qualitative agreement with most experiments and molecular dynamics simulations, helps us better understand the formation mechanism and internal structure of PEM, and can further guide experimental design to obtain PEM with desired properties. 



Fast Monte Carlo simulations with soft potentials
We have been very actively developing a class of novel Monte Carlo simulation methodologies, the socalled "fast Monte Carlo (FMC) simulations"[8,12], suitable for the study of equilibrium properties of manychain systems (e.g., polymer melts) with coarsegrained models. Due to their formidable computational requirements, full atomistic simulations cannot be applied at present to the study of manychain systems used in experiments. Coarsegrained models have to be used instead, where each polymer segment represents, for example, the centerofmass of a group of real monomers. While atoms cannot overlap, these coarsegrained segments certainly can. In conventional molecular dynamics or Monte Carlo simulations with coarsegrained models, however, hard excludedvolume interactions preventing segment overlapping (e.g., the LennardJones potential in continuum or the self and mutualavoiding walk on a lattice) are commonly used, leading to unrealistic or at best qualitative results.
The basic idea of FMC simulations is to use soft potentials that allow segment overlapping (that is, the repulsion between two coarsegrained segments is finite even when they completely overlap). This results in at least several orders of magnitude faster/better sampling of configuration space than conventional molecular simulations.[8,12] In particular, FMC simulation on a lattice is the fastest molecular simulation method to date.[12] More significantly, experimentally accessible fluctuations can be readily studied in FMC simulations, which are far beyond the reach of conventional molecular simulations.[15] Furthermore, direct comparisons of FMC simulations with the corresponding meanfield (e.g., selfconsistent field) theories for the same model system (thus without any parameterfitting) unambiguously quantify the effects of fluctuations/correlations neglected in the latter.[8,12] Last but not least, quantitative agreement between experimental measurements and FMC simulations even with coarsegrained lattice models can be achieved.[16]


Systematic and simulationfree coarse graining of polymeric systems
Polymeric systems not only need coarse graining as explained above, but are best suited for it as the large number of monomers on each chain (N_{m}>10^{3} in typical experiments) allows high levels of coarse graining. In our most recent work on systematic coarse graining, we quantitatively address the issue of how the effective potentials and properties of coarsegrained (CG) models vary with the coarsegraining level l=N_{m}/N, where N denotes the number of CG segments on each chain. Clearly, larger l means computationally more efficient models. Due to its reduced degrees of freedom (thus chain conformational entropy), however, a CG model cannot exactly reproduce the original system in all aspects. In order to choose the proper lvalues, it is necessary to quantify how well the original system is described by CG models with different l, which has rarely been done in the literature.
On the other hand, in most work on coarse graining, molecular simulations (i.e., molecular dynamics or Monte Carlo simulations) are used to obtain the structural and/or thermodynamic properties of both original and CG systems that need to be matched. This is computationally very expensive, particularly for original systems with large N_{m} (>10^{2}) where the statistical uncertainties can be too large for the simulation results to be meaningful due to the difficulty in efficient sampling of configuration space (this is exactly why coarse graining is needed). We therefore recently proposed the simulationfree strategy of coarse graining, where integralequation theories are used to obtain the structural and thermodynamic properties of both original and CG systems. These theoretical calculations can give quantitatively accurate results and are at least several orders of magnitude faster than molecular simulations.

