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43153-AC7
From Microscopic to Mesoscopic Descriptions: Coarse-Graining of Polymer Melts and Their Mixtures
Liquids of macromolecules are characterized by the presence of several length scales at which relevant phenomena take place. Processes occurring on different length scales are correlated, since the chemical nature of the macromolecule, which is defined at the monomer length scale and it is of the order of nanometers, determines the global properties of the molecules as well. One of the challenges in understanding the properties of complex fluids is to develop reliable theoretical approaches that formally correlate properties across the many length scales of interest.
Essential information about structure and dynamics of complex macromolecular liquids is gained by performing computer simulations. However the resolution of simulations does not allow for the full investigation of the system at all the length scale of interest because of the large number of degrees of freedom that need to be investigated. A computational technique that allows one to overcome this problem is multiscale modeling, where independent simulations are performed of the system coarse-grained at different levels of detail. To perform those simulations it is necessary to develop reliable theoretical models to coarse-grain the system.
With the support of this ACS-PRF grant, we have developed analytical methods to coarse-grain the structure of hompolymer melts and mixtures. In our model, each macromolecule is represented as an interacting soft-colloidal particle. The coarse-grained structures reproduce quantitatively results from united-atom simulations, supporting the validity of the proposed model. During the past year, we extended our approach to coarse-grain liquids of diblock copolymers.
Diblock copolymers are macromolecules in which a homopolymer chain is chemically bound to a second homopolymer chain of different chemical structure. Diblock copolymers are systems of great interest for their technological applications, because the two polymers, which have different physical properties, can produce materials with mixed physical properties. Below their phase transition, block copolymer liquids order in microscopic structures characterized by the block length scale. Developing the technology to produce micro-ordered structures of well-controlled size and shape requires an understanding of the processes that drive the formation of micro-ordered phases under different thermodynamic conditions of temperature and density as well as different chain composition, monomer structure, and degree of polymerization. Coarse-graining models of block copolymer molecules, in conjunction with a multiscale approach, are useful for simulating their properties on the large range of time and space scales of interest.
In our coarse-graining procedure diblock copolymer liquids are mapped into liquids of interacting soft colloidal dumbbells. Each dumbbell represents one macromolecule composed by two effective soft colloidal particles, having the dimensions of the block radii of gyration, and centered on the coordinates of the center-of-mass of each block. Total distribution functions for three different length scales are formally related in our analytical approach, which corresponds to coarse-graining the molecule at the monomer (the statistical segment length), block (the radius of gyration of a block), and polymer (the polymer radius of gyration) scales. In this way, our theory represents a mesoscopic model of polymeric liquid structures where total correlation functions are resolved at three different intramolecular length scales. In our model, the size of the two "blobs" varies depending on the chain composition, degree of polymerization, and segment length. Repulsive interactions between segments of different chemical nature are quantified by the interaction parameter. Finally, concentration-fluctuation stabilization enters through the polymer reference interaction site model theory for the monomer-level description, and deviations from mean-field theory are predicted by our coarse-grained approach as well. Analytical intermolecular total correlation functions between like and unlike coarse-grained blocks are predicted in both the real and reciprocal space.
As a test of our coarse-graining expressions, we compared theoretical predictions with computer simulation data of homopolymer melts in the athermal regime. Because in the high temperature regime concentration fluctuations are not present, we tested the ability of our description to capture the effect of architectural asymmetry. Analytical solutions showed quantitative agreement with united atom simulations.
We also investigate the behavior at the mesoscopic scale of our system as the temperature is modified and the system evolves toward its microphase separation transition. We observed that as the temperature decreases, the formation of self-contacts, AA and BB, becomes energetically favorable, while cross-contacts, AB and BA, are suppressed. This is the signature of increasing physical clustering, which occurs as the system approaches its phase transition. Moreover, we observed that asymmetric block copolymers cluster around the minority species. Finally, for all diblocks the theory predicts no sharp transition at the interface between A and B domains, which is a characteristic of the weak segregation regime: fluctuations still partially disorder the liquid, while it becomes increasingly correlated approaching its phase transition.
In conclusion, from our study emerges that our analytical procedure to coarse-grain diblock-copolymer liquids conserves the correct physical behavior, as observed experimentally, supporting the validity of the proposed procedure.
