Density Functional Theory Study On Stucture And Thermodynamic Properties Of Confined Complex Fluids

Compared with simple hard sphere fluids, the complex fluids such as rod-coil copolymers, ring polymers, electrolytes and ionic liquids have much richer phase behaviors. Accordingly, it is very important to study the structure and thermodynamic properties of complex fluids. In this thesis, we use configurational-biased (including crankshaft, chain regrowing, and cut rebridging) Monte Carlo simulation method and classical density functional theory (DFT) to study the structure and thermodynamic properties of complex fluids. Meanwhile, we use time-dependent density functional theory (TDDFT) which is based on the Poisson-Nernst-Planck equation to study the charging process of electric double layer capacitor. The main contents of this thesis are shown as below:(1) We proposed a novel PDFT for rod-coil copolymers with different size beads. We compared the results from our PDFT with those from Monte Carlo simulation method, and find that our PDFT could be successfully used to study the various rod-coil copolymers systems. For understanding the inhomogenous properties, we studied the structure and solvation effect of rod-coil copolymers confined in a nanoslit. We found that the steric effect of the coils played a key role in the solvation effect if the rod part was fixed. In addition, owing to the vacuum effect, the weak attraction around the classical contact of the rod-coil brushes is also observed. In short, the present theory can be easily applied to the other architecture polymers containing different size segments. It is expected that the calculation results in this work could provide useful reference to select the rod-coils as stabilizer for the protection of surfaces or the colloidal stabilization.(2) Owing to the importance of drug delivery in cancer or other diseases'therapy, the targeted drug delivery (TDD) system has been attracting enormous interest. Herein, we used the rod-coils PDFT proposed in the previous chapter to study the TDD system. In this work, we designed a novel TDD systems, i.e., rod-like nanocarrier based TDD system. For comparison, the monomer nanocarrier TDD system and the no nanocarrier one are also investigated. The results indicate that the drug delivery capacity of rod-like nanocarriers is about 62 timesthat of the no nanocarrier one, and about 6 times that of the monomer nanocarriers. The reason is that the rod-like nanocarriers would self-assemble into the smectic phase perpendicular to the membrane surface. Due to the self-assembly, the drug was forced to enter into the targeted cell. By contrast, the conventional monomer nanocarrier drug delivery system lacks self-assemble force to force the drug into the targeted cell. In short, the novel rod-like nanocarrier TDD system may improve the drugdelivery efficiency.(3) By modeling the ring-like molecule as a pearl necklace of freely jointed hard sphere, we develop a new equation of state (EOS) for the ring-like fluids on the basis of generalized Flory-Huggins (GFH) theory. Before proposing the new EOS of the ring-like fluids, we first modify the generalized Flory-Huggins theory for the chain fluids by incorporating a function related to the packing fraction into the insertion probability. The results indicate that the modified GFH EOS can predict the compressibility factors more accurately than the GFH EOS. Subsequently, the modified GFH theory-based EOS for the ring-like fluids is proposed. Compared to the Monte Carlo data, our EOS exhibits the best prediction among four EOSs for the compressibility factors. In addition, the modeling of inhomogeneous ring polymers remains a challenge in classical density functional theory (DFT) due to the difficulty in solving the direct bond connectivity of the ring architecture without free ends. By considering the feature that all of the segments in a ring are equivalent, we give an algorithm to solve the integral of direct bond connectivity for ideal ring polymers, and therefore propose a DFT for inhomogeneous ring polymers. Importantly, the DFT satisfactorily reproduces the data from the configurational-bias Monte Carlo (CBMC) simulations for ring polymers. The local density profiles from the DFT show that the bead density of inhomogeneous ring fluids is independent of ring size, which is also confirmed by the CBMC simulations. Interestingly, the behavior of solvation force for ring polymers is quite similar to that of the polymers with infinite chain length.(4) Density functional theory (DFT) calculations are typically based on approximate functionals that link the free energy of a multi-body system of interest with the underlying one-body density distributions. Whereas good performance is often proclaimed for new developments, it is difficult to vindicate the theoretical merits relative to alternative versions without extensive comparison with the numerical results from molecular simulations. Besides, approximate functionals may defy statistical-mechanical sum rules and result in thermodynamic inconsistency. Here, we present a contact-corrected density functional theory for ionic distributions at an interface that not only accounts for the steric effects and electrostatic correlations often ignored by conventional electrochemical methods but also conforms to the exact statistical mechanical sum rule for the contact ionic densities. The theoretical predictions are in excellent agreement with the simulation results for both the interfacial structure and electrochemical properties over a wide variety of electric double layer systems including those containing asymmetric electrolytes with multivalent ions.(5) We introduce a generic form of time-dependent density functional theory (TDDFT) to describe ion diffusion in electrochemical systems to account for steric effects and electrostatic correlations neglected in the Poisson-Nernst-Planck equations. By comparing the theoretical predictions from TDDFT and conventional electrokinetic methods for constant-voltage charging of the model electrochemical cells, we demonstrate that thermodynamic non-ideality plays a pivotal role in electrodiffusion even at relatively low electrolyte concentrations, and this effect cannot be captured by the lattice-gas model for the excluded volume effects. In particular, TDDFT predicts' wave-like' variation of the ionic density profiles that has not been identified in previous investigations. At conditions where there are no significant correlations between electric double layers from opposite electrodes, the charging kinetics follows an exponential behavior with a linear dependence of the relaxation time on the cell thickness in excellent agreement with the equivalent circuit model. However, the conventional electrokinetic model breaks down when the electrodes are at small separation, in particular for systems with low ionic strength or high charging voltage. In addition, we also study the charging kinetics of ionic liquid EDLs. By examining variations of the ionic density profiles and the charging density in response to an electrode voltage, we find that at certain conditions, the electrode charge shows a rapid surge in its initial response, rises quickly to the maximum, and then slowly decays toward equilibrium. The electrode charge and voltage may have opposite signs when the cell width is commensurate with the layer-by-layer ionic distributions. This unusual charging behavior can be explained in terms of the oscillatory structure of ionic liquids near the electrodes.