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Density functional theory of microphase separation in block copolymers and Monte Carlo simulations of polyelectrolyte electrophoresis
Abstract
In the first half of this dissertation, density functional theory of first order transitions was used to describe the ordering phenomena of amorphous diblock copolymers. The resulting formalism was then applied to the ordering of symmetric diblock copolymers to the lamellar morphology for values of $\chi$N above the microphase separation transition. $\chi$ refers to the Flory interaction parameter and N is the number of statistical segments comprising the copolymer. Three distinct regimes for the N dependence of the domain space, D, were identified. For 10.495 $<$ $\chi$N $<$ 12.5, the weak segregation limit is realized where D is proportional to N$\sp{0.5}$. For $\chi$N $>$ 105, the strong segregation limit is achieved where D is proportional to N$\sp{0.67}$. Between these limits, for 15 $<$ $\chi$N $<$ 95, a new regime with characteristics distinctly different from those of the weak and strong segregation regimes was found. Within this "intermediate" regime, D is proportional to N$\sp{0.72}$ and the domain boundaries support substantial fluctuations. The distinct features of the microscopic density profiles in the various regimes are discussed. In addition, density functional theory was employed to investigated the phase behavior of non-symmetric diblock copolymers. In the second half of this dissertation, Monte Carlo simulations were performed in order to study the dynamics of a polyelectrolyte chain in three-dimensional random porous media with an applied electric field. It was found that the dependence of the chain mobility, $\mu$, on the number of segments comprising the polymer, N, is in qualitative agreement with actual gel electrophoresis experiments. Further, three regions for the N dependence of the mobility were identified and determined to be a function of the average size of the polyelectrolyte in relation to the average pore size in the random medium. In the region of small N, the mobility is influenced primarily by collisions with the random media. As the average size of the polymer becomes comparable to the average pore size, the existence of entropic barriers has the effect of introducing a strong dependence of the mobility on N. In the high N regime, the polymer chains become significantly entangled with the random medium, further impeding the motion of the chains. However, in this high N regime, the chain dynamics cannot be explained by reptation. Lastly, it was demonstrated that the chain dynamics of a polyelectrolyte in the presence of a regular array of obstacles with an applied electric field defers from the dynamics of a chain in a random medium. Indeed, it was demonstrated that the presence of random medium gave rise to a much more efficient separation of polyelectrolytes of different N.
Subject Area
Polymer chemistry
Recommended Citation
Melenkevitz, James M, "Density functional theory of microphase separation in block copolymers and Monte Carlo simulations of polyelectrolyte electrophoresis" (1992). Doctoral Dissertations Available from Proquest. AAI9233109.
https://scholarworks.umass.edu/dissertations/AAI9233109