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We present a theory for polyelectrolyte systems: solutions and gels that allows the effective charge of the polymer backbone to self-regulate. Using a variational approach, we use an expression for the free energy of polyelectrolyte systems that accounts for all physically relevant contributions. This free energy is then minimized to predict the phase behavior of the system as a function of external variables such as temperature and salt concentration. In the first section, we present results for the phase separation of polyelectrolyte solution in salt-free solvents. We show that the daughter phases have different polymer charges from that of the mother phase. The critical point is also altered significantly by the charge self-regularization of the polymer chains. This work extends the progress made so far in the theory of phase separation of strong polyelectrolyte solutions to a higher level of understanding by considering chains which can self-regulate their charge. In the second part, we present results for the volume phase transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis are in agreement with existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the phase transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems. In the third part, we present results for the phase separation of polyelectrolyte solution in monovalent and divalent salty solvents. We tried some results for high volume fraction of the salt, those high salt calculation results will give us some ideas about the low temperature phenomena, however those results are un-physical. More calculations need to be done in order to discover the real physical range effects. It will cost more calculation hours, however it's doable based on the recent updated code.

A variety of new chiral one-carbon-bridged metallocene derivatives of titanium and zirconium have been prepared. Addition of the anions of cyclopentadiene, indene and fluorene to 6-t-butylfulvene and 6,6-dimethylfulvene produced the ligands t-BuCH(C$\sb5$H$\sb5$)R (R = C$\sb5$H$\sb5$, 22; C$\sb9$H$\sb7$, 23; C$\sb{13}$H$\sb9$, 26) and (CH$\sb3$)$\sb2$C(C$\sb5$H$\sb5$)R (R = C$\sb9$H$\sb7$, 24; 3-CH$\sb3$-C$\sb9$H$\sb6$, 25). The reaction of the ligands 22-26 with n-BuLi produced the corresponding bis-anions, which were reacted with titanium or zirconium tetrachloride at low temperature ($-$78$\sp\circ$C), to produce the complexes t-BuCH($\eta\sp5$-C$\sb5$H$\sb4$)(R)MCl$\sb2$ (R = $\eta\sp5$-C$\sb5$H$\sb4$, M = Ti, 27; R = $\eta\sp5$-C$\sb5$H$\sb4$, M = Zr, 29; R = $\eta\sp5$-C$\sb9$H$\sb6$, M = Ti, 30; R = $\eta\sp5$-C$\sb9$H$\sb6$, M = Zr, 31; R = $\eta\sp5$-C$\sb{13}$H$\sb8$, M = Zr, 32) and (CH$\sb3$)$\sb2$C($\eta\sp5$-C$\sb5$H$\sb4$)(R)MCl$\sb2$ (R = $\eta\sp5$-C$\sb9$H$\sb6$, M = Ti, 34; R = $\eta\sp5$-C$\sb9$H$\sb6$, M = Zr, 14; R = 3-CH$\sb3$-$\eta\sp5$-C$\sb9$H$\sb5$, M = Ti, 35; R = 3-CH$\sb3$-$\eta\sp5$-C$\sb9$H$\sb5$, M = Zr, 36). The structure of 34 is very rigid due to strain at the bridgehead carbon. The chlorine atoms in complexes 27 and 32 can be easily replaced by methyl groups. By treatment of 27 and 32 with MeLi in diethyl ether the corresponding dimethyl derivatives 28 and 33 were obtained. The influence of the symmetry of the bridge in metallocene Ziegler-Natta catalysis was tested. The chiral complex 32 was compared to the symmetric system $\rm (CH\sb3)\sb2C(\eta\sp5$-$\rm C\sb5H\sb4)(\eta\sp5$-$\rm C\sb{13}H\sb8)ZrCl\sb2({\bf 52})$ in the syndiospecific polymerization of propylene. The polymerization behavior of precursors 32 and 52 were very similar. The substituents on the bridgehead carbon had little or no influence on the polymerization process because of their remote location from the available coordination sites involved in the polymerization reaction. The symmetry of the cyclopentadienyl groups was also tested for the polymerization of propylene with metallocene systems. Precursors 14 and 36 polymerized propylene to low molecular weight materials in reduced activities compared to the symmetric precursor 52. The polymers obtained with 14 and 36 present a structure assigned to hemiisotactic chains. New sulfur and selenium derivatives of the mixed sandwich complex ($\eta\sp5$-$\rm C\sb5H\sb5)(\eta\sp7$-$\rm C\sb7H\sb7)Ti\ ({\bf 63})$ were prepared. Complexes ($\eta\sp5$-$\rm C\sb5H\sb5)(\eta\sp7$-$\rm C\sb7H\sb6$R)Ti (R = SCH$\sb3$, 82; SPh, 84; SePh, 86), ($\eta\sp5$-$\rm C\sb5H\sb4R)(\eta\sp7$-$\rm C\sb7H\sb7$)Ti (R = SCH$\sb3$, 81) and ($\eta\sp5$-$\rm C\sb5H\sb4R)(\eta\sp7$-$\rm C\sb7H\sb6$R)Ti (R = SCH$\sb3$, 80; SPh, 83; SePh, 85) were prepared by reaction of the mono- or dilithio-derivatives of 63 with one or two equivalents of the corresponding dichalcogenide. Compound 80 behaved as a bidentated ligand. Heterobimetallic derivatives 88-90 were obtained by treatment of 80 with Cr(CO)$\sb4$(nbd), Cr(CO)$\sb4$(nbd) and PtCl$\sb2$(PhCN)$\sb2$, respectively.

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