Much theoretical and experimental work has focused on chain dynamics in semidilute polymer solutions for over three decades. The fast relaxation mode (namely, the cooperative diffusion of chain segments between two neighboring entanglement points, i.e., the "blobs") has been well understood. But for the slow mode that observed from time to time, its earlier attribution to the "reptation" is clearly wrong. There are a school of people in the world who thought that it was due to some experimental artifacts. However, there are also many experimentalists who believe that it is real and try to explain it in different ways. Up to now, the questions about whether this observed slow mode is real and its nature are still remained as a challenging problem. In this study, dynamics of liner polystyrene semidilute solution in both toluene and cyclohexane was comparatively studied by laser light scattering. In toluene, a thermodynamically good solvent, four different narrowly distributed polystyrene standards over a wide molar mass range (1.15 x 105 - 6.85 x 106 g/mol) were studied. The highest concentration (C) studied was ∼21 times of the overlap concentration (C*) at which polymer chains start to "touch" each other. As expected, only one fast diffusive relaxation was observed, attributing to the blob diffusion The static and dynamic correlation lengths (xiD and xiS) are also expectedly scaled to the concentration as xiS or xiD ∼ C -0.72 +/- 0.02. In cyclohexane, a poor or marginal solvent, depending on the solution temperature, an additional slow relaxation mode repeatly appeared. In the range 32-50°C, the polystyrene chains extend as the temperature increases because cyclohexane becomes a better solvent. In this way, C* decreases. Therefore, we can use the solution temperature to switch such a polystyrene solution from dilute to semidilute for a given polymer concentration. By comparing the intensity contribution and characteristic decay time of the slow mode, we found that the temperature has a much stronger effects on the slow mode. Our results indicate that the fast and slow modes are coupled and the slow mode is due to relaxation of segments around the entanglement point, that is, the knots. These interacted segments fluctuation corresponds to some density with a correlation length longer than that of individual blobs. / On the way, we also studied the random copolymer poly(N-isopropylacrylamide - co- x 2'-methacryloylaminoethylene-3alpha,7alpha,12alpha-trihydroxy-5beta-cholanoamide) poly(NIPAM-co-xMACA) in dilute solutions. MACA is a methacrylamide derivative of bioactive cholic acid. The copolymers were made by free-radical polymerization and "x" represents the composition of MACA (1.0, 2.9 and 4.8 mol%). Poly(N-isopropylacrylamide) (PNIPAM) is a thermally sensitive polymer, namely, it is soluble in water with a lower critical solution temperature (LCST ∼32°C). Due to incorporation of different amounts of hydrophobic MACA, the LCST of the copolymer is shifted to different lower values. At temperatures higher than the LCST, the copolymer chains undergo intrachain contraction or/and interchain association, depending on the polymer concentration and chain structure. Our laser lightscattering study of such chain contraction and association reveal an unexpected result; namely, the formation of stable aggregates of these hydrophobically modified copolymer chains is stronger easier than PNIPAM homopolymer chains under the same conditions. Our finding that that insertion of more hydrophobic comonomers into a hydrophilic chain backbone surprisingly led to the formation of smaller aggregates in water is apparently contradict to our conventional wisdom. A higher content of hydrophobic MACA or a quick heating of the solution can make the intrachain contraction so dominant that each resultant aggregate on average only contains a few collapsed chains with a lower chain density. We successfully attributed the stabilization to the viscoelastic effect, namely, hydrophobic association inside each aggregate increases the chain relaxation time (taue). When taue becomes much longer than the interaction time (tau c) of two colliding aggregates, each aggregate behaves like a tiny non-adhesive "glassy" ball. This stabilization mechanism is completely different from our conventional thermodynamic consideration in which we normally try to make the particle surface hydrophilic to reduce tauc. We also observed that in the cooling process, the collapsed chains inside the aggregates swell first before they can detachment and dissolve in the solution. The hydrophobic association induced in the collapsed solute at higher temperatures cannot be completely removed even at a temperature as low as 10°C. The dilution of the copolymer solution can completely suppress interchain association so that individual chains can undergo an intrachain coil-to-globule transition. The association of a limited number of heteropolymer chains in dilute solutions to form a stable/metastable mesoglobular phase between single-chain globules and macroscopic precipitates resembles the association of some protein chains. / We further comparatively studied the chain dynamics of a pair of diblock poly(styrene-b-butadiene) (PS210-b-PB 960) and triblock poly(styrene-b-butadiene- b-styrene) (PS200-b-PB1815- b-PS200) copolymers in both dilute and semidilute toluene solutions. As expected, the mutual diffusion of individual chain in dilute solutions became a fast cooperative diffusion of the "blobs" for both the copolymers in semidilute solutions. Further increase of the polymer concentration also lead to an additional slow relaxation mode. For the triblock chains, there existed an extra middle relaxation mode between the fast and the slow modes. The concentration dependence of the average characteristic decay time of the fast mode (⟨tauf⟩) follows a scaling of 1/⟨tau f⟩ ∼ C-alpha with 0.33 < alpha < 0.44, much smaller than 0.75 (predicted) or 0.72 (observed) for linear homopolymer chains in a thermodynamically good solvent. Note that toluene is a less good solvent for PB block. Such a difference in solubility leads us to speculate that the PB and PS blocks are transiently segregated in semidilute solutions. The relaxation of these transient PB and PS richer domains might lead to the observed slow mode. Our speculation is supported by the appearance and disappearance of the slow relaxation mode in a polyisoprene-b-polystyrene- b-polyisoprene semidilute solution in cyclohexane, a selective solvent for PS block at lower temperatures because the solubility of PS decreases as the solution temperature. / Li Wei. / "September 2006." / Adviser: Chi Wu. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1664. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In this thesis, we focus on the problem of interactions between solids and fluids. / The main part is the study of the motion of a rigid body immersed in an incompressible fluid. First, for the case of 2D ideal flow, a global weak solution is derived. Second, for the case of viscous flow in 3D, the problem is investigated in the Lp--framework. We get a decomposition of Lp-space associated with the problem. Then We prove that the corresponding semigroup is analytic in L65 R3∩L pR3 (p ≥ 2). Our result yields a local in time existence and uniqueness of strong solutions taking initial data in L65 R3∩L pR3 (p ≥ 3). / The other part is some research about micro-macro models of polymeric fluids. We provide a new proof for the global well-posedness of the coupling systems in 2D. / Wang, Yun. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 112-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.