Thesis (Ph.D.)--University of Texas at Dallas, 2007. / Includes vita. Includes bibliographical references (leaves 185-196)

Mathematical models of reactors for the polymerization of methylmethacrylate (MMA) and propylene have been developed and analyzed in order to better understand the reactor dynamics and to determine conditions for improved operation. The exploration of the effects of mixing and heat transfer in an MMA polymerization reactor system has been conducted by the development of two models--an imperfect mixing model and a detailed model. To model imperfect mixing in polymerization, a reactor configuration using two tanks in parallel was used. Bifurcation diagrams developed using numerical analysis of the model have been drawn with two variable parameters, an exchange ratio, $\sigma$, and a volume ratio, $\kappa$. If both parameters are small, the lower solution branch of the steady state solutions is perturbed in comparison with a simple model which assumes perfect macro-mixing. If $\sigma$ increases ($\kappa$ = 0.1, $\sigma$ = 1.0), the shape of steady state solution curve differs significantly from that of a simple model as the feed temperature decreases. Two correlations for the overall heat transfer coefficient have been used to study the heat transfer. The steady state solutions of mass and energy balances in the reactor depend on the nature of the heat transfer correlation, as does the number of isola branches. The addition of coolant dynamics to the system results in no isola solution branches and no Hopf bifurcations. In olefin polymerization, a particle size distribution (PSD) in the polymerization reactor has been derived using population balances. Three reasonable reaction mechanisms for Ziegler-Natta catalysts, i.e., a simple reaction model, an active site reduction model, and a two sites model, have been used to derive the average number of active sites. It was observed that the PSD depends not only on residence time, but also on the reaction mechanism and that multiple active sites change the PSD slightly. The PSD, however, does not depend on initial catalyst volume. The mass and energy balances in the reactor have been derived to study the effect of PSD for each reaction mechanism on the reactor dynamics. It was observed that the PSD affects both bed height and particle volume. A feasible region for the reactor operation has been calculated using physical constraints. In a nonisothermal polymerization system, the reactor temperature does not change appreciably as catalyst injection rate increases. A unique steady state solution is found in a gas-phase continuous stirred-bed propylene polymerization reactor. The eigenvalues of the system of equations indicate that the steady state is unstable. A comparison with published data allows the observation that the actual reactor dynamics may be readily explained by using only the PSD derived from a simple reaction mechanism.

We investigate the effect of excess salt and simple shear on the dynamics and structure of semi-dilute aqueous solutions of cetyltrimethylatnmonium bromide and sodium salicylate. Small-amplitude oscillatory rheological measurements suggest a structural evolution from an entangled to a multi-connected network as the salt concentration is increased. Steady-shear measurements, however, show a significant departure from the Cox-Merz rule. This departure occurs at shear rates where $\eta\sp{\*}\propto\omega\sp{-0.92\pm0.08}$ and $\eta\propto\dot\gamma\sp{-0.51\pm0.06}$ and is attributed to the formation of large shear-induced structures. The critical shear rate $\dot\gamma\sb{\rm c}$ at which the Cox-Merz rule fails approximates the inverse of the terminal relaxation time, $\tau.$ Small angle light scattering (SALS) under shear was used to probe the mesoscopic structure and revealed novel scattering patterns exhibiting two-fold symmetry along the flow direction at low salt concentration, four-fold symmetry along the vorticity direction at moderate salt concentration and two-fold symmetry along the vorticity direction at high salt concentration. The SALS patterns were in qualitative agreement with the structural evolution from entangled to connected network as the salt concentration is increased and were suggestive of a local shear induced isotropic-to-nematic transition as well as a shear-induced string phase. Three-dimensional flow birefringence was used to probe average micellar orientation and revealed that at high salt concentration and high shear rate the micelles appear to retain a considerable degree of their connected structure.

The complex rheological behavior of nearly critical gels of two high molecular weight flexible polymer precursor systems, vulcanizing polybutadienes above the entanglement molecular weight, $\rm M\sb{e},$ and endlinking polydimethylsiloxane below $\rm M\sb{e},$ was measured. The search for characteristic relaxation patterns resulted in a simple model which describes these patterns in a quantitative way with a minimum number of parameters. Both systems exhibit similar relaxation behavior in the terminal zone which changes dramatically during the crosslinking process. This pattern is represented by a modified Chambon-Winter gel spectrum with a relaxation exponent, n, which decreases with increasing degree of crosslinking. This spectrum is cut off at the longest relaxation time of the partially crosslinked polymer, $\rm\lambda\sb{max}.$ The entanglement and glass transition regions of the polybutadiene system are represented by the BSW spectrum. The entanglement and glass transition regions of the precursor polymer are less affected than the terminal relaxation by the gelation process, only the slope of the entanglement power law decreases due to polydispersity effects. The model parameters $\rm\lambda\sb{max}$ and G$\rm\sb{e}$ (equilibrium modulus) exhibit characteristic scaling behavior with respect to the distance from the gel point, $\rm\vert p-p\sb{c}\vert.$ A box-like contribution H$\sb{\infty}$ to the spectrum appears for samples beyond the gel point. The proposed model passes the self-consistency test by predicting the mechanical behavior (at different frequencies) as a function of the extent of reaction and other rheological observations during the sol-gel transition. The effect of large deformation flow on the crosslinking material was investigated. The samples were macroscopically destroyed at high shear rates and stresses which prevented the detection of any influence the flow might have on the gel time. No influence could be detected at smaller deformations or lower stress levels. Finally, the effect of changes in molecular weight distribution on time-resolved rheometry were studied for several different architectures. For the case of crosslinking polybutadiene, a critical mutation number of approximately 0.2 was found beyond which the experiment results in unreliable data.

In designing a reactor system to produce a resin, the limits of feasible molecular weights and conversions provide targets and alternatives for the design and a rapid assessment of feasibility. To find the feasibility limits for polymers a geometric method called the attainable region has been developed in terms of quantities which can be specified during production: moments of the molecular weight distribution for homopolymers and average compositions for copolymers. These quantities can be related to properties and calculated in simulations. However, the key is to find the limits of these quantities without fully specifying the reactor system. From the attainable regions for free-radical polymerizations, maximum and minimum molecular weights and the reactor systems corresponding to these limits have been determined. In particular, it is found that isothermal polymerizations can produce molecular weights an order of magnitude greater than adiabatic systems. The highest molecular weights are substantially above those typically produced, and so products with different properties than those currently made may be possible. From the feasibility limits it was determined that the highest molecular weights are produced in an isothermal continuous stirred tank reactor, and when only adiabatic reactors are considered the maximum molecular weight is produced in a plug-flow reactor. These extremes of perfect backmixing and plug-flow arise because the type of mixing which produces the highest molecular weight depends on whether molecular weight increases or decreases with conversion. For copolymers, the attainable region shows the limiting reactor systems and feasible average compositions. The results show that through a simpler method one can find the feasible copolymer compositions. These limiting compositions are bounded by the feed composition and the product of a plug-flow (or batch) reactor. Along with the attainable regions of molecular weights and copolymer compositions, other dependent variables can be determined and developed into "corresponding regions." These regions show in two dimensions the limits for dependent variables when finding the feasibility limits of an attainable region. In the case of homopolymers, corresponding regions show the polydispersities, initiator concentrations, and residence times for the associated attainable molecular weights. For copolymers the corresponding regions show the conversions, molecular weights, and residence times for attainable copolymer compositions. These regions can be used to find alternatives for reactor system designs. Thus, with these methods, one can find the feasible products, target reactor systems for achieving the limiting products, and generate alternatives for reactor systems that meet product specifications.

The effect of flexibility and branching on the rheology of wormlike polymers in different concentration regimes was investigated. The goal was to understand flexibility's role in the aggregation behavior and dynamics of wormlike star polymers in isotropic solutions as well as how flexibility controls phase behavior and the response of shear-induced structures in nematics. Two shear response modes were detected for semidilute solutions of 3-arm star PHIC. The fast mode is attributed to the alignment of free chains, with the degree of alignment increasing with molecular weight. Unusually, no linear regime was observed for the lowest molecular weight sample (M W = 44,000), with the fast mode birefringence response scaling as [special characters omitted]. This scaling exponent approaches unity with increasing molecular weight. The slow mode response diminished with molecular weight. Static and dynamic light scattering at and below c*, suggests this mode is due to aggregates of size decreasing with molecular weight. This is inconsistent with aggregation caused by solvent quality. For a particular sample, the aggregate radius of gyration appears independent of concentration, though the aggregate number and hence degree of scattering does increase with concentration. It is possible that van der Waals type interactions cause this aggregation and that these forces are increasingly inhibited as the star arms become less rodlike. The role of molecular weight and hence flexibility in shear induced structure transitions, such as striations during shear startup and banding during relaxation, was probed through small angle light scattering. Striations during shear startup and banding during relaxation are found to occur only above a molecular weight independent critical characteristic shear rate, [special characters omitted] above which elastic forces are able to overcome viscous forces which tend to inhibit these structure transitions. τs, the characteristic texture relaxation time for banding, is molecular weight dependent. They were not seen for the lowest molecular weight (where the flexibility, L/α ∼ 1.3) since a minimum flexibility (and hence chain elasticity) is needed for these texture changes to occur. From τs, the minimum molecular weight for these shear induced complex texture transitions is estimated as 27,000 (L/α ∼ 2.1) for 37 wt% poly(n-hexyl isocyanate) in 1,1,2,2-tetrachloroethane. The strain dependence of the structure transitions during shear startup and the preshear rate dependence of the banding phenomenon are thought to be functions of the persistence length of the polymer chains rather than flexibility since they show no molecular weight dependence. The characteristic lengthscale for banding does decrease with molecular weight. Increasing molecular weight and hence flexibility also lowers the decay rate of the bands since the rotational and translational cooperative diffusivities are lower.

The properties of a product made of semi-crystalline polymers strongly depend on both molecular parameters and on the processing conditions applied. This dissertation is focused on flow-induced structure formation correlating the material and crystallization time scales with the structure development in isotactic polypropylene (iPP) after a temperature quench. Morphological changes during the quiescent (no flow prior to crystallization) and shear-induced (with flow prior to crystallization) isothermal crystallization have been monitored with optical microscopy, light scattering and rheology. The experiments have the purpose to identify the effects of shear rate, total strain, molar mass and high molecular weight fraction on the crystallization of iPP. Dimensionless quantities are introduced to correlate the characteristic time scales with structure development; namely, the Weissenberg number ( We), consisting of the product of the applied shear rate and a material characteristic relaxation time ([special characters omitted]) is introduced to demonstrate the transition from spherulitic to oriented structure. A dimensionless characteristic crystallization time scale (τ), defined as the ratio of the experimental time and a characteristic crystallization time, and allows for comparison of crystallization patterns of samples with different molecular specifications (molecular weight, molecular weight distribution) and at different thermo-mechanical conditions. Wide-angle X-ray diffraction (WAXD) and differential scanning calorimetry (DSC) show the characteristics of the crystalline populations present in the cooled samples after completion of crystallization.

An experimental reaction polymerization facility was built to study polymerization kinetics using metallocene catalysts and it is described in detail. It has been used to evaluate the performance of methylaluminoxane (MAO)-activated metallocene catalysts in slurry-mode propylene homopolymerization. Experiments using two relatively low activity C2 symmetric catalytic species, rac-ethylenebis(1-indenyl)zirconium dichloride (I) and rac-ethylenebis(4,7-dimethyl-1-indenyl)zirconium dichloride (II) were performed at different process conditions where polymerization kinetics are the rate limiting step. The rates of propylene reaction in a factorial set of experiments at different levels of monomer pressure and reaction temperatures were measured. Mass transfer coefficients for transport of propylene gas into the liquid solvent were calculated at different polymer solid contents in the liquid phase. A chemical mechanism for the homopolymerization of propylene by metallocene catalysts was proposed, and a model formed by a series of population balances was created. Kinetic parameters for polymer chain initiation, deactivation, and propagation were found through non-linear regression methods based on the instantaneous rate of reaction. The method of moments was used to determine estimated number and weight average degrees of polymerization for the polypropylenes produced, based on experimental values from high temperature Gel Permeation Chromatography. Characterization of the final product by 1H Nuclear Magnetic Resonance revealed the nature of the various polymer end-groups. These end-groups assisted in determining the modes of chain termination, and confirmed the feasibility of the proposed chemical mechanism. The dominant end-group in I/MAO based polypropylene was found to be vinylidene, whereas 2- cis-butenyl was for II/MAO. This fact suggested different termination patterns for both systems. Measurement of the initial concentration of the cationic active complexes was identified as an important factor in the determination of kinetic parameters of the model. A method for their estimation is proposed.

Computational quantum chemistry was used as a tool to predict needed thermochemistry and kinetics for two classes of problems: formation and destruction of NOx pollutants and development of new fire-resistant polymers. Of the latter, polycarbodiimides and polyhydroxyamides (PHA's) were studied. Different methods were used: HF/6-31 G(d), BAC-MP4 (bond-additivity corrections to UMP4 energies and HF vibrational frequencies), PM3 semi-empirical, and combinations. On the NOx problem, work focused on using theory to generate improved kinetics in H2/O2/NOx combustion. The results were a set of thermochemical data and highpressure-limit kinetics for NOx formation and destruction. Hartree-Fock structures and frequencies and fourth-order Moeller-Plesset energies were used for reactions of H/N/O-species involving H1N1O1 , N1O2, N2O1, H1N 2O1, and N2O2 surfaces, including NH + NO ↔ N2O + H, N2O + O ↔ NO + NO, N + OH ↔ NO + H, N + O2 ↔ NO + O, and N + NO ↔ N2 + O. Thermochemical results were discussed in the form of potential energy surfaces. In general, BAC-MP4 heats of formation compared consistently well to literature data. The results generated from this work allowed evaluation of pressure-dependent kinetics and, ultimately, a refined group of reactions for the NOx mechanism. Strengths of particular bonds and bonding combinations in polycarbodiimides were calculated. Work focused on effects of R groups, chain size and stereoregularity on bond dissociation energies (BDE). Specifically, five polycarbodiimide systems were studied: (1) R=R′=H, (2) R=R′ =CH3, (3) R=R′=CH2CH 3, (4) R=CH(CH3)(Phenyl), R′=H, and (5) R=CH(CH3)(phenyl), R′=CH 3. Methyl- and ethyl-substituted polycarbodiimides decreased the bond strength of the central C-N bond. Ligands on the amine (backbone) nitrogen weakened its chain C-N bond dramatically. However, a lower barrier reaction has also been identified. Results imply rapid, concerted unzipping of this polymer, a result consistent with experiment. For the polyhydroxyamide (PHA) system, a model cyclization reaction of PHA to polybenzoxazole (PBO) was evaluated. PHA cyclization to PBO has been studied experimentally, but a detailed theoretical reaction surface has never been evaluated. Moreover, a plausible mechanism by which PHA arrives at PBO had not been previously determined. The calculated overall heat of reaction was thermoneutral, and decomposition was determined to occur at 212°C, compared to the 215°C experimental value. The hydrogen-transfer reaction and a four-center concerted transition-state reaction were found to be the limiting steps.

We have developed a modular rheo-optical apparatus to study the flow properties of liquid crystals. Its main components are shearing device, strong magnetic field, and optical microscope. We performed experiments on well defined initial morphologies with uniform molecular alignment. The monodomains were achieved with strong magnetic fields (4.7T). Time resolved conoscopy is the primary optical technique in our investigation. We propose a simple relation between the distribution of alignment angles over the sample thickness and the conoscopically measured angle, to quantitatively measure the alignment angle in shear flow. We followed the relaxation of a shear induced splay deformation in small molecule model systems (N-(p-methoxybenzylidene)-p-butyl aniline (MBBA), pentyl-cyano-biphenyl (5CB) and a commercially available mixture OMI4244, and devised a model, based on the diffusion equation, to determine the rotational diffusivity from the relaxation process. The director alignment behavior of the SMLC's in shear flow is well described by the two dimensional Leslie-Ericksen model. The effect of director elasticity can clearly be seen in our experiments, resulting in a decrease of the steady state alignment angle at smaller Ericksen numbers. We found that there is no strain rate dependence of the director vorticity from 0.002/s to 2/s for poly-($\gamma$-benzyl-D/L-glutamate) (PBG). We determined ${\alpha\sb2/\alpha\sb3}$ = 44 for a 20% solution of 280.000 molecular weight PBG in m-cresol at 20$\sp\circ$C. The conoscopic interference pattern vanished after 8 strain units from an initially planar alignment and shearing could be reversed up to 10 strain units to completely recover the initial monodomain. Liquid crystalline polymers (LCP) are known to arrange into periodic director patterns during flow. We studied this for shear flow of lyotropic poly $\gamma$-(benzyl-glutamate) as a model system, which is a well characterized synthetic poly ($\alpha$ amino acid) with rigid chain architecture and well defined conformations. The molecules were are aligned uniformly as the starting condition. This so called monodomain morphology was obtained by use of strong magnetic fields. The shear apparatus is placed in an optical microscope, which is set up for conoscopy to allow direct observation of the shear induced rotation of the molecules. After a small strain during which the molecules rotate around the vorticity axis, they 'break out' sideways and form a three dimensional spatially periodic pattern. The shear induced instabilities have been observed under crossed polars as spatially periodic patterns (bands), some researchers observing them during flow and and others after cessation of shearing$\sp{(27, 42, 58, 59)}$. Bands, which develop during shear flow of poly (benzyl glutamate) (PBG) have been reported in 1980$\sp{(36)}$. However, later workers have failed to reproduce their findings and periodic pattern are believed to occur only after cessation of flow. Our findings solve a long standing controversy in the literature about the formation of periodic director pattern during flow. By varying the initial molecular orientation with respect to the flow direction we could show that the periodic pattern does not depend on the shear direction; it is governed by the director of the initial monodomain.