An experimental study on on-line optimizing control of free radical bulk polymerization in a rheometer-reactor assembly under conditions of power failure

An experimental study on the on-line optimizing control of a sample free radical bulk polymerization system, namely, methyl methacrylate (MMA), is carried out in a rheometer-reactor assembly. Two initiator loadings and three cases involving external disturbances (power failure) are studied. The disturbances are assumed to be of two kinds: one that leads to a sudden increase in the temperature of the reaction mass (cooling water pump failure) over the planned temperature history, T(t), and one leading to a sudden drop in the temperature (heater failure). The temperature and the viscosity, η, histories are used to describe the ‘state’ (conversion, x_m, and weight-average molecular weight, M_w) of the polymerizing mass. The polymerization is first carried out under an off-line computed optimal temperature history, T_op(t), obtained using the adapted jumping gene version of the elitist genetic algorithm (GA-II-aJG). A planned disturbance is introduced after the start of polymerization and continues for a pre-specified duration. A new optimal temperature history, T_reop(t), is calculated on-line (in about 3 min of real time) using GA-II-aJG. This is implemented as soon as the disturbance is rectified. Experimental values of x_m(t), M_w(t) and η(t) are also measured. These are observed to be in good agreement with model predictions for all the cases. It is found that the information on the viscosity of the reaction mass can be used effectively for on-line optimizing control. This can help ‘save’ the batch (give a product having the desired values of the average molecular weights) optimally, in as short a reaction time as possible. The effect of re-tuning of the model parameters using experimental data on the temperature, T_exp(t), and the viscosity, η(t), is also demonstrated.     

Food treatment with high pressure carbon dioxide: Saccharomyces cerevisiae inactivation kinetics expressed as a function of CO2 solubility

Experimental survival curves of Saccharomyces cerevisiae cells exposed to high pressure carbon dioxide (HPCD) treatments under several constant temperatures (35, 40 and 50 °C), pressures (7.5, 10.0 and 13.0 MPa) and suspended in distilled water with different sodium phosphate monobasic buffer concentrations (0.02, 0.10, 0.20 and 0.40 M) were obtained. The Peleg model was applied to the isobaric and isothermal conditions described by the power law equation log[S(t)] = −btⁿ, where S(t) is the momentary survival ratio and ‘b’ and ‘n’ are the rate and the shape parameters, respectively. The values of the coefficients ‘b’ and ‘n’ were calculated for each experiment at fixed pressure and temperature. For each suspending medium the power law model was proposed to describe the combined effects of pressure and temperature. Taking into account the CO₂ solubility as a function of the sodium phosphate monobasic concentration, ‘b’ and ‘n’ were correlated to the CO₂ solubility values and temperature. An equation was proposed for ‘b’ as a function of CO₂ solubility and temperature while ‘n’ was a weak function of temperature. The resulting equation was much simpler that the one obtained correlating the microbial inactivation to pressure and temperature and, more important, it was independent of the suspending medium. The results indicate that the coupling of carbon dioxide solubility, also predicted with commercial software, and the use of inactivation models referred to solubility and temperature may provide a powerful instrument for the interpretation of microbial inactivation experiments and for the design of HPCD processes and equipments.     

Modelling the post treatment process of model implants prepared by in situ polymerized poly(ε-caprolactone) using a BF3-glycerol catalyst system

The post treatment process of a poly(ε-caprolactone) (PCL) model implant prepared using a boron trifluoride (BF₃) catalyst and glycerol initiator by in situ polymerisation process for craniofacial and maxillofacial treatment is modelled using a ‘moving-boundary’ diffusion model. A numerical method was used to solve a system of diffusion equations of the model. The variable diffusion coefficient (D) was correlated with crystallinity (x_c) of the polymer which is a function of its molecular weight (M_w) and its degradation rate constant (k_d), D=f(x_c(M_w,k_d)). The post treatment time and the molecular weight retained after post treatment can be obtained using this model. The modelling results show that the process is potentially suitable for manufacturing thin model implants of complex shape.     

Unique morphology and properties study of polyacrylate obtained via frontal photopolymerization

Remarkable radial temperature distribution at the advancing reaction front was determined in frontal photopolymerization (FPP). Through SEM observation of the cross-fracture section and vertical fracture section for the heat-insulated FPP polymer rod, a cylindrical multi-layer structure was first observed in the FPP product. A sleeve-like model was proposed to describe the unusual morphology on the basis of polymer self-drawing and convection around reaction front. Vertical gradient distribution of molecular weight and its polydispersity in the poly(isobornyl acrylate) rod obtained via FPP was found through GPC determination, which might be developed as an in situ self-fractionation technique for polymer. Thermal analysis of the polymers showed that the FPP tended to produce purer polymer than the traditional thick film photopolymerization.     

Supercooling (ΔT) dependence of nano-nucleation of PE by SAXS and proposal of a new nucleation theory

Degree of supercooling (ΔT) dependence of nano-nucleation was studied by means of small angle X-ray scattering (SAXS) and a new nucleation theory was proposed. We obtained the ΔT dependence of size distribution f(N,t) directly, where N is number of particle and t is time, which concluded that the “induction period” of crystallization is not controlled by so called “spinodal decomposition” but by nucleation one. It clarified that the critical nano-nucleation mainly controls not only the steady nano-nucleation but also macro-crystallization experimentally as the zero-th approximation by using the newly obtained ΔT dependence of f(N,t) and nucleation rate (I) of macroscopic crystal obtained by means of optical microscope (OM). Time evolution of total free energy of nucleation of a huge closed system δG(t) was obtained experimentally for the first time, which clearly confirmed that nano-nucleation is the process where δG(t) passes through an activation barrier and reaches the most stable state by completion of melt-solid (crystal) phase transition due to well known “Ostwald ripening”. We proposed a new nucleation theory by introducing a “mass distribution function Q(N,t) ∝ Nf(N,t)”. We proposed a new basic equation of the mass conservation law, ∂Q(N,t)/∂t=−∂j(N,t)/∂N, where j(N,t) is net flow. This solved the serious problem in classical nucleation theory (CNT), where so called “fundamental kinetic equation” does not satisfy the mass conservation law. The coupling of our “real image” and correct theory will enable us to realize the ultimate structure and physical properties of materials, which should be a very interesting “fruit”.     

Long-range forces between C nanotubes and between C cages: Some polarizability bounds and scaling approximations yielding interaction energies at intermediate separations

Recent work of Schröder and Hyldgaard leads us to propose for the interaction energy per unit length ?(d, R) between two parallel C nanotubes of equal radii R at distance d, the approximate scaling property ?(d, R) = f(R)d⁻⁵I(R/d) where I is known. The function f(R) is expected to be model dependent. Contact is then made with the classic study of Girifalco et al. In addition, some results are presented for interaction energy between ‘almost spherical’ C cages. Specifically considered are (i) the HOMO-LUMO gap and (ii) bounds on polarizabilities.     

Size distribution and shape of nano-nucleus of polyethylene simultaneously determined by SAXS

Nucleation mechanism of polymers was studied by means of small angle X-ray scattering (SAXS) by improving our two previous studies. The first one showed first direct SAXS observation of nucleation of polyethylene (PE). The second one reported how “size distribution f(N,t)” of nuclei of nano-meter size (nano-nuclei) evolves with time (t), where N is number of “repeating unit” in a nucleus. Unfortunately the f(N,t) was obtained by incorrect analysis of SAXS intensity (I_X), i.e., too simple one-dimensional (1D) nucleus was assumed to analyze the I_X. In this paper, we determined simultaneously correct f(N,t) and “two-dimensional (2D) shape” of nano-nucleus. From this it is clarified that nano-nucleus shows significant fluctuation in size and shape and repeats frequent generation and disappearance, which corresponds to the conclusion that the end surface free energy of the nano-nucleus (σ_e(nano)) is 1/5 times as large as that of macroscopic crystal (σ_e(macro)). f(N,t) decreased with increase of N. f(N,t) increased and saturated with increase of t.     

Solids flow pattern in gas-flowing solids-fixed bed contactors. Part II: Mathematical modeling

In this paper a mathematical model for solids flow in gas-flowing solids-fixed bed contactors is developed. The presented four-parameter model assumes plug flow with axial dispersion in the dynamic, fast moving solids zone and the exchange of particles from this zone with the static zones. The complex dynamic behavior of the ‘static’ particles is described with a model of exchange between the dynamic and three static zones: (a) the ‘fast’ exchanging, (b) the ‘slow’ exchanging and (c) the ‘dead’ zone.The model parameters are optimized on the basis of two different tracer experiments: the step change response at the outlet—x_dyn, and the static holdup response—x_st. The model was tested for seven experimental series which correspond to different operating conditions (e.g., different superficial gas velocity and solids mass flux).The influence of the operating conditions on the model parameters is presented and discussed. Model reduction was also implemented in order to analyze the model simplifications and alternatives. Model sensitivity analysis was performed as well.     

Multiscale micromechanical modeling of polymer/clay nanocomposites and the effective clay particle

Polymer/clay nanocomposites have been observed to exhibit enhanced mechanical properties at low weight fractions (W_c) of clay. Continuum-based composite modeling reveals that the enhanced properties are strongly dependent on particular features of the second-phase ‘particles’; in particular, the particle volume fraction (f_p), the particle aspect ratio (L/t), and the ratio of particle mechanical properties to those of the matrix. These important aspects of as-processed nanoclay composites require consistent and accurate definition. A multiscale modeling strategy is employed to account for the hierarchical morphology of the nanocomposite: at a lengthscale of thousands of microns, the structure is one of high aspect ratio particles within a matrix; at the lengthscale of microns, the clay particle structure is either (a) exfoliated clay sheets of nanometer level thickness or (b) stacks of parallel clay sheets separated from one another by interlayer galleries of nanometer level height, and the matrix, if semi-crystalline, consists of fine lamella, oriented with respect to the polymer/nanoclay interfaces. Here, quantitative structural parameters extracted from XRD patterns and TEM micrographs (the number of silicate sheets in a clay stack, N, and the silicate sheet layer spacing, d₍₀₀₁₎) are used to determine geometric features of the as-processed clay ‘particles’, including L/t and the ratio of f_p to W_c. These geometric features, together with estimates of silica lamina stiffness obtained from molecular dynamics simulations, provide a basis for modeling effective mechanical properties of the clay particle. In the case of the semi-crystalline matrices (e.g. nylon 6), the transcrystallization behavior induced by the nanoclay is taken into account by modeling a layer of matrix surrounding the particle to be highly textured and therefore mechanically anisotropic. Micromechanical models (numerical as well as analytical) based on the ‘effective clay particle’ were employed to calculate the overall elastic modulus of the amorphous and semi-crystalline polymer-clay nanocomposites and to compute their dependence on the matrix and clay properties as well as internal clay structural parameters. The proposed modeling technique captures the strong modulus enhancements observed in elastomer/clay nanocomposites as compared with the moderate enhancements observed in glassy and semi-crystalline polymer/clay nanocomposites. For the case where the matrix is semi-crystalline, the proposed approach captures the effect of transcrystallized matrix layers in terms of composite modulus enhancement, however, this effect is found to be surprisingly minor in comparison with the ‘composite’-level effects of stiff particles in a matrix. The elastic moduli for MXD6-clay and nylon 6-clay nanocomposites predicted by the micromechanical models are in excellent agreement with experimental data. When the nanocomposite experiences a morphological transition from intercalated to completely exfoliated, only a moderate increase in the overall composite modulus, as opposed to the expected abrupt jump, was predicted.     

Temperature dependence of piezoelectric properties on Nd and V co-substituted Bi4Ti3O12 ceramics for ceramic resonator applications

The temperature dependences of the piezoelectric properties of (Bi_4−yNd_y)_1−(x/12)(Ti_3−xV_x)O₁₂ [BNTV-x, y (x = 0.01, y = 0.00–1.00)] were investigated for environmentally friendly lead-free piezoelectric ceramic resonators with low-temperature coefficients of resonance frequency, TC-f. The |TC-f| in the (33) mode improved with increasing concentration of modified Nd ions, y, and exhibited the smallest |TC-f| value of 77.4 ppm/°C at y = 0.75 (BNTV-0.75). The |TC-f| in the other vibration mode (t), was also investigated for the BNTV-0.75 ceramic, and a smaller value of 42 ppm/°C was obtained. The (t) mode of the BNTV-0.75 ceramic showed excellent piezoelectric properties: Q_m = 4200, Q_e max = 31 and TC-f = −49.8 ppm/°C. These properties are very similar to those of commercialized hard PZT ceramics for resonator applications. The BNTV-0.75 ceramic seems to be a superior candidate material for lead-free piezoelectric applications of ceramic resonators.     

Supramolecular complexes: lamellar structure and crystalline transformation

Interfacial reaction of highly-branched polyethyleneimine (PEI) with octadecanoic acid (OA) was performed to prepare a series of supramolecular complexes (PEI(OA)_x). The complexes at solid state have typical lamellar structure, and the interlamellar distance can be modulated by the OA content. The long period values of the supramolecular complexes measured by SAXS were found to be dependent on the compositions, which are in good consistency with those measured by TEM. For example, the long period values from SAXS for PEI(OA)_0.76, PEI(OA)_1.03, and PEI(OA)_1.67 were 46.5, 62.7, and 56.2 Å, respectively. The corresponding data from TEM were 45.7, 60.7, and 56.6 Å, respectively. A model was proposed for the construction mode of the side alkyl chains (crystallization region) associated with PEI backbone (amorphous region), in which the side alkyl chains were arranged to be ‘end-to-end’ packing for the x=1 complex, while an ‘interdigitated structure’ of the side alkyl chains was deduced for the x>1 and x<1 complexes. Temperature variable FT-IR combination investigation of the scissoring band, rocking band, and stretching band of methylene (CH₂) and vibrational band of carbonyl group (CO) indicated that the crystalline form of the crystallization region in the lamellae can be transformed from orthorhombic to hexagonal with the temperature increasing, and vice versa.     

Characterization of polydimethylsiloxane elastomer degradation via cross-linker hydrolysis

Degradation kinetics based on rheological studies are reported for endlinked silane terminated polydimethylsiloxane (PDMS) networks cross-linked with 2,4,6-triallyloxy-1,3,5-triazine as a function of cross-link density and the relative humidity to which the network is exposed. These unique PDMS networks cure in the absence of water but degrade under humid conditions due to cross-linker hydrolysis. Rheological measurements show an exponential decay of the storage modulus (G′) with time under conditions of high humidity (greater than 45%) and a linear decay under conditions of low humidity (lower than 22%). Optical studies show that at high humidity two domains exist wherein a domain of degraded polymer fluid surrounds a central region of a soft elastomer. However, a uniform degradation with absence of any interface is observed under low humidity conditions. Thus a crossover from ‘surface’ degradation from the edge to ‘bulk’ degradation is observed between 45 and 22% relative humidity. The time to degrade to half the original modulus (t_1/2) ranges from a few hours at high humidity to days at low humidity. At high humidity t_1/2 scales with cross-link density, but it is independent of cross-link density at low humidity. A result that is consistent with ‘surface’ degradation and ‘bulk’ degradation, respectively.     

Acceleration of reaction fronts by hydrodynamic instabilities in immiscible systems

We are studying the propagation of a reaction front in an immiscible liquid-liquid system under the condition of a mass transfer across the interface accompanied by a neutralization reaction. The system, when placed in a vertical Hele-Shaw cell, shows a buoyancy-driven cellular structure penetrating into the aqueous bulk solution. By tilting the Hele-Shaw cell to the horizontal position, the penetrative convection vanishes in favor of a planar reaction front. At higher acid concentrations this reaction-diffusion state is replaced by a Marangoni convection interacting with the front propagation. We show that the scaling behavior of the reaction front position, x_f, with time shows a characteristic crossover. In the long-time limit all systems obey x_f∼t^(0.49±0.02) and differ only in the timespan needed to enter this diffusion-controlled state. For an intermediate time all reaction-diffusion systems display a x_f∼t^(1.50±0.06) law. Both convection types observed in the system operate at Damköhler numbers, Da∼0.1, and lead to an acceleration of the front propagation by at least a factor of four. The influence of the Marangoni convection is even stronger at the beginning due to the higher flow velocities, . However, Marangoni convection rapidly relieves the driving concentration gradients. Therefore, the buoyancy-driven convection wins the competition with respect to the front acceleration for intermediate and long times.     

Chemical composition and tolerance factor at the morphotropic phase boundary in (Bi0.5Na0.5)TiO3-based piezoelectric ceramics

A quantitative relation between the morphotropic phase boundary (MPB) composition and the tolerance factor (t) in (Bi_0.5Na_0.5)TiO₃ (BNT)-based piezoelectric ceramics was established. The t value of the MPB compositions in BNT-based ceramics is around 0.990–0.993 and is independent of the types of added compounds. In order to experimentally demonstrate it, two piezoelectric ceramic systems (1 ? x)(Bi_0.5Na_0.5)TiO₃–x(Ba_1?aSr_a)TiO₃, a = 0.05 and 0.3 (BNBST5-x and BNBST30-x, x < 12%), were used. X-ray diffraction patterns and the lattice parameter investigations revealed that these two systems formed solid solutions within the studied stoichiometry and showed a rhombohedral–tetragonal phase transformation. Furthermore, both the structure analysis and electric properties measurements indicated that the MPB compositions were BNBST5-6 and BNBST30-8 and their corresponding t value were 0.9900 and 0.9903, respectively. The results confirm the relation between the MPB composition and t value and provide a method for designing new piezoelectric materials.     

Rheological characterization of a charged cationic hydrogel network across the gelation boundary

The in situ rheological behavior across the gelation threshold has been investigated for an affine network of a completely charged cationic monomer (3-acrylamidopropyl)-trimethylammonium chloride (APTMAC1) when it is crosslinked with a neutral crosslinker (N,N′-methylenebisacrylamide) to form a fully charged novel cationic hydrogel. The elastic moduli (G′) near the gel point (during the crosslinking or ‘curing’ process) show a power law dependence of the form G′(t)=ε^z, where ε=((t−t_c)/t_c) is the distance from the gel point (t_c). The critical exponent, z, for the hydrogel series investigated is estimated to be 1.5, slightly lower than the predictions based on percolation theory (z∼1.7-1.9). From the equilibrium (after the curing process) rheological measurements of a series of samples, it is inferred that there is a critical crosslinker mole percent (X_c) with respect to the monomer concentration, required to form a well-defined three-dimensional network with a solid-like behavior. The value of this X_c is found to be between 0.5 and 1%. The theoretically predicted value of X_c using the percolation theory (for the percolation of crosslinks, G₀(X)∝[|X−X_c|/X_c]^z) and the exponent estimated from the in situ measurements (z=1.5), is X_c∼0.6, which is in good agreement with the experiments. The results may have applicability in translating from bulk systems to the nanoscale in hydrogel design.     

Later-stage spinodal decomposition in polymer solution under high pressure—analyses of qm and Im

Later-stage spinodal decomposition (SD) of polymer solutions (polypropylene/trichlorofluoromethane) induced by pressure-jump was examined in situ as a function of pressure P by using time-resolved light scattering method with the cell designed for high pressure and high temperature. The time-evolution of the magnitude of scattering vector q_m(t,P) at maximum scattered intensity and the maximum scattered intensity I_m(t,P) were analyzed in order to characterize the coarsening processes of the later-stage SD, where t refers to time after the onset of pressure-jump. The changes in q_m(t,P) and I_m(t,P) with t at different P's were found to fall onto the respective master curves on the reduced plots, indicating that the scaling postulate is valid not only for the coarsening behaviors at different temperatures but for those at different P's.     

Confocal imaging of porosity in hardened concrete

We present the results of an exploratory 3D study of fine pore structures in hardened cement paste. A laser scanning confocal microscope was used in reflected (epi) fluorescent imaging mode, allowing for the very high optical resolution of features well below 1 μm in size. Images of pore structures were captured using a ‘reverse imaging contrast’ technique where spaces in the material were impregnated with a fluorescent, dyed epoxy-resin, and scanned in the x-y plane by a laser probe. A vertical ‘stack’ of these optical sections was acquired by imaging sequentially through the z-axis. Using this technique it was possible to observe, partially hydrated cement grains, porous natural quartz aggregate interfaces, micro-cracking in the hydrated cement paste and aggregate particles, as well as fine capillary pores and very small air voids. Operating at the limit of its capability the microscope was able to perform high resolution imaging of the internal areas of partially reacted cement grains, and pore structures approximately 0.17 μm across were measured. 3D models were produced to help visualise the true morphology and distribution of porous features.     

Enzymatic polymerization of polythiophene by immobilized glucose oxidase

In this study ‘green’, environmentally friendly enzymatic reaction-based synthesis of conducting polymer polythiophene (PTP) is proposed. Glucose oxidase (GO_x) was shown as an effective catalyst, which, in the presence of glucose, produces hydrogen peroxide suitable for the oxidative polymerization of PTP under ambient conditions at neutral pH. Enzymatically induced formation of the PTP layer over GO_x-modified graphite rod electrode (GRE) was demonstrated and evaluated amperometrically and by attenuated total reflectance – Fourier transform infrared (ATR-FTIR) spectroscopy. Surface morphology of GO_x- and PTP-modified GR electrodes was characterized by atomic force microscopy. It was clearly shown that the apparent kinetic Michaelis constant (K_M(app.)) of GO_x/PTP-modified GRE increased by increasing the duration of polymerization reaction. Therefore, enzymatic polymerization could be applied in adjustment and/or tuning of K_M(app.) and other kinetic parameters of GO_x-based electrodes used in biosensor design.     

Properties and structure of (As2Se3)1 − z (SnSe)z − x(GeSe)x and (As2Se3)1 − z (SnSe2)z − x(GeSe2)x glasses

Two valence states of tin atoms in (As₂Se₃)_{1 ? z} (SnSe)_{z ? x}(GeSe)_x and (As₂Se₃)_{1 ? z} (SnSe₂)_{z ? x}(GeSe₂)_x glasses are identified by Mössbauer and photoelectron spectroscopy. It is demonstrated that the presence of doubly charged tin ions in the structural glass network does not give rise to impurity conduction or impurity optical absorption. The inference is made that these glasses can be treated as semiconductor solid solutions.     

Interpretation of dynamic scattering from polymer solutions

The theoretical results available for the interpretation of the dynamic scattering from polymer solutions have been re-examined. The scattering law S(q, t) is formulated using the eigenfunction expansion method and the linear response theory. All previously known exact expressions of S(q, t) for a single unperturbed Gaussian chain have been re-derived using the first method to demonstrate the interrelationships among the various approaches to calculation of S(q, t). The results are cast into new forms which, in many cases, are more convenient for both numerical and analytical discussions. The infinite chain results are obtained from the exact closed expression of S(q, t) for ring polymers as a special case as N → ∞. Questions like the effect of the draining parameter on the shape of S(q, t), the positive definiteness of the diffusion tensor, and the possibility of measuring the eigenvalue of the first internal mode through light scattering, have been included in the discussions.A new method has been proposed for the interpretation of the dynamic scattering experiments in terms of the initial slope, Ω, of In S(q, t). The quantity Ω can also be identified as the first cumulant of S(q, t). The advantage of this method is that $\text{Ω(q)}$ can be calculated for all q values as a function of temperature and concentration by combining the linear response theory and the blob model of chain statistics. Consequently, one is not restricted to the asymptotic small- and intermediate-q regions in order to interpret the scattering experiments. The analytical and numerical results giving $\text{Ω(q)}$ under various conditions have been presented. Using infinite chain results it is shown that Ω acts as a characteristic frequency in the sense that in both the small- and intermediate-q regions, In S(q, t) can be scaled to a q-independent shape function when time is expressed as $\text{Ωt}$. This property facilitates the measurement of Ω from S(q, t)-data using a known shape function. The feasibility of the method has been demonstrated using light scattering data on polystyrene in toluene in the transition region between small- and intermediate q-regions.