Dwell time and average dwell time methods based on the cycle ratio of the switching graph

A new method to find an upper bound on dwell time and average dwell time for switched linear systems is proposed. The method is based on computing the maximum cycle ratio and the maximum cycle mean of the directed graph that governs switchings. For planar switched systems, an upper bound for dwell time and average dwell time can be estimated by considering only the cycles of length two.     

HYDRODYNAMIC STUDIES IN A HALF SLOT-RECTANGULAR SPOUTED BED COLUMN

Experiments were carried out in a half slot-rectangular spouted bed to investigate the effects of slot width and lower section basal angle on column hydrodynamics. Flow regimes, minimum spouting velocity, spouting and maximum pressure drops, and maximum spoutable bed height were determined for 4?mm diameter polyethylene particles. The results are compared with those for conventional cylindrical and rectangular spouted beds. Correlations for each hydrodynamic parameter are developed and compared with equations available in the literature.     

Temperature effect on the swelling of PAAm‐κ‐carrageenan composites

The steady‐state fluorescence (SSF) technique was used for studying swelling of disc‐shaped polyacrylamide (PAAm)‐κ‐carrageenan (κC) composites which were prepared by free‐radical crosslinking copolymerization at 80°C. Pyranine was introduced as a fluorescence probe during polymerization. Swelling experiments were performed in water at various temperatures by real‐time monitoring of the pyranine (Py) fluorescence intensity, I which decreased as swelling proceeded. Stern–Volmer equation is modified for low quenching efficiencies to interpret the behavior of Py intensity during the swelling of PAAm‐κC composites. The Li‐Tanaka equation was used to determine the swelling time constants, τ₁, and cooperative diffusion coefficients, D₀, from fluorescence intensity, weight, and volume variations of the composites at various temperatures. It was observed that τ₁ first decreased up to 40°C and then increased; naturally, D₀ increased up to 40°C and then decrease for all κC content gels. Swelling activation energies, ΔE, were measured for the swelling composites, which are found to be exothermic and endothermic in between 30–40 and 40–60°C, respectively. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Film formation of poly (methyl methacrylate) latex with pyrene functional poly (divinylbenzene) microspheres prepared by click chemistry

This work reports on the application of steady state fluorescence (SSF) technique for studying film formation from poly(methyl methacrylate) (PMMA) latex and poly(divinylbenzene) (PDVB) microsphere composites. Pyrene (P) functionalized PDVB cross‐linked spherical microspheres with diameters of 2.5 μm were synthesized by using precipitation polymerization technique followed by click coupling reaction. The diameter of the PMMA particles prepared by emulsion polymerization were in the range of 0.5–0.7 μm. PMMA/PDVB composite films were then prepared by physically blending of PMMA latex with PDVB microspheres at various composition (0, 1, 3, 5, 10, 20, 40, and 60 wt%). After drying, films were annealed at elevated temperatures above T_g of PMMA ranging from 100 to 270°C for 10 min time intervals. Evolution of transparency of the composite films was monitored by using photon transmission intensity, I_tr. Monomer (I_P) and excimer (I_E) fluorescence intensities from P were measured after each annealing step. The possibility of using the excimer‐to‐monomer intensity ratio (I_E/I_P) from PDVB microparticles as a measure of PMMA latex coalescence was demonstrated. Diffusion of the PMMA chains across the particle–particle interfaces dilutes the dyes, increasing their separation. The film formation stages of PMMA latexes were modeled by monitoring the I_E/I_P ratios and related activation energies were determined. There was no observable change in activation energies confirming that film formation behavior is not affected by varying the PDVB composition in the studied range. SEM images of PMMA/PDVB composites confirmed that the PMMA particles undergo complete coalescence forming a continuous phase in where PDVB microspheres are dispersed. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

Temperature dependence of oxygen diffusion into clay‐doped PS films

Fluorescence technique was employed for the measurement of the diffusion coefficient of oxygen into polystyrene (PS) latex/modified Na‐activated bentonite (MNaLB) clay composite films. Three different MNaLB content (0, 5, and 20 wt%) composite films were prepared from PS/MNaLB mixtures by annealing them at 200°C, above the glass transition temperature of PS for 10 min. To determine the diffusivity of oxygen in PS/MNaLB composite films, diffusion measurements were performed over the temperature range from 25 to 70°C. Pyrene (P) was used as the fluorescent agent. The diffusion coefficients (D) of oxygen were determined by combining the fluorescence quenching method with Fickian transport model, and were found as a function of temperature for each MNaLB content film. The results showed that D values are strongly dependent on both temperature and clay content in composite film. It was also observed that D coefficients obey Arrhenius behavior, from where diffusion activation energies were measured. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers     

Particle size effect on the film‐forming process of PS/PBA composite latexes

In this work, the effect of hard particle size and blend ratio on the film formation behavior of hard polystyrene (PS) and soft poly(n‐butyl acrylate) (PBA) latex blends was studied by means of steady‐state fluorescence and UV–visible techniques in conjunction with atomic force microscopy. Three different sets of latexes were synthesized: PBA latex (diameter 97 nm), pyrene (P)‐labeled large PS (LgPS; diameter 900 nm), and small PS (SmPS; diameter 320 nm). Two different series of latex blends (LgPS/PBA and SmPS/PBA) were prepared with varying blend composition at room temperature separately. Films were then annealed at elevated temperatures above glass transition (T_g) temperature of PS. Fluorescence intensity (I_P) from P and photon transmission intensity (I_tr) were measured after each annealing step to monitor the stages of film formation. The results showed that a significant change occurred in I_P and I_tr at a certain critical weight fraction (R_c) of PBA. Below R_c, two distinct film formation stages, which are named as void closure and interdiffusion, were seen. However, at PBA concentrations nearer to or above R_c, no film formation can be achieved. Comparing to the LgPS/PBA, the sintering process of SmPS/PBA particles occurred at much lower temperatures. Film formation stages for R < R_c were modeled, and related activation energies were calculated. Void closure (ΔH) and interdiffusion (ΔE) activation energies for SmPS/PBA were also found smaller in comparing with LgPS/PBA series. However, ΔH and ΔE values were not changed much with the blend composition for both series. POLYM. COMPOS., 31:1637–1652, 2010. © 2009 Society of Plastics Engineers     

Film formation of nano‐sized hard latex (PS) in soft polymer matrix (PBA): An excimer study

This work reports steady state fluorescence (SSF) technique for studying film formation from pyrene (P)‐labeled nano‐sized polystyrene (PS) and poly(n‐butyl acrylate) (PBA) hard/soft latex blends. Blend films were prepared from mixtures of PS and PBA in dispersion. Eight different blend films were prepared in various hard/soft latex compositions at room temperature and annealed at elevated temperatures above glass transition temperature (T_g) of polystyerene. Monomer (I_P) and excimer (I_E) intensities from P was measured after each annealing step to monitor the stages of film formation. The evolution of transparency of latex films was monitored using photon transmission intensity, I_tr. Film morphologies were examined by atomic force microscopy (AFM). The results showed that as the amount of hard component (PS) in the blend is decreased, a significant change occurred in both I_E/I_P and I_tr curves at a certain critical weight fraction (50 wt%) of PS hard latex. Two distinct film formation stages, which are named as void closure and interdiffusion were seen in (I_E/I_P) data above this fraction. However, below 50 wt% PS no film formation was observed. AFM pictures also confirmed these findings. Void closure and interdiffusion stages for (50–100) wt% range of PS were modeled and related activation energies were determined. There was no observable change in activation energies confirming that film formation behavior is not affected by varying the blend composition in this range. POLYM. COMPOS., 31:1611–1619, 2010. © 2009 Society of Plastics Engineers     

Drying of heterogeneous hydrogels formed with various water contents: A photon transmission study

Drying of acrylamide (AAm) gels was monitored by using a photon transmission technique. These hydrogels are formed from AAm and N,N′‐methylenebis(acrylamide) (Bis) with various water contents by the free‐radical crosslinking copolymerization (FCC). The transmitted light intensity, I_tr, increased continuously as AAm gels were dried. The increase in I_tr was attributed to the decrease in the scattered light intensity, I_sc, which might be originated from the contrast between frozen blob clusters and holes in the drying gel. A decrease in I_sc was modeled by using Rayleigh's equation where drying times with various exponents were found to be proportional to the size of the holes. It was observed that the radius of holes, ξ_c, decreased in various powers of the drying time depending on water content used during FCC. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1944–1951, 2001     

Swelling of heterogels in good solvents; a fast transient fluorescence study

The swelling of disc-shaped heterogels were studied using Fast Transient Fluorescence Technique (FTRF). Disc-shaped heterogels were prepared by combination of methyl-methacrylate (MMA) and styrene (S) with ethylene glycol dimethacrylate (EGDM) as a crosslinker agent in the presence of 2,2′-azobisisobutyronitrile (AIBN). Pyrene (P_y) was introduced as an extrinsic floroprobe during polymerisation. Lifetimes of P_y were measured during in situ swelling processes of heterogels in good solvents to determine the relation between the diffusion and solvent quality. An equation is derived for low-quenching efficiencies to interpret the behavior of lifetime of P_y during swelling. Li-Tanaka equation was employed to determine the cooperative diffusion coefficients, D_c in heterogels, which were found to be strongly correlated with the chosen solvent and the polymeric material in the heterogel system.     

Silicon and Chlorine Substituted Unsaturated Polymers: ROMP of (bicyclo[2,2,1]hept-5-en-2-yl)ethylchlorodimethylsilane via Mo-based catalyst

Ring opening metathesis polymerization (ROMP) of a norbornene derivative that contains silicon and chlorine, (bicyclo[2,2,1]hept-5-en-2-yl)ethylchlorodimethylsilane, by using electrochemically produced active catalyst species (MoCl₅–e⁻–Al–CH₂Cl₂) was investigated. Silicon and chlorine containing unsaturated polymer was characterized by ¹H, ¹³C, and ²⁹Si-NMR and FTIR spectroscopy. The thermal behavior of the polymer was determined by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA).