Morphological properties of flocs under turbulent break‐up and restructuring processes

Bentonite flocculation was performed in a Taylor–Couette reactor coupled with an in situ method of image acquisition and analysis. A hydrodynamic sequencing is imposed to perform successive cycles of flocculation and breakage. Depending on the shear rate applied during the breakage step, one or two cycles are needed after the first flocculation step to recover a full reversibility on both size and shape factors. The breakup step produces flocculi that are the building blocks for the next. The re‐flocculation steps produce smaller sizes and more regular shapes than the initial growth step. The floc size is calibrated by the turbulence as the radius of gyration is close to the Kolmogorov microscale whereas the floc structure is determined by flocculi aggregates. An analysis of the change of the flocs morphology, despite of their diversity, can also be achieved thanks to some relevant moments of the distributions. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3706–3716, 2017     

Dilute solution properties of randomly branched poly(methyl methacrylate)

Randomly branched poly(methyl methacrylate) samples were prepared by copolymerization with different amounts of ethylene dimethacrylate. The molecular weight distributions, radius of gyration distributions, and intrinsic viscosity distributions were measured by size exclusion chromatography with refractive index, multiangle light-scattering, and viscosity detectors. The effect of branching on the radius of gyration was compared with the effect on the intrinsic viscosity. It was found that the intrinsic viscosity contraction factor gⁱ scales with the radius of gyration contraction factor g, with the exponent, ϵ, having a value in the range 0.8–1.0. © 1996 John Wiley & Sons, Inc.     

Effect of flow field heterogeneity in coagulators on aggregate size and structure

Aggregate size and structure were investigated under turbulent conditions in stirred tank (ST) and Taylor–Couette‐type (TC‐type) devices. Root‐mean‐square radius of gyration, 〈Rg〉, and zero‐angle intensity of scattered light, I(0), were acquired as a function of stirring intensity, characterized by an experimentally obtained average hydrodynamic stress, 〈τ〉exp, determined by torque measurements. Evaluating aggregate images revealed that aggregate structure and shape are independent of the device type. However, in TC‐type devices, the aggregates grow to three to four times larger sizes than inside ST, although the same 〈τ〉exp was used in both coagulators. As confirmed by computational fluid dynamics, this can be attributed to the differences in the maximum hydrodynamic stress in ST compared with those in TC‐type devices. In contrast, the power‐law scaling of 〈Rg〉 and I(0) with 〈τ〉exp is preserved for all investigated devices, with an exponent approximately equal to ?0.5 and ?0.7, respectively. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Solution properties of polyaniline

Solution properties of polyaniline (PANI) synthesized at various temperatures were studied using static light scattering (SLS), intrinsic viscosity, and dynamic light scattering (DLS). We demonstrated that average radius of gyration 〈R_g〉, intrinsic viscosity [η], and average hydrodynamic radius 〈R_H〉, of polyaniline molecules in dilute N‐methyl‐2‐pyrrolidinone (NMP) solutions increased with decreasing synthesis temperatures, i.e.; increasing molecular weight. SLS data demonstrate that second virial coefficient (A₂) decreased with increasing particle sizes suggesting that solubility of PANI in NMP decreased with increasing particle sizes. We also find that the polymers extend as the polymer concentration is lowered and that the increase in the hydrodynamic radius can be expressed by a power law of the electrostatic screening length. This behavior is typical of polyelectrolytes in dilute solution, providing a basis for understanding the conformation changes of this metallic polymer in solution. Copyright © 2009 Society of Chemical Industry     

Solution properties of hyperbranched polymers and synthetic application for amphiphilic star‐hyperbranched copolymers by grafting from hyperbranched macroinitiator

Hyperbranched polystyrenes (PS) were prepared by living radical photopolymerization of N,N‐diethyldithiocarbamoylmethylstyrene (DTCS) as an inimer under UV irradiation. Branched PS with an average chain length between branching points of four styrene units was also prepared by living radical copolymerization of DTCS with styrene. The ratio of radius of gyration to hydrodynamic radius R_G/R_H for these hyperbranched polymers was in the range 0.82–0.89 in toluene. The translational diffusion coefficient D(C) showed a constant value in the range of 0–14 × 10^?3 g ml^?1 in toluene. It was found from these dilute solution properties that hyperbranched PSs formed a unimolecular structure even in a good solvent because of their compact nature. These hyperbranched PSs exhibited large amounts of photofunctional carbamate (DC) groups on their outside surfaces. Subsequently, we derived amphiphilic star‐hyperbranched copolymers by grafting from hyperbranched macroinitiator with 1‐vinyl‐2‐pyrrolidinone. These star‐hyperbranched copolymers were soluble in water and methanol. © 2001 Society of Chemical Industry     

Coagulation of bentonite suspension by polyelectrolytes or ferric chloride: Floc breakage and reformation

Coagulation process usually involves different hydrodynamic conditions, in particular when it is followed by a filtration step. In this study, coagulation performance was investigated under a wide range of shear stress. Floc behaviour was followed in-line by laser granulometry to determine size distribution and structure. Synthetic suspension of bentonite in tap water was used as a reference for mineral solids in surface water. Three cationic polymers (polyamine based and polyDADMAC) and ferric chloride were tested using different coagulation reactor geometries. Jar-test indicated coagulation performance under mild hydrodynamic conditions and Taylor–Couette reactors were used to create shear stresses up to 8 Pa. Flocs formed with ferric chloride are not able to grow under middle shear stress like 1.5 Pa. On the contrary, polyelectrolytes lead to large flocs, dense (D_f = 2.6) and resistant to shear stress. A qualitative comparison of floc resistance to shear depending on hydrodynamic conditions and coagulant type is given through the calculation of the strength factor. Fractal dimension measurements indicate a mechanism of particle erosion when flocs are subjected to a higher shear stress in Taylor–Couette reactor. Floc re-growth is also investigated, and breakage appears to be non-reversible regardless of coagulant and conditions experimented.     

EFFECT OF POLYMER MOLECULAR WEIGHT, SOLVENT AND CASTING SOLUTION COMPOSITION ON THE PORE SIZE AND THE PORE SIZE DISTRIBUTION OF POLYETHERSULFONE (VICTREX) MEMBRANE

The effect of the molecular weight of polyethersulfone (Victrex) polymers, the nature of the solvent and the polymer concentration on the effective hydrodynamic radius of polymer in the membrane casting solution was investigated. The membranes were prepared from the casting solutions studied above and ultrafiltration experiments were performed with polyethylene glycol solutes. The average pore sizes and the pore size distributions on the membrane surfaces were further calculated from the ultrafiltration performance data obtained above. Strong correlations were found between the effective hydrodynamic radius of the polymer in the casting solution and the average pore size on the membrane surface. The mechanism of the pore formation was proposed on the basis of the polymer size—pore size correlation.     

Nano‐scaled ordering of hyperbranched and star‐hyperbranched polymers

Hyperbranched polystyrenes (HPS) were prepared by living radical polymerization of 4‐vinylbenzyl N,N‐diethyldithiocarbamate (VBDC) as an inimer under UV irradiation. These HPS exhibited large amounts of photofunctional diethyldithiocarbamate (DC) groups on their outside surfaces. We derived star‐HPS (SHPS) by grafting from such HPS macroinitiator with methyl methacrylate (MMA) or ethyl methacrylate (EMA). The ratios of radius of gyration to hydrodynamic radius R_g/R_h for HPS and SHPS in tetrahydrofuran (THF) were in the range of 0.74–0.90 and 1.05–1.12, respectively. HPS and SHPS behaved in a good solvent as hard and soft spheres, respectively. We demonstrated the structural ordering of both branched polymers in THF through small‐angle X‐ray scattering (SAXS), by varying the polymer concentration. As a result, HPS and SHPS formed face‐centered‐cubic (fcc) and body‐centered‐cubic (bcc) structures, respectively, near the overlap threshold (C*). © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3340–3345, 2006     

Particle size and distribution of biodegradable poly‐D,L‐lactide‐co‐poly(ethylene glycol) block polymer nanoparticles prepared by nanoprecipitation

A biodegradable block copolymer, poly‐D ,L ‐lactide (PLA)‐co‐poly(ethylene glycol) (PEG), was prepared by the ring‐opening polymerization of lactide with stannous caprylate [Sn(Oct₂)] as a catalyst; then, the PLA–PEG copolymer was made into nanoparticles by nanoprecipitation under different conditions. The average molecular weight and structure of PLA–PEG were detected by ¹H‐NMR and gel permeation chromatography. The sizes and distributions of the nanoparticles were investigated with a laser particle‐size analyzer. The morphologies of the nanoparticles were examined by transmission electron microscopy. The effects of the solvent–nonsolvent system, operation conditions, and dosage of span‐80 on the sizes and distributions of the nanoparticles are discussed. The results show that acetone–water was a suitable solvent–nonsolvent system and the volume ratio of the nonsolvent phase to the solvent phase (O/W) (v/v), the concentration of PLA–PEG in the solvent phase, and the dosage of span‐80 had important effects on the particle sizes and distributions. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1884–1890, 2005     

FUNGAL-INDUCED REDISTRIBUTION OF KRAFT LIGNIN MOLECULAR WEIGHT BY MULTI-ANGLE LASER LIGHT SCATTERING

Culture broths from Phanerochaete chrysosporium and Trametes cingulata, combined with co-factors such as hydrogen peroxide, dithiothreitol, copper, iron, and manganese ions were examined for the ability to modify lignin structure. High-performance size exclusion chromatography (HP-SEC) coupled to multi-angle laser light scattering (MALLS) detection was used to determine the effect of several white rot fungi, pH values, enzymes, and co-factors on the molecular weight distribution of treated kraft lignin. The analytical procedure tracked changes in molecular weight distribution, radius of gyration, and hydrodynamic radius. Results showed changes in the molecular weight distribution of lignin components when treated with combinations of factors. The induced cultures showed more lignin depolymerization for the specific lignin samples in which they were initially grown. The distribution in the radius of gyration became narrower with time, indicating that molecular conformation changed to a more uniform molecular shape. H₂O₂ and DTT showed the most significant changes in lignin molecular weight distribution.     

Mean-square radius of gyration and hydrodynamic radius for topological polymers evaluated through the quaternionic algorithm

We evaluate numerically the mean-square (MS) radius of gyration and the diffusion coefficient for topological polymers such as ring, tadpole, double-ring, and caged polymers and catenanes. We consider caged polymers with any given number of subchains, and catenanes consisting of two linked ring polymers with a fixed linking number. Through Kirkwood’s approximation we evaluate the hydrodynamic radius, which is proportional to the inverse of the diffusion coefficient, for various topological polymers. Here we take the statistical averages over configurations of topological polymers constructed through the quaternionic algorithm, which generates uniform random walks connecting given two points. It gives ideal chains with no excluded volume. We evaluate numerically the ratio of the square root of the MS radius of gyration to the hydrodynamic radius for several topological polymers, and show for them that the ratio decreases as the topology becomes more complex.     

Synthesis and polyelectrolyte behavior of poly(methacrylic acid) star polymers

Poly(tert‐butyl methacrylate) [P(tBMA)] star polymers were synthesized by copolymerization of p(tBMA) macroinitiator with ethylene glycol dimethacrylate via atom transfer radical polymerization method. P(tBMA) stars had a narrow molecular weight distribution (M_w/M_n = 1.06–1.15). The ratio of radius of gyration to hydrodynamic radius R_G/R_H, which indicates inner segment density, was in the range 1.16–1.22 in tetrahydrofuran (THF) (arm number f = 25–142). These stars behaved not as hard spheres but as soft spheres in THF. Poly(methacrylic acid) stars were obtained by the hydrolysis of P(tBMA) arms. We investigated the conformation of star polyelectrolyte as a function of pH and ionic strength by means of dynamic light scattering (DLS). The hydrodynamic diameter increased gradually from 18.8 to 48.3 nm as a function of the solution pH. In addition, we compared experimental results with theoretical models for star polyelectrolytes. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Comparison of size distribution data from dynamic light scattering and size-exclusion chromatography

The intensity-defined distribution functions of hydrodynamic radii of equivalent spheres, R_h, obtained from dynamic light-scattering experiments using the CONTIN procedure via the Stokes formula were compared with distributions of gyration radii, R_g, determined by size-exclusion chromatography. The number-, weight-, and intensity- (z)-defined R_g distributions accessible from size-exclusion chromatography experiments were calculated using the Flory-Fox relation. Reliable ratios of average radii, R_g/R_h, for linear polystyrenes having narrow, broad, or bimodal molecular weight distributions were obtained in toluene. Care should be taken to utilize properly averaged experimental quantities. For instance, the CONTIN DLS data evaluation procedure yields the z-average of the inverse of the hydrodynamic radius, 〈1/R_h〉_z^?1. © 1995 John Wiley & Sons, Inc.     

Friction Coefficient and Mobility Radius of Fractal-Like Aggregates in the Transition Regime

The influence of geometric properties and particle size on mobility properties of fractal-like aggregates was studied in the mass and momentum-transfer transition regimes. Two methodologies were investigated. The Collision Rate Method (CRM) that determines the slip correction factor through the ratio of two fictitious Brownian particle-aggregate effective collision rates, and the Adjusted Sphere Method (ASM) that assumes the existence of a virtual, flow-independent adjusted sphere with the same slip correction factor as the aggregate over the entire transition regime. The simulated fractal-like aggregates were synthetic as they were generated via a cluster–cluster agglomeration algorithm. The CRM was used to calculate the adjusted-sphere radius of various aggregates: we found it to be weakly dependent on the monomer Knudsen number for Kn greater than 0.5. Numerical expressions for the aggregate orientationally-averaged projected area and the adjusted-sphere radius are proposed. Both expressions depend on geometric, non-ensemble averaged quantities: the radius of gyration and the number of monomers. The slip correction factor and the mobility radius of DLCA and RLCA aggregates were calculated using the ASM: for a given number of monomers, fractal dimension and prefactor, and Knudsen number their values were approximately constant (averaged over aggregate realizations). A fractal-like scaling law based on the mobility radius was found to hold. The mobility fractal dimension and prefactor were determined for different aggregates. The hydrodynamic radius, proportional to the friction coefficient, and the dynamic shape factor of DLCA and RLCA aggregates were also calculated.     

LIQUID-LIQUID RELATIVE PERMEABILITY: NETWORK MODELS AND EXPERIMENTS

Two different but related two-dimensional network models are used to elucidate the concept of relative permeability in simultaneous liquid-liquid flow in porous media. The first model is designed for monosized sphere packs while the other, consisting of spherical pore chambers interconnected by capillaries of variable length and radius, is intended for more general porous media. The effects of various operating conditions and physical factors—pressure gradient, wettability, surface tension, throat and pore size distributions, imbibition or drainage—on relative permeability are studied. Experimental data are also presented to confirm various aspects of the theory.     

The effect of a concentration‐dependent viscosity on particle transport in a channel flow with porous walls

The transport of a dilute suspension of particles through a channel with porous walls, accounting for the concentration dependence of the viscosity, is analyzed. In particular, we study two cases of fluid permeation through the porous channel walls: (1) at a constant flux and (2) dependent on the pressure drop across the wall. We also consider the effect of mixing the suspension first compared with point injection by considering inlet concentration distributions of different widths. We find that a pessimal inlet distribution width exists that maximizes the required hydrodynamic pressure for a constant fluid influx. The effect of an external hydrodynamic pressure, to compensate for the reduced transmembrane pressure difference due to osmotic pressure, is investigated. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1891–1904, 2014     

Destabilization of model silica dispersions by polyelectrolyte complex particles with different charge excess,hydrophobicity, and particle size

Nonstoichiometric polyelectrolyte complex dispersions (PECs) with different charge excess and hydrophobicity as well as different average hydrodynamic particle size were used to induce flocculation of oppositely charged silica dispersions. PECs were formed with poly(diallyldimethylammonium chloride) (PD) as polycation and poly(styrene‐p‐sodium sulfonate) (NaPSS) and poly(acrylamide‐co‐sodium acrylate) (PR2540) as polyanions. PD was used as single polymer flocculant too. Flocculation process was characterized by optical densities of supernatants OD₅₀₀, by UV/VIS spectrometry, and determination of average floc sizes D(v; 0.5) as well as volume distribution of floc sizes by laser diffraction and determination of sedimentation velocity s by means of LUMiFuge? 114. It was found that the reaction process between silica and the used flocculants could be divided into three intervals (destabilization, flocculation optimum, and restabilization) as it is known for all other polymer flocculants. For an effective flocculation of a charged substrate, both electrostatic as well as hydrophobic interactions play an important role. The interval up to the beginning of the flocculation optimum is mainly ascertained by electrostatic interactions (the charge density of the flocculant) but the broadness of flocculation optimum depends largely on hydrophobic interactions. Hydrophobic interactions also play an important role for shear stability of the formed flocs. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3776–3784, 2007     

Prediction of sedimentation coefficients of random coil polymers

The concentration dependence of the radius of gyration and the equivalent hydrodynamic radius of polymers in solution is described well by a model developed in earlier work. The calculated hydrodynamic volumes of solvated polymers are combined with the statistical mechanical calculations of Burgers for hard spheres to predict sedimentation coefficients at finite concentrations. The predicted values are in good agreement with experimental results.     

Characterization by dilute solution and rheological methods of polystyrene and poly(methyl methacrylate) produced with a tetrafunctional peroxide initiator

Polystyrene (PS) and poly(methyl methacrylate) (PMMA) samples produced by the bulk homopolymerization of styrene and methyl methacrylate with a tetrafunctional peroxide initiator (JWEB50) are characterized in detail by various solution and rheological methods. For comparison purposes, “linear” PS and PMMA samples were produced under similar conditions with a monofunctional initiator (TBEC). The four sample types were characterized by size exclusion chromatography (SEC) setups to determine molecular weight, radius of gyration, and intrinsic viscosity distributions. Contraction factors were calculated and indicated evidence of branching for polystyrene produced with JWEB50 while no such effects were observed with PMMA. The rheological behavior of the samples was subsequently investigated by performing oscillatory shear and creep experiments. Compared to the “linear” material, samples produced with JWEB50 exhibited a reduction in zero‐shear viscosity that was attributed to long‐chain branching. Retardation spectra were calculated based on creep data and converted to dynamic compliances that were then combined with the oscillatory data. This provided master curves spanning a much wider frequency range than could be obtained experimentally. Examination of various viscoelastic functions showed evidence of long‐chain branching for both polystyrene and poly(methyl methacrylate) samples produced with JWEB50. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1340–1355, 2007     

Capsule permeability via polymer and protein ingress/egress

Static incubation tests, where microcapsules and beads are contacted with polymer and protein solutions, have been developed for the characterization of permselective materials applied for bioartificial organs and drug delivery. A combination of polymer ingress, detected by size‐exclusion chromatography, and protein ingress/egress, assessed by gel electrophoresis, provides information regarding the diffusion kinetics, molar mass cutoff (MMCO) and permeability. This represents an improvement over existing permeability measurements that are based on the diffusion of a single type of solute. Specifically, the permeability of capsules based on alginate, cellulose sulfate, polymethylene‐co‐guanidine were characterized as a function of membrane thickness. Solid alginate beads were also evaluated. The MMCO of these capsules was estimated to be between 80 and 90 kDa using polymers, and between 116–150 kDa with proteins. Apparently, the globular shape of the proteins (radius of gyration (R_g) of 4.2–4.6 nm) facilitates their passage through the membrane, comparatively to the polysaccharide coil conformation (R_g of 6.5–8.3 nm). An increase of the capsule membrane thickness reduced these values. The MMCO of the beads, which do not have a membrane limiting their permselective properties, was higher, between 110 and 200 kDa with dextrans, and between 150 and 220 kDa with proteins. Therefore, although the permeability estimated with biologically relevant molecules is generally higher due to their lower radius of gyration, both the MMCO of synthetic and natural water‐soluble polymers correlate well, and can be used as in vitro metrics for the immune protection ability of microcapsules and microbeads. This article shows, to the authors' knowledge, the first reported concordance between permeability measures based on model natural and biological macromolecules. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1165–1175, 2000