Bimodal particle size distribution polymer/oligomer combinations for printing ink applications

This paper describes a study in which anionically stabilised acrylic latices with a bimodal particle size distribution, produced by blending polymer particles of 50 and 350 nm in different blend ratios, are blended with oligomers. Reversibility, rheology, drying behaviour, film formation and blocking resistance of these systems were studied Reversibility appears to show two regions of linear dependence on the total particle surface area. The lower the surface area, the lower the amount of oligomer needed for good reversibility. The rheological data was fitted by the Krieger–Dougherty equation and it appeared that both in the presence and absence of oligomer an 80/20 large/small blend exhibited the highest maximum packing fraction. Short drying times were obtained with bimodal blends at high solids content and the drying profiles could be explained by the Croll model. The presence of oligomer was shown to exhibit a positive effect on film formation and when the oligomer is hard, the blocking resistance is already very good at low oligomer content, resulting in a very good MFT/blocking resistance balance. The latter can also be obtained when as well the size as the T_g of the polymer particles is varied.     

Process model for latex film formation: Optical clarity fronts

We examined the drying behavior of latex both theoretically and experimentally. The theory extends a model for horizontal drying fronts in films with nondeformable particles to incorporate particle deformation by a capillary deformation mechanism. The pressure in the fluid, causing particle compaction, arises from flow through the packed bed to ensure evaporation from all wet areas of the film. We predicted the position of a front of volume fraction unity passing across a semi-infinite film as it dries. Experimentally, the position of the transition from a cloudy film to optical clarity was tracked visually in films comprised of either single component soft latex particles, 20°C above the glass transition, or a blend containing 35% non-deformable hard latex particles. For an initial volume fraction of 0.33, we found excellent agreement between theory and experiment. For an initial volume fraction of 0.05, the agreement is less, although still qualitative. The limitations of the model with respect to the knowledge of physical parameters and initial conditions are discussed. One major implication of the model is that deformation of soft latex particles displaces large amounts of water and, consequently, slows progression of the drying front. Harder particles and shallow initial film profiles produce more pronounced drying fronts. Dept. of Chemical Engineering, Princeton, NJ 08544. Emulsion Polymers Institute and Dept. of Chemical Engineering, Bethelhem, PA 18015.     

Liquid permeability of packed bed with binary mixture of particles

We investigate the effect of binary sized packing on the permeability of water flow through a column packed with binary mixture of spherical particles. The size ratios λ of large to small particles are chosen to be 1.4 and 2.5. Particle packing density for binary mixture of the particles is larger than that for equal sized particles and shows the maximum around the particle blending ratio at which large particles are densely packed and all the small particles fill the void among the large particles. This behavior is observed in both experimental results and theoretical estimation. The variation pattern of packing density with the blending ratio does not agree with that of permeability. The permeability increases with relative fraction of large particles at the maximum packing. Experimental results for the permeability are compared with three theoretical models. Variation pattern of the permeability with the blending ratio from these theoretical models agrees with that from the experiment. Theses theoretical models are in good agreement each other.     

Film formation from pigmented latex systems: Drying kinetics and bulk morphologies of ground calcium carbonate/functionalized poly(n‐butyl methacrylate‐co‐n‐butyl acrylate) blend films

The drying kinetics and bulk morphology of pigmented latex films obtained from poly(n‐butyl methacrylate‐co‐n‐butyl acrylate) latex particles functionalized with carboxyl groups and ground calcium carbonate blends were studied. Latex/pigment blends with higher carboxyl group coverage on the latex particle surfaces dried faster than films with few or no carboxyl groups present. The latex/pigment dispersions also dried faster when there was more stabilizer present in the blend system because of the hydrophilic nature of the stabilizer. The net effect of increasing the pigment volume concentration in the blend system was to shorten the drying time. The bulk morphologies of the freeze‐fractured surfaces of the pigmented latex films were studied with scanning electron microscopy. Scanning electron microscopy analysis showed that increased surface coverage of carboxyl groups on the latex particles in the latex/pigment blends resulted in the formation of smaller pigment aggregates with a more uniform size distribution in the blend films. In addition, the use of smaller latex particles in the blends reduced the ground calcium carbonate pigment aggregate size in the resulting films. Scanning electron microscopy analysis also showed that when the initial stabilizer coverage on the latex particles was equal to 18%, smaller aggregates of ground calcium carbonate were distributed within the copolymer matrix of the blend films in comparison with the cases for which the initial stabilizer coverage on the latex particles was 8 or 36%. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2267–2277, 2006     

Drying and cracking of soft latex coatings

The minimum film formation temperature (MFFT) is the minimum drying temperature needed for a latex coating to coalesce into an optically clear, dense crack-free film. To better understand the interplay of forces near this critical temperature, cryogenic scanning electron microscopy (cryoSEM) was used to track the latex particle deformation and water migration in coatings dried at temperatures just above and below the MFFT. Although the latex particles completely coalesced at both temperatures by the end of the drying process, it was discovered that particle deformation during the early drying stages was drastically different. Below the MFFT, cracks initiated just as menisci began to recede into the packing of consolidated particles, whereas above the MFFT, partial particle deformation occurred before menisci entered the coating and cracks were not observed. The spacing between cracks measured in coatings dried at varying temperatures decreased with decreasing drying temperature near the MFFT, whereas it was independent of temperature below a critical temperature. Finally, the addition of small amounts of silica aggregates was found to lessen the cracking of latex coatings near the MFFT without adversely affecting their optical clarity.     

Control of particle size distribution for the synthesis of small particle size high solids content latexes

A polymerization process to synthesize bimodal latexes with maximum particle diameters below 350 nm and solids content above 65 wt% has been developed.The process is based on an iterative strategy to determine the optimal particle size distribution that gives the maximum packing factor for a given range of particle sizes and at a given solids content. The calculated optimal bimodal PSD was experimentally obtained in a seeded semi-continuous emulsion polymerization reaction as follows: in the first step, a polymer seed latex was loaded in the reactor and grown, under monomer starved conditions, until a given particle size. At this point a fraction of the same seed was added to the reactor and the feed was continued until the desired particle size distribution and solids content were achieved. The point at which the seed was added again to the reactor and the amount of seed required were determined by the iterative strategy and depended on the competitive growth rate ratio of large and small particles that is an input for the iterative strategy.Implementation of the solution obtained from the iterative strategy, and for the first time in the open literature, led to the production of a coagulum free and stable bimodal latex with 70 wt% of solids content and particle sizes below 350 nm.     

Transparent,conductive polymer blend coatings from latex-based dispersions

Flexible, transparent and conductive polymer blend coatings were prepared from aqueous dispersions of poly(3,4-ethylenedixoythiophene)/poly(styrenesulfonate) [PEDOT/PSS] gel particles (∼80 nm) and latex (∼300 nm). The stable dispersions were deposited as wet coatings onto poly(ethylene terephthalate) substrates and dried at 80 °C. Microstructure studies using tapping mode atomic force microscopy (TMAFM) indicate that a network-like microstructure formed during drying at 0.03 volume fraction PEDOT/PSS loading. In this network-like structure, the PEDOT/PSS phase was forced into the boundary regions between latex. In addition, migration of the PEDOT/PSS particles towards coating surface is likely during drying of the aqueous dispersions. The addition of a small amount of dimethyl sulfoxide (DMSO) in dispersions altered the distribution of the PEDOT/PSS phase. As PEDOT/PSS concentration increases to 0.15 volume fraction, the coating surface is dominated by the PEDOT/PSS phase. The effect of DMSO on microstructure becomes less apparent as PEDOT/PSS concentration increases. The conductivity of the polymer blend coatings increases in a percolation-like fashion with a threshold of ∼0.02 volume fraction PEDOT/PSS. The addition of DMSO in dispersions enhanced the coating conductivity beyond the threshold by more than two orders of magnitude. The highest conductivity, ∼3 S/cm, occurs at 0.20 volume fraction PEDOT/PSS concentration. The polymer blend coatings have good transparency with only a weak dependence of transparency on wavelength due to the small refractive index difference between filler and matrix.     

Viscosity of Electrostatically Stabilized Dispersions of Monodispersed, Bimodal, and Trimodal Silica Particles

Effect of particle size and polydispersity on the viscosity and maximum packing fraction of aqueous colloidal dispersions has been studied. For dispersions of mono-sized particles, the results indicate that there is a linear relationship between the log(η) (viscosity) and particle size at a fixed shear rate and volume fraction of solids. However, there is a particle diameter at which there is a decrease in the dependency of viscosity on particle size as the slope of the linear plots of log(η) versus particle diameter changes to a smaller value. Preliminary calculations indicate that this particle size may correspond to a separation distance at which electrostatic energy as compared with the thermal energy of the particles can be ignored. In the case of bimodal dispersions, the viscosity is affected by both absolute size and the ratio of the two sizes. The effect of particle size ratio on the viscosity was investigated using bimodal dispersions of the same size coarse particles, but fines of different sizes. There is a critical volume ratio below which bimodal dispersions of larger size ratios show lower viscosities than systems of smaller size ratios. Above this volume ratio of the two sizes, the trend becomes reversed and the fines will have a dominant effect on the viscosity behavior of the bimodal system. Statistically designed experiments were carried out using trimodal mixtures of monodispersed silica particles and it was shown that tridispersed suspensions demonstrate similar behavior as bidispersed suspensions, with a minimum in viscosity observed as a function of particle volume ratio.     

The Segregation of Surfactant upon Film Formation of Latex Dispersions: an Investigation by Energy Filtering Transmission Electron Microscopy

We investigated the local distribution of emulsifier in dried films cast from latex dispersions. Energy filtering transmission electron microscopy (EFTEM) allowed the detection of heteroatom-containing domains in unstained samples by electron spectroscopic imaging and elemental mapping. If the samples were prepared at temperatures above the minimum film-forming temperature (MFT), separated domains of surfactant were observed in detachment replicas and ultrathin sections. If the preparation was carried out below MFT the emulsifier was retained at the particle surface and similar observations could not be made. It is suggested that the mobility of the emulsifier at the surface of the particles is increased upon deformation and coalescence in the process of film formation, and that this mobility is a prerequisite for its segregation. Both processes do not take place upon drying below MFT, owing to lower mobility. The correlation between the process of film formation and the segregation of surfactant is discussed for both a dispersion of poly(vinylacetate) and one of polyacrylate.     

Properties and processing characteristics of open-celled foams produced by leaching NaCl from high density polyethylene

The properties and processing characteristics of open-celled foams produced by leaching small NaCl particles from high density polyethylene has been investigated. In a random dispersion of salt particles in the polymer matrix a minimum volume loading of 40 percent was required to produce an open-celled foam. The time required to remove this quantity of salt with 50°C water was 100 min. The maximum porosity of the foam is limited to the maximum packing fraction of the salt. For randomly dispersed isotropic particles the maximum packing fraction is approximately 0.64. Because the composite rapidly loses melt strength as the filler content nears the maximum packing fraction, the practical upper limit of extruded foam porosity is approximately 0.60.     

Compressive mechanical properties of partially sintered porous alumina of bimodal particle size system

This paper examined theoretically and experimentally packing behavior, sintering behavior and compressive mechanical properties of sintered bodies of the bimodal particle size system of 80 vol% large particles (351 nm diameter)–20 vol% small particles (156 nm diameter). The increased packing density as compared with the mono size system was explained by the packing of small particles in 6-coordinated pore spaces among large particles owing to the similar size relation between 6-coordinated spherical pore and small particle. The sintering between adjacent large particles dominated the whole shrinkage of the powder compact of the bimodal particle size system. However, the bimodal particle size system has a high grain growth rate because of the different curvatures of adjacent small and large particles. The derived theoretical equations for the compressive strengths of both mono size system and bimodal particle size system suggest that the increase in the grain boundary area and relative density by sintering dominate the compressive strength of a sintered porous alumina. The experimental compressive strengths were well explained by the proposed theoretical models. The strength of the bimodal particle size system was high at low sintering temperatures but was low at high sintering temperatures as compared with that of mono size system of large particles. This was explained by mainly the change of grain boundary area with grain growth. The stress–strain relationship of the bimodal particle size system showed an unique pseudo-ductile property. This was well explained by the curved inside stress distribution along the sample height. The inside stress decreases toward the bottom layer. The fracture of one layer of sintered grains over the top surface proceeds continuously with compressive time along the sample height when an applied stress reaches the critical fracture strength.     

Distribution of particles during solvent evaporation from films

We examine films, subject to evaporation, that contain particles. The volume fraction of particles increases as solvent is removed up to a maximum value of close packing. The governing equation for evolution of particle volume fraction is derived and numerical solutions obtained for various Peclet numbers. For large Peclet numbers an asymptotic solution gives the position and functional form of a front of close packed particles which passes through the film. For intermediate Peclet numbers the scaling for the spatial gradient in volume fraction is found to be Pe^1/2. This is different from conventional sedimentation, where convection rather than diffusion dominates.     

Effect of loading-rate on fracture micromechanism of methylmethacrylate-butadiene-styrene polymer blend

Methylmethacrylate-butadiene-styrene (MBS) polymer blends having two different types of rubber particle distribution, monomodal and bimodal, were prepared, and their fracture properties and fracture mechanisms were investigated under quasi-static and impact loading. A fracture property, maximum J-integral J_max, was evaluated at both loading-rates, and it was shown that J_max values of the bimodal MBSs are much greater than that of the monomodal with small particles, and slightly better than that of the monomodal with large particles. Thick damage zones were observed in the crack-tip regions in the bimodal and monomodal with large particles, indicating larger energy dissipation during fracture initiation than in the monomodal with small particles in which damage zone is much thinner. TEM micrographs exhibit that extensive plastic deformation under quasi-static rate and multiple craze formation under impact loading rate are the primary toughening mechanisms in the bimodal MBS blends. By assessing both fracture properties and transparency, the bimodal blend with blend ratio: 2.5/7.5 (=140 nm/2.35 μm; total rubber particle content is 10 wt%) was proved to show the best performance as MBS polymer blend with satisfiable transparency and high fracture resistance.     

高固含量多分散粒径分布乳液的研究2.二元种子法制备二元分散粒径分布乳液

通过在聚合过程中加入第２种子乳液，制备出了具有二元分散粒径分布的乳液，研究了第２种子乳液量对乳液粒径及粒径分布的影响。实验结果表明，通过改变第２种子乳液的量可以调节乳液搂闰径及粒径分布。当大粒子质量分数为８０％时，乳液粘度最小。通过粒径分布的多分散化，可显著降低乳液的最低成膜温度。     

A generalized model to predict the viscosity of solutions with suspended particles. IV. Determination of optimum particle-by-particle volume fractions

A new approach has been introduced to establish the optimum composition for all particles within a mixture or suspension to achieve the optimum packing fraction, φ_n, and/or the minimum viscosity, η. The derivation to obtain the optimum particle volume fraction assumed that a previously developed optimum composition for binary particles applied to any two particle volumes V_i and V_j in the mixture. The composition of the maximum packing fraction for a mixture of more than two particles was then assumed to be calculable from the optimized relationship of each separate binary pair of particle volumes V_i and V_i in the mixture. This derived equation was successfully shown to predict the optimum particle-to-particle composition of McGeary's experimentally measured binary, tertiary, and quaternary mixtures. The difference between the calculated and measured volume fractions was no greater than 3.85% and, in most instances, was significantly less than 3.85%. The maximum packing fractions, φ_n, determined experimentally by McGeary, were also successfully predicted to better than 3.26%. Theoretical particle-to-particle volume fractions evaluated for an example pressure-agglomerated latex appeared to predict the particle-size distribution only within a narrow range of particle sizes. However, when the theoretical and experimental results were evaluated as a function of the number of particles for each particle diameter, it was apparent that the agglomerated distribution closely approximated the theoretical optimum distribution above 600 Å. Agreement with theory below 600 Å was unsatisfactory. The decrease in viscosity of the example agglomerated latex appeared to have been enhanced as the optimum theoretical particle-size distribution was approached. © 1994 John Wiley & Sons, Inc.     

High solid content multisized emulsion copolymerization of styrene,butyl acrylate,and methacrylic acid

Polymer lattices with a multimodal particle size distribution (PSD) polymer latex were prepared by introducing additional surfactants during the semicontinuous emulsion polymerization of styrene, butyl acrylate, and methacrylic acid. The polymerization was investigated by following the variation of the particle size, the size distribution, the number of particles, the T_g of the different particle sizes, and the total conversion at different steps of the polymerization process. The results show that bimodal and trimodal PSD polymer lattices can be obtained by this method and that the secondary generation of particles is greatly influenced by the nature and the amount of additional surfactants, as well as the moment when they are introduced. When the amount of additional surfactants is increased, the diameters of both the small and large particles decrease and the number of particles in each of the populations increases. Earlier introduction of these surfactants favors the generation and the growth of the small particles and thereby leads to a reduction of the relative fraction of large particles in the final latex. On introduction of 7 wt % of additional surfactants, based on the total monomers, 100% of the monomers of the second-stage polymerization were consumed to form the small particles. This fraction decreases with a decreasing amount of the additional surfactants. These results were further demonstrated by measuring the T_g's of both the large and the small particles of two lattices, in which the T_g's of the copolymers produced in each of the stages were different. High solid content (>65%), low viscosity, and coagulum-free lattices have been obtained through secondary nucleation, and a minimum in viscosity was found when the weight fraction of the large particles was around 80%. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 70: 2667–2677, 1998     

Mechanical properties of films prepared from model high‐glass‐transition‐temperature/low‐glass‐transition‐temperature latex blends

The mechanical properties of films prepared from model high‐glass‐transition‐temperature (T_g)/low‐T_g latex blends were investigated with tensile testing and dynamic mechanical analysis. Polystyrene (PS; carboxylated and noncarboxylated) and poly(n‐butyl methacrylate‐co‐n‐butyl acrylate) [P(BMA/BA); noncarboxylated] were used as the model high‐T_g and low‐T_g latexes, respectively. Carboxyl groups were incorporated into the PS latex particles to alter their surface properties. It was found that the presence of carboxyl groups on the high‐T_g latex particles enhanced the Young's moduli and the yield strength of the PS/P(BMA/BA) latex blend films but did not influence ultimate properties, such as the stress at break and maximum elongation. These phenomena could be explained by the maximum packing density of the PS latex particles, the particle–particle interfacial adhesion, and the formation of a “glassy” interphase. The dynamic mechanical properties of the latex blend films were also investigated in terms of the carboxyl group coverage on the PS latex particles; these results confirmed that the carboxyl groups significantly influenced the modulus through the mechanism of a glassy interphase formation. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2788–2801, 2002     

Modelling the zero shear viscosity of bimodal high solid content latex: Calculation of the maximum packing fraction

Different rheological tests were performed on monodisperse polystyrene latices and mixtures of two different latices with different particle sizes. A critical volume fraction φ_c was defined for each of the latices. Subsequently, a method based on the estimation of the porosity of a bed of randomly placed spherical particles was adapted to allow us to define the maximum packing fraction for any bimodal system. This method can be used for any ratio of particle diameter and volume fraction for the two populations provided one has knowledge of the critical volume fractions of related monodisperse latices (see Pishvaei et al., 2005. Polymer 46, 1235-1244). The model was tested experimentally, and rheological tests allowed us to validate the values of the critical volume fraction (φ_c) of different bimodal latices. A master curve of viscosity vs. polymer concentration was obtained using the concept of reduced volume fraction. The results prove that we can predict the viscosity of multimodal systems from the knowledge of monomodal packing fraction.     

Two-step migration of particles in evaporating bimodal suspension films at high Peclet numbers

During the drying of bimodal colloidal suspensions containing particles of various sizes, smaller particles preferentially migrate to the top surface under particular drying conditions, leading to undesirable drying defects in batteries and in other coating applications. Despite extensive previous studies, the migration mechanism is far from being understood because few in situ observations are available to support the hypotheses. To remedy this, we use real-time photoluminescence (PL) microscopy to investigate the migration of small fluorescent latex particles co-dispersing with large nonemissive latex particles. Comparing the measured PL intensity with that predicted by a model allows us to determine the quantity of small particles near the evaporating surface. The results reveal that the fluorescent particles segregate in two steps: The primary segregation occurs early in the evaporation stage, whereas the secondary stepwise migration occurs when the air–liquid interface invades the particle consolidation layer. The latter migration is attributed to the flow-induced motion of small particles that move through interstitial spaces between large particles.     

Film formation from pigmented latex systems: Mechanical and surface properties of ground calcium carbonate/functionalized poly(n‐butyl methacrylate‐co‐n‐butyl acrylate) latex blend films

The mechanical and surface properties of films prepared from model latex/pigment blends were studied using tensile tests, surface gloss measurements, and atomic force microscopy. Functionalized poly(n‐butyl methacrylate‐co‐n‐butyl acrylate) [P(BMA/BA)] and ground calcium carbonate (GCC) were used as latex and extender pigment particles, respectively. The critical pigment volume concentration of this pigment/latex blend system was found to be between 50 and 60 vol % as determined by surface gloss measurement and tensile testing of the blend films. As the pigment volume concentration increased in the blends, the Young's modulus of the films increased. Nielsen's equations were found to fit the experimental data very well. When the surface coverage of carboxyl groups on the latex particles was increased, the yield strength and Young's modulus of the films both increased, indicating better adhesion at the interfaces between the GCC and latex particles. When the carboxyl groups were neutralized during the film formation process, regions with reduced chain mobility were formed. These regions acted as a filler to improve the modulus of the copolymer matrix and the modulus of the resulting films. The carboxyl groups on the latex particle surfaces increased the surface smoothness of the films as determined by surface gloss measurement. When the initial stabilizer coverage of the latex particles was increased, the mechanical strength of the resulting films increased. At the same time, rougher film surfaces also were observed because of the migration of the stabilizer to the surface during film formation. With smaller‐sized latex particles, the pigment/latex blends had higher yield strength and Young's modulus. Higher film formation temperatures strengthen the resulting films and also influence their surface morphology. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4550–4560, 2006