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The importance of maximizing the particle packing fraction in a suspension by maximizing average particle size ratio of D₅/D₁ has been adequately shown to be important as previously reported in the literature. This study aims to extend that analysis to include the best formulation approach to maximize the packing fraction with a minimum number of monodisperse particle sizes.

An existing model previously developed by this author was modified theoretically to optimize the ratio used between consecutive monodisperse particle sizes. This process was found to apply to a broad range of particle configurations and applications. In addition, five different approaches for maximizing average particle size ratio D̅₅/D̅₁ were addressed for blending several different particle size distributions. Maximizing average particle size ratio D̅₅/D̅₁ has been found to result in an optimization of the packing fraction. Several new concepts were also introduced in the process of maximizing the packing fraction for these different approaches.

The critical part of the analysis to maximize the packing fraction with a minimum number of particles was the theoretical optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size. This study also clarified the recent incorrect claim in the literature that Furnas in 1931 was the first to generate the maximum theoretical packing fraction possible for n different particles that was actually originally developed in conjunction with the Sudduth generalized viscosity equation. In addition, the Furnas generated equation was also shown to give significantly different results from the Sudduth generated equation.

Experimental data involving monodisperse particles of different blends with a minimum number of particle sizes that are truly monodisperse are often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.

The expanded model presented in this article provides practical guidelines for blending pigments using a minimum number of monodisperse particle sizes that can yield much higher ratios of the particle size averages D̅₅/D̅₁ and thus potentially achieve significantly improved properties such as viscosity.

The model presented in this article provides the first apparent guidelines to control the blending of pigments in coatings by the optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size.

In part I of this study a new dry coating analysis was developed relating pigment cluster voids and pigment particle distribution to the pigment cluster dispersion coefficient, C_q, and the critical pigment volume concentration (CPVC). Part II of this study has addressed a wet coating analysis to relate pigment particle size distribution and viscosity in a coating formulation to the pigment cluster dispersion coefficient.

This study introduced the relationships for the wet coating by building on the dry coating evaluations introduced in part I of this study. Part II of this study showed that the CPVC for a solvent based coating can be significantly influenced by a change in the viscosity measured interaction coefficient, σ, as influenced by a change in an additive such as the surfactant concentration in the matrix or polymer phase of the coating. The CPVC was also shown to be strongly influenced by a separate analysis of the pigment particle size distribution to modify the coating viscosity.

It was pointed out recently that an increase in flow additive increased the CPVC but decreased viscosity. Consequently, it was shown theoretically in this study that viscosities compared at the same relative viscosity, η/η₀, and at the same filler composition, f_i, using the generalized viscosity model would require decrease in the interaction coefficient, σ, to increase the global volume fraction of filler or pigment, Φ_F. This implied that a measurement of the interaction coefficient, σ, should be a direct measure of the ability of the CPVC to be modified. A minimum viscosity from the generalised viscosity model also resulted at the maximum packing fraction, which in turn was found to increase the CPVC of the coating. Consequently, part II of this study has yielded a useful relationship between the cluster dispersion coefficient, C_q, and the interaction coefficient, σ, from the generalised viscosity model.

While the experimental measurement of the parameters to isolate the clustering concepts introduced in this study may be difficult, it is expected that better quantitative measurement of clustering concepts will eventually prove to be very beneficial to providing improved suspension applications including coatings. The close relationship introduced in this study between clustering concepts and viscosity should provide an improved ability to measure the parameters to isolate clustering in coatings and other suspension applications.

The theoretical relationship developed in this study between the pigment cluster dispersion coefficient, C_q, and CPVC and the theoretical and experimental relationship between CPVC and the viscosity interaction coefficient, σ, inferred a direct relationship between C_q and the viscosity interaction coefficient, σ. Consequently, it was shown that the theoretical pigment cluster model developed in this study could be directly related to the experimental matrix additive composition controlling viscosity in a coating formulation. The practical implication is that the measurement tools introduced in this study should significantly influence future suspension formulations to provide better measurement and control of clustering and viscosity in coatings and other suspension applications.

Part II of this study has shown how a useful relationship can be generated between the interaction coefficient, σ, from the generalised viscosity model and the pigment cluster dispersion coefficient, C_q, developed in part I of this study. In addition, this study also showed that effective control of the CPVC of a coating can be modified by judicious control of the interaction coefficient using pigment particle size distribution and/or viscosity control additives in a wet coating analysis.

This paper attempted to show the potential relationship between five different interaction coefficients relating solvents and polymers. This review addressed primarily a comparison between the polymer-solvent interaction coefficients obtained from two different types of models. These two primary polymer-solvent interaction coefficients included the Flory-Huggins interaction coefficient developed from thermodynamic colligative properties and the polymer-solvent Sudduth interaction coefficient obtained from the generalized viscosity equation. The other three interaction coefficients included Hildebrand solubility parameter and the interaction coefficients or constants for the Huggins and Kraemers models that are normally generated from viscosity measurements. The paper aims to discuss these issues.

These five different interaction coefficients were compared from theoretical considerations as well as on the basis of available experimental data.

Remarkably the polymer-solvent interaction coefficients for both Flory-Huggins interaction coefficient and the Sudduth interaction coefficient were found to be dimensionless and approximately of the same value. In addition, when both interaction coefficients are negative then both describe solvents. In addition, both interaction coefficients describe a plasticizer when they are in the range of 0 to ½. Finally both interaction coefficients describe a non-solvent or a suspension when both are greater than 1. The Hildebrand solubility parameter was found to be directly related to the Flory-Huggins interaction coefficient. The viscosity constants for the Huggins and Kraemers models were found to be included as subsets of the Sudduth generalized viscosity model.

The strong apparent relationship between these five different interaction coefficients to predict the interaction between polymers and solvents is strongly indicated based on the results from this study. However, approximately half of these interaction coefficients have been derived to be evaluated from colligative properties and half were derived to be evaluated from viscosity measurements.

In general, it is much easier to obtain viscosity measurements compared to the evaluation of the colligative properties. Therefore, if a direct relationship can be shown between these five different interaction coefficients, then it would appear to be much easier to evaluate polymer-solvent interactions from the interaction coefficients obtained from viscosity measurements.

This is the first time that these five interaction coefficients have been compared in such a way that shows their direct relationship even though half of these interaction coefficients have been derived to be evaluated from colligative properties and half were derived to be evaluated from viscosity measurements.

This study aims to introduce a new theoretical approach to blend spherical and non‐spherical particles in a coating to improve its viscosity characteristics.

Theoretical analysis has been used to modify an existing model developed by this author to apply to a broad range of particle configurations.

Non‐spherical particles like fibres or discs in a suspension or coating have been found to have three different viscosity response regions. Consequently, the viscosity of suspensions or coatings with these types of particles appears to have two apparent maximums as a function of concentration. Improved viscosity control of coatings have been found to be directly achievable by blending particles with different shapes based on the concentration relative to this first maximum. This optimisation process has been found to be better understood using a new variable which has been described as the “sphericity”, s. The “sphericity”, s, as described in this study has been defined as the relative ratio of the surface to volume fraction for a non‐spherical particle to that of a sphere of equivalent volume.

Experimental data involving monodisperse particles of different configurations is often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.

The model presented in this paper provides practical guidelines to blending pigments with different particle shapes to control the viscosity of coatings and suspensions.

The model presented in this paper provides the first apparent guidelines to control the blending of pigments in coatings and composites with different particle shapes using the “sphericity” of the pigment particle.

The purpose of this paper is to expand the theoretical meaning and application of the separate components of the interaction coefficient as obtained from the generalized viscosity model.

Both theoretical and experimental analysis have been utilized to better understand the meaning of the separate components of the interaction coefficient obtained from the generalized viscosity model. Analysis of the experimental data of Schaller and Humphrey has been used to successfully isolate the separate components of the interaction coefficient.

The relative unhindered volume is the volume outside the sphere of influence of a particle that is responsible for the viscosity characteristics of a coating. This is the volume available for particles to move in the suspension and still contribute to the viscosity. The smaller the relative unhindered volume the higher the viscosity. As the interaction coefficient, σ, increases the particles increase their interaction with each other and the relative unhindered volume decreases. Using the data of Schaller and Humphrey, it was found that the interaction coefficient agreed best with the theoretical expectation relative to particle size when the ionic strength was low. At high levels of ionic strength, the solvent‐particle component of the interaction coefficient was dominant and the influence of particle size on the interaction coefficient was minimal.

Only one set of experimental data was successfully utilized for illustrative purposes in this study but the resulting analysis has implicated a broad range of practical applications. In addition, the general theoretical concepts elucidated relative to the interaction coefficient should still be applicable independent of the experimental results.

The analysis presented in this paper provides several practical guidelines to separate and control the charge component of pigments in a suspension from their size component using the interaction coefficient as described in this study. Consequently, the results of this study should provide several new practical approaches to use when attempting to control the viscosity of suspensions for a broad range of practical applications and for a broad range of suspension types including coatings.

This is the first time that the theoretical statistical character of the interaction coefficient as indicated in the generalized viscosity model has been specifically elucidated. In addition, the relatively simple experimental separation of the interaction coefficient into its size and electrical components has been shown to be widely applicable in this paper.

The primary objective of this two part study was to show theoretically how pigment cluster voids and pigment distribution can influence the critical pigment volume concentration (CPVC) and consequently the properties of a dry coating. In Part I of this study a pigment clustering model with an analytical solution has been developed that was a modification of an earlier model by Fishman, Kurtze, and Bierwagen that could only be solved numerically.

The original derivation of the clustering concept developed by Fishman et al. resulted in a mathematical analysis which was only able to be solved numerically and was found to be very tedious to utilize directly. In this study, a new successful derivation utilizing some of the original concepts of Fishman et al. was generated and shown to result in a practical and much more useable analytical analysis of the clustering concept. This new model was then applied directly to quantify the influence of flow agents or surfactants in a coating formulation on the CPVC as described by Asbeck.

It was found that the largest deviation from 100 per cent pigment dispersion with no pigment clusters occurred just before and just after the ultimate CPVC (UCPVC). A theoretical relationship was also found between the pigment cluster dispersion coefficient, C_q, and CPVC. This result was consistent with the experimental relationship between CPVC and the per cent flow additive as found by Asbeck. The density ratio of overall coating to the pigment density was found to go through a maximum at a global volume fraction of pigment that was slightly greater than the UCPVC as expected for a mechanical property. It was also identified that mechanical failure of most coating formulations should be apparent at either the “Lower Zero Limit” or the “Upper Zero Limit” global volume fraction pigment as defined in this study.

While the experimental measurement of the parameters to isolate the clustering concepts introduced in this study may be difficult, it is expected that better quantitative measurement of clustering concepts will eventually prove to be very beneficial to providing improved suspension applications including coatings.

The theoretical relationship developed in this study between the pigment cluster dispersion coefficient, C_q, and CPVC and the experimental relationship between CPVC and the per cent flow additive found by Asbeck inferred a direct relationship between C_q and the per cent flow additive. Consequently, it was shown that the theoretical pigment cluster model developed in this study could be directly related to the experimental matrix additive composition in a coating formulation. The implication is that the measurement tool introduced in this study can provide better measurement and control of clustering in coatings and other suspension applications.

In this study, a new successful derivation utilizing some of the original concepts of Fishman et al. was generated and shown to result in a practical and much more useable analytical analysis of the clustering concept. This new model was then applied directly to quantify the influence of flow agents or surfactants in a coating formulation on the CPVC as described by Asbeck.

The purpose of this paper was to show that the generalised viscosity model can correctly characterise suspension data over both a wide range of concentration as well as a wide range of temperature. A second objective of this study was to show theoretically and experimentally how the interaction coefficient from the generalised viscosity model also appears to have some thermodynamic properties.

In this study, many well‐known suspension equations were shown mathematically to be subsets of the generalised viscosity equation. The generalised viscosity equation was also found to be able to be reduced mathematically to two well‐known dilute solution equations (Huggins and Kramer's equations) as well. The relationship between Huggins and Kramer's constants and the interaction coefficient from the generalised viscosity equation yielded the potential to evaluate the solubility characteristics of the interaction coefficient. The value of the interaction coefficient was then found to be able to be evaluated as a function of temperature to enhance an understanding of the thermodynamic characteristics of the interaction coefficient using the data of Bueche.

In this study, a polymer plasticiser system involving polymethyl methacrylate in the plasticiser diethyl phthalate yielded an interaction coefficient, σ, primarily in the expected plasticiser range from 0< σ<1. It was also found that the generalised viscosity equation fit Bueche's polymer plasticiser data remarkably well over the whole concentration range for temperatures ranging from 30°C to 140°C. This study also appeared to show that the interaction coefficient from the generalised viscosity model can apparently characterise thermal transitions as well as thermodynamic solubility for a polymer solute (i.e. polymethyl methacrylate) when viscosity is evaluated over a wide temperature range. This result was particularly significant since Bueche's data covered 25 decades of viscosity on a log scale.

This is the first paper to successfully explore the thermodynamic characteristics of the interaction coefficient of the generalised viscosity equation. This opens up new avenues for evaluating the solubility and thermodynamic characteristics of various additives in solutions and polymeric formulations.

Market-based approaches to environmental management are increasingly common. In 1983 when Joeres and David published their pioneering collection, Buying a Better Environment, the concept was seen as at best novel, and at worst far-fetched. Yet today, conservation and water quality credits are for sale in many developed countries, and the idea of payment for ecosystem services is ubiquitous in environmental policy circles. This paper traces that shift from command-and-control to market-based environmental management through analysis of the evolving practice of stream mitigation banking (SMB) in the US. In the most common form of SMB today, a for-profit company buys land with a damaged stream on it and restores it to produce mitigation credits which can then be purchased by developers to fulfill their permit conditions under the Clean Water Act. Though decidedly noncommercial in origin, SMB was converted into for-profit tradable regulatory mechanism in 2000 and has since spread rapidly across the US with the strong support of the US Environmental Protection Agency. Using Bourdieu’s field concept as a framework, I argue that the neoliberal transformation of mitigation banking is a product of both relations within the regulatory field, of that field’s relations with the fields of science, and of power.

Within the past 20 years hiking and backpacking have enjoyed rapid growth among Americans as favorite outdoor activities. From 1965 to 1977 the number of hikers almost tripled, from 9.9 million to 28.1 million, while national forest visitor days among hikers and mountaineers increased from 4 million in 1966 to 11 million in 1979. Accompanying this growth in interest has been a boom in books about the sport. These include both “how‐to‐do‐it” volumes and guides to specific geographical areas. Each year brings another spate of books, yet to this compiler's knowledge no bibliography of hiking guides to the Rocky Mountains, one of North America's premier outdoor regions, has yet been attempted. This bibliography is an effort to correct that situation.

The paper aims to study how global pharmaceutical companies such as Pfizer have managed the challenges of pharmaceutical patent expiry.

A case study method was applied. The best-selling brand drug over the past 10 years – Lipitor – was chosen as the case target.

For dealing with this, this paper describes all the details of the corresponding strategies of Pfizer before and after patent expiration of Lipitor. Before patent expiry, Pfizer undertook the activities of direct-to-consumer marketing, pricing strategy for competition, legal delay and me-too drug R&D. After patent expiry, Pfizer chose to carry out continuous marketing for brand, rebate strategy, authorized generics and change to over-the-counter. In addition, diversity and globalization strategy was applied before and after patent expiry.

This research provides strong implication for managing pharmaceutical products before and after patent expiry.

It is strongly recommended for both brand and generic drug companies to design strategies to meet the challenges of pharmaceutical patent expiry.

For the global pharmaceutical market, a conclusion can be drawn that, nowadays, the “patent cliff” is the most significant factor influencing decision-makers to consider futuristic policies. Further, it is also a considerably effective solution for reducing health-care costs for policymakers.

This paper contributes to the field of patent expiry management in high-tech industries such as pharmaceuticals.