In the area of industrial crystallization, population balances are used to model how the number and properties of the crystals in a crystallizer are generated and eventually appear as the solid product. A population balance is a mathematical description of conservation of number of particles, and accounts for how the number of particles having a particular set of properties (e.g., size, shape, density) may change during the process. The population balance has the same format as a mass balance or an energy balance. However, while mass and energy are conserved, particles having specific properties are not, and the population balance aims to account for how various mechanisms lead to changes. Traditionally, a population balance is a number balance, accounting for the number of particles of each particular size. Even though linear size is by far the most common particle characteristic on which the balance is based, other independent variables of the particle phase space can be of interest and modeled. By particle phase space is meant the multidimensional space of various particle properties. The population balance can also be formulated with more than one independent variable describing different particle properties. For example, if two linear dimensions of the particle are used in its characterization and are included in the modeling, we obtain a balance that also contains a description of shape changes, not only size changes.

In previous chapters, the simple case of two-component systems, i.e., one single solute crystallizing in a solvent (or solvent mixture), was mainly considered. However, because crystallization is most often employed as a purification process, numerous impurities resulting from the upstream part of the process are necessarily present in solution, such as buffer components, residual reactants, intermediates, or by-products. These impurities may affect the crystallization process and the resulting crystal properties, even at low concentration. Besides, additives are sometimes placed intentionally in solution with a view to tuning certain crystal properties. The mechanisms by which impurities and additives dissolved in solution affect the crystallization process can be rationalized in a common framework, so they will both be placed under the umbrella of foreign species in this chapter. The species to be purified will instead be referred to as the host species.

Precipitation and crystallization are the key production steps for shaping the application properties of pigments. Although the technical features of the particle-formation technologies and process design considerations applied for pigment synthesis are quite similar to those for other sparingly soluble substances, some unique differences exist. These differences are to a large extent related to the special application properties of pigments, that is, the coloristic quality of pigments; pigment stability toward light, weather, heat, and chemicals; and their dispersability in application media. To facilitate a better understanding of how the operating conditions applied during precipitation and crystallization control the application properties, this chapter starts with a detailed discussion on the different types of pigments and their properties in Section 16.2. In particular, the discussion is focused on color. Some theoretical background on color perception and color systems is given with the aim of providing the fundamentals for understanding the quality characteristics of pigments. Moreover, it is discussed in some detail how pigment coloristic properties can depend on particle size, and some aspects of the influence of particle size, particle size distribution, and particle morphology on color are also discussed. However, a thorough understanding of these influences is not fully established, and this is still an important field of ongoing research that is aimed at providing solid and rational foundations to pigment particle technology.

Crystallization is one of the most important separation and product-formation technologies in the chemical industry. Typical advantages of crystallization are the low energy consumption, mild process conditions, and high product purity that can be obtained in a single separation step. The future impact of crystallization is even expected to increase further because many new high-added-value products are often in crystalline form. However, future crystalline products are also subject to increasingly stringent product quality requirements related to, for example, flowability, filterability, bioavailability, stability, and dissolution behavior. Product quality requirements for crystalline products typically vary strongly depending on the field of application.

Crystallization is one of the main separation and purification processes in the pharmaceutical, biotechnology, food, microelectronics, fine and bulk chemicals industries. The production of more than 70 percent of all solid products involves at least one crystallization as a key processing step, which can have a significant effect on the overall performance of the entire production process and the properties of the final product. The control of crystallization processes is challenging because of the highly nonlinear dynamics, large variations in length and time scales at which the various simultaneous mechanisms occur, variations in crystallization rates over time owing to variations in the impurity profiles of chemical feedstocks, unexpected polymorphic transformations, and nonideal mixing conditions.

Most crystallizations in the pharmaceutical industry are not carried out by crystallization scientists. The Cambridge Structure Database (CSD) contains over 850,000 crystal structures, and the number of organic molecules that have been isolated as solids is much larger. In many cases these isolations have not been repeated or scaled up. Yet this task, namely the development of robust, reproducible crystallization processes, is the main topic of this chapter. By way of introduction, meet the types of molecules, the types of people, and the nature of the industry.

Crystallization can be regarded as a self-assembly process in which randomly organized molecules in a fluid come together to form an ordered three-dimensional molecular array with a periodic repeating pattern. It is vital to many processes occurring in nature and manufacturing. Geologic crystallization is responsible from huge deposits of carbonates, sulfates, and phosphates that often grow in mountains and quarries. This process occurs over long periods of time, often at high temperatures and pressures, and results in large and usually highly ordered crystals such as diamond.

Batch crystallization is different from continuous crystallization in that the withdrawal of crystal product for the batch system is made only once at the end of the batch run. Batch crystallization may also include the semibatch system, in which one or more feed solutions are added to the crystallizer at a constant or variable rate throughout all or part of the batch.

Batch crystallization is different from continuous crystallization in that the withdrawal of crystal product for the batch system is made only once at the end of the batch run. Batch crystallization may also include the semibatch system, in which one or more feed solutions are added to the crystallizer at a constant or variable rate throughout all or part of the batch.

Precipitation generally refers to a relatively rapid formation of a sparingly soluble crystalline – or sometimes amorphous – solid phase from a liquid solution phase. Precipitation is rather poorly understood when compared with crystallization of more soluble materials. It generally involves the simultaneous and rapid occurrence of nucleation and growth together with the so-called secondary processes, such as Ostwald ripening and agglomeration. In many cases, these processes are difficult to separate and investigate independently and mechanistically.