# Crystallization

Crystallization or crystallization is the process by which a solid is formed, where atoms or molecules are highly arranged in a structure known as a crystal . Some of the ways in which crystals form are by precipitating a solution , freezing , or sometimes by deposition directly from a gas . The properties of the resulting crystals depend largely on factors such as temperature , air pressure and , in the case of liquid crystals , the evaporation time of the liquid..

Crystallization occurs in two major steps. The first is nucleation, the appearance of a crystalline phase from a supercooled liquid or a supersaturated solvent. The second phase is known as crystal growth, which is an increase in the size of the particles and leads to a crystallized state. An important characteristic of this phase is that the loose particles form layers on the surface of the crystal and lock themselves in open anomalies such as pores, crevices, etc.

Most minerals and organic molecules crystallize readily, and the resulting crystals are usually of good quality, that is, without any visible defects. However, large biochemical particles such as proteins are often difficult to crystallize. The ease with which molecules crystallize strongly depends on the intensity of nuclear forces (in the case of minerals), intermolecular forces (organic and biochemical substances) or intramolecular forces (biochemical substances).

Crystallization is also a chemical solid–liquid separation technique, which involves the mass transfer of a solute from a liquid solution to a pure solid crystalline phase. In chemical engineering, crystallization occurs in a crystallizer. Crystallization is therefore related to precipitation, although the result is not amorphous or disordered, but a crystal.

## Process

There are two major events in the crystallization process, nucleation and crystal growth that are driven by thermodynamic properties as well as chemical properties. Nucleation in crystallizationis the phase where solute molecules or atoms dispersed in the solvent begin to assemble into clusters on a microscopic scale (increasing the solute concentration in a small area), which become stable under current operating conditions. These stable groups form the nucleus. Therefore, clusters need to reach a critical size in order to become stable nuclei. Such critical sizes are determined by many different factors (temperature, supersaturation, etc.). It is in the phase of nucleation that atoms or molecules are arranged in a defined and periodic way that defines crystal structure – note that “crystal structure” is a special term that refers to the relative arrangement of atoms or molecules, Properties of crystals (size and shape) are not macroscopic, although they are a result of the internal crystal structure.

Crystal growth is followed by an increase in the size of the nucleus that succeeds in achieving the critical cluster size. Crystal growth is a dynamic process occurring in equilibrium where solute molecules or atoms move out of solution, and dissolve back into solution. Supersaturation is one of the driving forces of crystallization, as the solubility of a species is an equilibrium process quantified by Ksp Depending on the conditions, either nucleation or growth may be dominant over the other, determining the size of the crystal.

Many compounds have the ability to crystallize with slightly different crystal structures, a phenomenon known as polymorphism. Some polymorphs can be metastable, meaning that although it is not in thermodynamic equilibrium, it is kinetically stable and requires some input of energy to initiate a change in the equilibrium phase. Each polymorph is actually a different thermodynamic solid state and crystal polymorphs of the same compound exhibit different physical properties, such as dissolution rate, size (angle between facets and facet growth rate), melting point, etc. For this reason, polymorphism is of prime importance in the industrial manufacturing of crystalline products. Additionally, crystal phases can sometimes be interconverted by such changes as varying factors such as temperature from rutile phases to anatase titanium dioxide.

## In nature

There are many examples of the natural process that involves crystallization.

Geological time scale process examples include:

• stalactite/stalagmite, forming rings;

Examples of human time scale processes include:

• formation of snowflakes;
• Crystallization of honey (almost all types of honey crystallize).

## Methods

Crystal formation can be divided into two types, where the first type of crystal is composed of a cation and an anion, also known as a salt, such as sodium acetate. The second type of crystal is composed of unmodified species, for example menthol. [1]

Crystal formation can be achieved in a variety of ways, such as: cooling, evaporation, addition of a second solvent to reduce the solubility of the solute (the technique known as antisolvent or sink-out), solvent layering, Sublimation, cation or anion replacement, as well as other methods.

Formation of a supersaturated solution does not guarantee crystal formation, and often requires scratching a seed crystal or glass to create a nucleation site.

A typical laboratory technique for crystal formation is to dissolve a solid in a solution in which it is partially soluble, usually at high temperatures to achieve supersaturation. The hot mixture is then filtered to remove any insoluble impurities. The sieve is allowed to cool slowly. The crystals formed are then filtered and washed with a solvent in which they are not soluble, but miscible with the mother alcohol. The process is then repeated to increase the purity in a technique known as re-crystallization.

For organic molecules that contain solvent channels to retain the three-dimensional structure, microbatch [2] , crystallization [3] under oil and vapor diffusion have been common methods.

### Specialized equipment

Equipment for the main industrial processes for crystallization.

1. Tank crystallizer . Tank crystallization is an older method that is still used in some special cases. In tank crystallization, saturated solutions are allowed to cool in open tanks. After some time the mother liquor is drained and the crystals are removed. Controlling the nucleation and size of crystals is difficult. citation needed ] Typically, labor costs are very high. citation needed ]

## Thermodynamic view

The crystallization process appears to violate the second principle of thermodynamics. Whereas most processes that yield more systematic results are achieved by applying heat, crystals typically form at lower temperatures—particularly by supercooling. However, the entropy of the universe increases due to the release of the heat of fusion during crystallization, thus the principle remains unchanged.

The molecules of a pure, complete crystal, when heated from an external source, will become liquid. This happens at sharply defined temperatures (different for each type of crystal). As it liquefies, the complex architecture of the crystal collapses. Melting occurs because the entropy ( S ) gain in the system by the spatial randomization of molecules outweighs the enthalpy ( H ) loss due to breaking crystal packing forces :

{\displaystyle T(S_{\text{liquid}}-S_{\text{solid}})>H_{\text{liquid}}-H_{\text{solid}},}

With regard to crystals, there are no exceptions to this rule. Similarly, when molten crystals are cooled, the molecules will return to their crystalline form when the temperature drops beyond that. This is because thermal randomization of the surroundings compensates for the loss of entropy that results from the re-ordering of molecules within the system. Liquids that crystallize upon cooling are the exception rather than the rule.

The nature of the crystallization process is governed by both thermodynamic and kinetic factors, which can make it highly variable and difficult to control. Factors such as impurity level, mixing arrangement, vessel design and cooling profile can have a major impact on the size, number and shape of crystals produced.

## Dynamics

As mentioned above, a crystal is formed following a well-defined pattern, or structure, which is determined by the forces acting at the molecular level. As a result, during the process of its formation the crystal is in an environment where the concentration of the solute reaches a certain critical value before it changes position. Solid formation, which is impossible below the solubility limit at a given temperature and pressure condition, may then occur at a concentration higher than the theoretical solubility level. The difference between the actual value of the solute concentration at the crystallization limit and the theoretical (constant) solubility limit is called supersaturation and is a fundamental factor in crystallization.

### Nucleus

Nucleation is the initiation of a phase change in a small area, such as the formation of a solid crystal from a liquid solution. This results in rapid local fluctuations at the molecular scale in a homogeneous phase that is in a state of metastable equilibrium. Total nucleation is the sum effect of two categories of nucleation – primary and secondary.

#### Primary nucleation

Primary nucleation is the initial formation of a crystal where no other crystals are present or where, if crystals are present in the system, they have no effect on the process. This can happen in two situations. The first is homogeneous nucleation, which is nucleation that is not affected in any way by the solid. These solids include the walls of the crystalline vessel and particles of a foreign substance. The second category, then, is heterogeneous nucleation. It occurs when solid particles of foreign matter cause an increase in the rate of nucleation that otherwise cannot be observed without the existence of these foreign particles. Homogeneous nucleation rarely occurs in practice because of the high energy required to initiate nucleation without a solid surface to catalyze the nucleation.

Primary nucleation (both homogeneous and heterogeneous) is modeled with the following:

{\displaystyle B={\dfrac {dN}{dt}}=k_{n}(c-c^{*})^{n},}


Where fromb is the number of nuclei formed per unit volume per unit time,N is the number of nuclei per unit volume,n is a rate constant,c is the instantaneous solute concentration,* is the solute concentration at saturation,( c – * ) is also known as supersaturation,n is an empirical exponent that can be as large as 10, but is usually between 3 and 4.

#### Secondary nucleation

Secondary nucleation is the formation of a nucleus due to the impact of microscopic crystals existing in the magma. [5] Simply put, secondary nucleation occurs when crystal growth is initiated by contact with other existing crystals or “seeds”. [6] The first type of known secondary crystallization is caused by fluid shear, the second by collisions between pre-existing crystals, either with a solid surface of the crystallizer or with other crystals themselves. Fluid-shear nucleation occurs when the liquid travels at high speed in a crystal, sweeping away nuclei that would otherwise join a crystal, allowing the drifting nuclei to form new crystals. Contact nucleation has been recognized as the most effective and common method for nucleation. Benefits include the following: [5]

• Allows for easy control without unstable operation, thanks to low kinetic order and rate-proportional supersaturation.
• Occurs at low supersaturation, where the growth rate is optimal for good quality.
• The low energy required at which crystals collide keeps existing crystals from breaking into new crystals.
• Quantitative fundamentals have already been isolated and are being incorporated into practice.

The following model, although somewhat simplified, is often used to model secondary nucleation:

{\displaystyle B={\dfrac {dN}{dt}}=k_{1}M_{T}^{j}(c-c^{*})^{b},}

Where from

k 1 is a rate constant,
m t is the suspension density,
j is an empirical exponent that can be up to 1.5, but is usually 1.
b is an empirical exponent that can be up to 5, but is usually 2.

### Development

Once the first small crystal, the nucleus, it acts as a convergence point (if unstable due to oversaturation) for solute molecules touching the crystal – or near the crystal – so that it forms its own in successive layers. to increase the dimension. The growth pattern resembles an onion ring, as shown in the figure, where each color indicates the same mass of solute; This mass forms increasingly thin layers due to the increasing surface area of ​​the growing crystal. The rate of growth expressed in kg/(m 2 *h) of the supersaturated solute mass that the parent nucleus can hold in one time unitis called , and it is a constant specific to the process. The growth rate is influenced by many physical factors, such as the surface tension of the solution, pressure, temperature, relative crystal velocity in solution, Reynolds number, and so forth.

Therefore the main values ​​to control are:

• supersaturation value as an index of the amount of solute available for crystal growth;
• The total crystal surface in unit liquid mass, as an index of the potential of the solute on the crystal;
• retention time, as an index of the probability of a molecule of solute coming into contact with an existing crystal;
• The flow pattern, again as an index of the probability of a solute molecule to come into contact with an existing crystal (high in laminar flow, low in turbulent flow, but the opposite applies to the probability of contact).

The first value is a result of the physical characteristics of the solution, while the others define the difference between a well-designed and a poorly designed crystallizer.

### Size distribution

The appearance and size range of the crystalline product is extremely important in crystallization. If further processing of crystals is desired, larger crystals with uniform size are important for washing, filtration, transport and storage, as larger crystals are easier to filter from solution than smaller crystals. Furthermore, larger crystals have a smaller surface area to volume ratio, allowing for higher purity. This high purity is due to the low retention of the mother liquor which contains impurities, and a small loss of yield when the crystals are washed to remove the mother liquor. In special cases, for example, during drug manufacturing in the pharmaceutical industry, Smaller crystal sizes are often desired to improve drug dissolution rates and bioavailability. Theoretical crystal size distribution can be estimated as a function of operating conditions with a fairly complex mathematical procedure called population equilibrium theory (using population equilibrium equations).

## Main crystallization processes

Some of the important factors affecting solubility are:

• concentration
• Temperature
• Solvent Mixture Composition
• difference of opinion
• ionic strength

So one can identify two main families of crystallization processes:

• cold crystallization
• evaporative crystallization

This division is not really clear, because hybrid systems exist, where cooling is done through evaporation, thus achieving the concentration of the solution at the same time.

One crystallization process often referred to in chemical engineering is fractional crystallization. It is not an isolated process, but a special application of one (or both) of the above.

### Cold crystallization

#### Application

Most chemical compounds that dissolve in most solvents show so-called direct solubility, that is, the solubility limit increases with temperature.

Therefore, whenever the conditions are favourable, crystal formation occurs only by cooling the solution. cooling hereA relative term is: austenite crystal as a steel is above 1000 °C. An example of this crystallization process is the production of Glauber’s salt, which is a crystalline form of sodium sulfate. In the diagram, where the equilibrium temperature is on the x-axis and the equilibrium concentration (as a mass percentage of the solute in a saturated solution) is on the y-axis, it is clear that the sulfate solubility quickly decreases below 32.5 °C. Is. Assuming a saturated solution at 30 °C, by cooling it to 0 °C (note that this is possible for freezing-point depression), precipitation of the sulfate mass corresponds to a change in solubility by 29% (equilibrium). . value 30 °C) to about 4.5% (at 0 °C) – a really large crystal mass precipitates, as sulfate enters the hydration water,

There are limitations to the use of cooling crystallization:

• Many solutes precipitate as hydrates at low temperatures: in the previous example this is acceptable, and also useful, but it can be harmful, for example, providing a mass of water of hydration to reach a stable hydrate crystallization form. is greater than water: a block of hydrate solutes will form – this is the case with calcium chloride );
• The coldest points will have maximum supersaturation. These may be heat exchanger tubes that are sensitive to scaling, and heat exchange may be greatly reduced or turned off;
• A decrease in temperature usually implies an increase in the viscosity of a solution. Too high a viscosity can give hydraulic problems, and the laminar flow thus created can affect the crystallization dynamics.
• This does not apply to compounds with reverse solubility, a term to indicate that the solubility increases with a decrease in temperature (an example is with sodium sulfate where the solubility is reversed above 32.5 °C).

#### Cooling crystallizer

The simplest cooling crystallizers are tanks provided with a mixer for internal circulation, where temperature reduction is achieved by heat exchange with an intermediate fluid circulating in a jacket. These simple machines are used in batch processes, such as in the processing of pharmaceuticals, and are prone to scaling. Batch processes typically provide a relatively variable quality of product with a batch.

The Swenson–Walker Crystallizer is a model, especially employed by the Swenson Co. around 1920, having a semicylindric horizontal hollow trough, consisting of a hollow screw conveyor or some hollow disc, into which a cooling fluid is delivered, during rotation. Dip on a longitudinal axis. The refrigerating fluid is sometimes circulated in a jacket around the cistern. The crystals precipitate on the cold surfaces of the screw/disc, from where they are removed by scrapers and settle at the bottom of the trough. The screw, if provided, pushes the slurry towards a discharge port.

A common practice is to cool the solution by flash evaporation: when during a particular T a liquid at temperature 0 is transferred to a chamber at a pressure P 1 such that the liquid saturation T is lower than that of 1 T at temperature P 0 , the liquid will release heat by the temperature difference and the amount of solvent, whose total latent heat of vaporization is equal to the difference in enthalpy. In simple words, a part of a liquid is evaporated and cooled.

In the sugar industry, vertical cooling crystallizers are used to remove molasses in the final crystallization stage downstream of the vacuum pan, before centrifugation. The mesquite enters the crystallizer at the top, and the cooled water is pumped through a pipe in the counterflow.

### Evaporative crystallization

Another option is to achieve crystal precipitation by raising the solute concentration above the solubility limit, at a nearly constant temperature. To achieve this, the solute/solvent mass ratio is increased using the technique of evaporation. This process is insensitive to changes in temperature (as long as the hydration state remains unchanged).

All considerations on the control of crystallization parameters are similar to those of the cooling model.

#### Evaporative crystallizer

Most industrial crystallizers are of the evaporative type, such as the very large sodium chloride and sucrose units, producing more than 50% of the total world production of crystals. Most common type of forced circulation(FC) is the model (see Evaporator). A pumping device (a pump or an axial flow mixer) keeps the crystal slurry in homogeneous suspension throughout the tank, including the exchange surfaces; By controlling the pump flow, control of the contact time of the crystal mass with the supersaturated solution is achieved with the appropriate velocity at the exchange surfaces. Oslo, mentioned above, is a refinement of the evaporative forced circulation crystallizer, which has longer retention times (usually lower in FC) and a larger crystal settling area to separate the heavier solution regions from the clear liquid. Equipped with. Evaporative crystallizers produce larger average crystal sizes and have narrower crystal size distribution curves. [7]

### dtb crystallizer

Whatever the form of the crystallizer, in order to achieve an effective process control, it is important to control the retention time and crystal mass, in order to achieve optimum conditions in terms of crystal specific surface and fastest possible growth. This is achieved by a separation of the crystals from the liquid mass, in order to manage the two flows in a different way. The practical approach is to demonstrate gravity to be able to extract (and possibly separately recycle) the (nearly) clear liquid, while managing the mass flow around the crystallizer to obtain the exact solution density elsewhere. Is. A typical example is the DTB ( Draft Tube and Baffle) of Richard Chisham Bennett (a Svenson engineer and later Svenson’s president) in the late 1950s.) is the crystallizer. The DTB crystallizer (see picture) has an internal circulator, usually an axial flow mixer – yellow – pushed upward in the draft tube while an annulus outside the crystallizer has a settling region; In this the exhaust solution moves upward at a very low velocity, so that the larger crystals settle down – and return to the main circulation – while below a given grain size only the fine is removed and eventually reduced by increasing or decreasing the temperature. is destroyed, leading to additional construction. Oversaturation. Semi-complete control of all parameters is achieved as DTF crystallizers provide finer control over crystal size and characteristics. [8]This crystallizer, and derived models (crystals, CSCs, etc.) may be the ultimate solution if not for a major limitation in evaporative capacity due to the limited diameter of the vapor head and the relatively low external circulation. Allows a large amount of energy to be supplied to the system.