Supersaturation Control and Heterogeneous Nucleation in

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Ind. Eng. Chem. Res. 2010, 49, 11878–11889

Supersaturation Control and Heterogeneous Nucleation in Membrane Crystallizers: Facts and Perspectives Gianluca Di Profio,*,† Efrem Curcio,‡ and Enrico Drioli‡ Institute on Membrane Technology, ITM-CNR, Rende, Italy, and Department of Chemical and Materials Engineering, UniVersity of Calabria, Rende, Italy

The interest to combine membrane operations and solution crystallization has grown in the past several years. This approach has been put into practice in several forms of membrane-assisted crystallization (MAC) processes, among which is membrane crystallization (MCr) technology. The main features of MCr are (1) the use of membranes as precision devices to control the composition of the crystallizing solution, by opposing a welldefined and tunable resistance to mass flow occurring in the vapor phase; (2) the action of the porous surface of the membrane as a suitable support to activate heterogeneous nucleation mechanisms; (3) the possibility to induce nucleation and crystal growth in separate sites, thus reducing the risk of membrane fouling even when the same membrane supports heterogeneous nucleation. Thanks to these fundamental options, combined together in a unique apparatus, advantages like (i) improved control of the supersaturation degree and the rate of its generation; (ii) the possibility for the crystallization to be initiated at low supersaturation levels; (iii) the enhancement of the crystallization kinetics; and (iv) improved overall process efficiency can be achieved, even for large and complex molecules like proteins. The most interesting developments and the more exciting perspectives for this novel technology have been reviewed in this paper. 1. Introduction Crystallization is one of the most important separation and product formulation processes in the chemical industry. It is currently employed to produce innumerous daily used products like additives for hygiene and personal care commodities, pharmaceuticals, fine chemicals, pigments, and several others. Generally, crystal properties have a remarkable impact with respect to their uses. Crystals’ morphology (intended as crystal shape, habit, size, and size distribution) is crucial in this sense. Specific crystals’ shapes are preferred for more efficient downstream operations like filtration, drying, compaction, and storage. Particles’ size has remarkable influence in heterogeneous catalysts: smaller size is associated to a higher surface to volume ratio and thus enhanced efficiency.1,2 Monodisperse in size and uniformly shaped crystals are better suited to achieve a constant dissolution rate and bioavailability in the case of drugs. Polymorphism is another aspect which plays a primary role in the pharmaceutical industry.3 This is because the different polymorphic forms of the same substance display their own physicochemical characteristics so that each of them can be considered as a specific material, different from the others; this would also have significant consequences in the protection of intellectual properties. Crystals with elevated structural order are also necessary to resolve at an atomic level the tridimensional structure of biomacromolecules, by X-ray diffraction analysis, to design and synthesize appropriate drugs.4 Despite this, current approaches to crystallization still suffer of some limitations which affect both product quality and process efficiency. Irreproducibility in the final crystal characteristics is mainly associated with poor supersaturation control due to imperfect mixing, reduced and inhomogeneous distribu* To whom correspondence should be addressed. Mailing address: Via P. Bucci Cubo 17/C 87036, Rende (CS). Tel.: +39 0984 492010. Fax: +39 0984 402103. E-mail: [email protected]; gdiprofio@ hotmail.com. † Institute on Membrane Technology, ITM-CN. ‡ University of Calabria.

tion over the plant of solvent removal or antisolvent addition points, and a reduced possibility to modulate the supersaturation generation rate.5 In currently used industrial evaporator crystallizers, the limited available surface area for evaporation limits the rate at which supersaturation is generated. Moreover, thermally sensitive molecules cannot be normally processed by these approaches. The possibility to develop new equipments and strategies, by which crystallization processes can be operated in a more controlled way, would represents a fundamental success in this story. On these bases, in the past few years, several attempts were done to introduce membrane operations in crystallization. In fact, membranes represent a technology which well satisfies the concepts of the process intensification strategy and the rationalization of chemical productions, leading to significant innovation in both processes and products. Accordingly, membrane technology has been thought as a valid instrument to introduce significant improvements in crystallization.6 This paper overviews current development of what is defined by the authors membrane crystallization technology and outlines main advantages, current limitations, and potential impacts for the future. 2. Membranes and Crystallization Operations Occurrence of crystallization phenomena has being observed since the beginning in the utilization of membranes. However, the interest in this event was principally addressed to adopt strategies aiming to avoid it, because crystal formation above the membrane surface or inside the pores would provoke dramatic flux decline7–10 and precocious degradation of the membrane itself.7,11 On the bases of these experiences, crystallization occurring during membrane operations was initially considered only as a side effect.12 The first application of a membrane unit properly as a crystallizer dates to 1986, when the precipitation of calcium oxalate in reverse osmosis (RO) hollow fibers were used to simulate the early stages of stone formation in the renal tubules.13–15 In 1989, the possibility to crystallize a solute in a

10.1021/ie100418z  2010 American Chemical Society Published on Web 06/14/2010

Ind. Eng. Chem. Res., Vol. 49, No. 23, 2010

controlled manner by using membrane distillation (MD) at sufficiently high concentration was proposed.16 In 1991, the same concept was put in practice by recovering Taurine crystals during pharmaceutical wastewater purification.17 In the same year, RO membranes were tested for the controlled crystallization of biomacromolecules in an osmotic dewatering system.18 Other than MD and RO, no significant applications of other membrane operations for crystallization have been explored until the end of the 1990s. As a rare example, Sluys et al.19 described a membrane-assisted crystallization (MAC) process for the softening of drinking water in which microfiltration (MF) was used to increase the concentration of a suspension of foreign seeds, up to the level required for seeded crystallization. In 2001 the term membrane crystallizer (MCr)sand membrane crystallizationswas coined.20 It refers to the innovative concept by which crystal nucleation and growth is carried out across a well-controlled pathway, starting from an undersaturated solution, by adjusting solution composition (supersaturation) by means of a membrane. The working principle of what is defined today as a membrane crystallizer can be considered as the extension of the membrane distillation/osmotic distillation concepts. According to this design, porous hydrophobic membranes were used to crystallize inorganic salts,20–26 small organic compounds,27 and bio(macro)molecules.28–34 High-quality protein crystals, suitable for X-ray diffraction analysis at atomic resolution, were grown by using this approach.31,35,36 In more recent years, other MAC operations based on nanofiltration (NF)37 and, mainly, on RO38–43 stages, to concentrate a stream prior to batch cooling crystallization, have been studied. MF membranes have been used to dose an antisolvent in a crystallizing solution (or vice versa) to produce solid particles with narrow crystal size distribution (CSD).44,45 The same concept was used later for the crystallization of L-asparagine monohydrate.46 In this system, solutions (whatever the crystallizing solution or the antisolvent) are pressed directly in the liquid phase through the porous membrane by overcoming its breakthrough pressure. In a diverse approach, the extension of the membrane crystallization concept to antisolvent operation, where a porous membrane is used to dose the amount of antisolvent in the crystallizing solution, has been proposed later.47 Here, solvent/ antisolvent composition inside the crystallizing solution is controlled by migration in the vapor phase, according to the general concept of the membrane crystallization process and, dissimilarly with the above-mentioned configuration, not by forcing it in the liquid phase through the membrane. In a further design of MAC, crystals were obtained after a reaction occurring between two solutions contacted by a porous membrane. Crystals of BaSO4 were obtained after a solution of a BaCl2 had been pressed through the membrane into a K2SO4 solution on the other side. The resulting supersaturation induced nucleation and particles grew on the lumen side of hollow fibers membranes.48,49 According with the excursus above, membrane-assisted crystallization can be classified, in dependence of the different working principles, as (1) Membrane distillation/osmotic distillation-based processes, where under the action of a gradient of vapor pressure as driving force, solvent molecules sweep up from the feed side, diffuse in vapor phase through a porous membrane, and recondensate on the opposite side generating supersaturation in the crystallizing solution;

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(2) Hybrid processes in which pressure-driven membrane operations (mainly RO) are used to concentrate a solution, by solvent removal in the liquid phase while the solute is retained by the membrane, due principally to a sizeexclusion effect, and crystals are recovered in a separate tank often operated at lower temperature and with seeding; (3) MAC where an antisolvent is forced directly in the liquid state into the crystallizing solution (or vice versa) through the pores of a membrane under a pressure gradient and, as long as it diffuses in the crystallizing solution, exchanges with the original solvent thus producing the abrupt abatement of solubility and solute precipitation; (4) Antisolvent membrane crystallization (AMCr), where dosing of the antisolvent in the crystallizing solution is carried out by means of a membrane in vapor phase, according with the same working principle described in the point 1; (5) Membrane-assisted operations where two solutions containing different reactants are contacted, in the liquid state, by means of a porous membrane so that a solid crystalline product separates after (chemical) reaction among them upon diffusion in the liquid reaction medium. Although membranes are involved in all the above-described MAC configurations, working on the base of diverse principles, with the term membrane crystallization the authors refer in this paper only to the processes as those described in points 1 and 4, and only these configurations will be discussed in the remainder of this review. 3. Working Principle of Membrane Crystallizers Detailed relations and models for heat and mass transport in MCr can be derived from the same concepts developed for membrane distillation and osmotic distillation.50–59 Therefore, their thorough description is outside the scope of this review and only some fundamental equations, related to mechanism introduced in the points 1 and 4 of the previous section, will be described here. In its current general conception what is defined as a membrane crystallizer is a system in which a solution containing a nonvolatile solute, which is likely to be crystallized (defined as the crystallizing solution or feed or retentate), is contacted, by means of a porous membrane, with a solution on the distillate side. The membrane might be made by polymeric or inorganic materials or by a combination of both in a hybrid or composite configuration. Hollow fibers as well as flat sheet membranes can be employed indifferently. When the membrane is prevented to be wet from the adjacent solutions, no mass transfer through its porous structure is observed directly in the liquid phase, but the two contacted subsystems are subjected to mass interexchange in the vapor phase. Wetting of the membrane, with the consequent deleterious direct passage of liquids, can be avoided when the pressure of the liquids is lower than the entry limit (Pentry), defined by the Young-Laplace equation:60 Pentry ) -

2γL cos R rp

(1)

where γL is the liquid surface tension, rp is the pore radius, and R is the contact angle between the membrane and the solution. Equation 1 shows that for R comprised between 90° and 180° Pentry is positive. This means that hydrophobic membranes must be used for hydrophilic (aqueous) crystallizing solutions while hydrophilic membrane materials can be potentially suitable for

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the crystallization of species soluble in organic (oleophilic) media. For a pressure lower than Pentry, the two liquids are stopped at the entrance of each pore on both membrane sides. Crystals’ nucleation and growth in the feed solution is induced when supersaturation is generated by removing solventsincreasing solute concentration above its solubility limitsor by adding an antisolventswhich reduces the solubility of the solute in the mixed solvent/antisolvent solution. Accordingly, the role of the membrane in MCr is not as a sieving barrier to select the transport of specific components, but as a physical support able to generate and sustain a controlled supersaturated environment in which crystals can nucleate and grow. In the porous structure, if surface diffusion is assumed negligible, mass transfer can be affected by viscous resistance (resulting from the momentum transferred to the supported membrane), Knudsen diffusion resistance (due to collisions between molecules and membrane walls) or ordinary diffusion (due to collisions between diffusing) molecules.58 Predominance, coexistence, or transition between all of these different mechanisms are estimated by comparing the mean free path of diffusing molecules to the mean pore size of the membrane. In MCr usually macroporous membranes (pore size >50 nm) are used to provide consistent transmembrane flux (productivity). Considering its diameter at room temperature and pressure (2.75 Å), the approximate mean free path of water molecule passing through the membrane in vapor phase is in the same order of the pore size. Therefore, the reduced Knudsen-molecular diffusion transition form of the dusty-gas model (neglecting surface diffusion) can be used to describe vapor flux Ji across the membrane:50 Ji ) -

(

)

0 DwkDw-a ∆p 1 M RTavg D0 + p Dk δ w-a a w

Dwk )

2εrp 3τ

8RTavg πM

ε 0 Dw-a ) 4.46 × 10-6 Tavg2.334 τ

(2)

(3)

(4)

where ∆p is the vapor pressure gradient across the membrane, rp is the pore radius, δ is the membrane thickness, τ is the tortuosity factor, M the molecular weight, Tavg the average temperature, and Dwk is the Knudsen diffusion coefficient. In the frequent case of nonideal mixtures, the vapor-liquid equilibrium is described in terms of partial pressure pi, vapor pressure of pure i (p0i ), and activity coefficient ξi, according to the relationship: pi ) Pyi ) p0i ai ) p0i ξixi

(5)

where xi and yi are the liquid and vapor mole fraction, respectively. The vapor pressure p0 of a pure substance varies with temperature according to the Clausius-Clapeyron equation: dp0 λ ) dT RT2

(6)

where λ is the latent heat of vaporization. The expression for activity coefficient in diluted aqueous ionic solutions can be derived from the Debye-Hu¨ckel theory: log ξ( ) -|z+z1 |Ψ√I

(7)

Here ξ( is the activity coefficient of the electrolyte, Ψ is a constant which depends on the temperature and solution permittivity, z( is the ion valence, and I the ionic strength of the solution, given by I)

1 2

∑z

2 i

ci

(8)

i

According to eqs 2-8, transmembrane flux of a component from one phase to the other depends on both the driving force ∆p and the membrane characteristics: ε, rp, τ, δ. Migrating molecules experience a resistance which depends on these properties, which are fixed once a specific membrane is chosen, while the strength of the driving force is fixed by the combination of some operating conditions affecting ∆p. The different parameters which might affect ∆p would influence both the extent and the rate of evaporation. As ∆p is directly proportional to the activity gradient ∆a of the volatile component(s) and it is also dependent on temperature, the driving force is established by a temperature or an activity difference between the two contacted solutions. In the first case, the system is said to be a thermal membrane crystallizer; when the driving force is due to an activity gradient, generated by a difference in ionic strength, the system is named an osmotic (or isothermal) membrane crystallizer. The specific mechanism for mass transport depends on the operational configuration. Two cases may exist: (1) solvent evaporation membrane crystallizer (thermal or isothermal), in which solvent is removed in vapor phase from the crystallizing solution, and (2) antisolvent membrane crystallizer, where an antisolvent is dosed in the vapor phase inside the crystallizing solution by means of the membrane. Under the action of the driving force, solvent or antisolvent molecules sweep up in vapor phase from the site where their vapor pressure is higher, move through the porous membrane, and recondensate in the liquid state on the lower vapor pressure side, thus generating supersaturation and, hence, nucleation and crystal growth. The effective excess of solute concentration with respect to its solubility (supersaturation, S), and the rate of its variation, depends on the transmembrane flux. As supersaturation is the driving force for crystallizationsand both nucleation and crystal growth rates depend on itsthe final properties of the crystals can be affected by acting on S, by selecting the membrane with the opportune characteristics and adjusting the working conditions. 4. Operational Configurations 4.1. Solvent Evaporation Membrane Crystallizer. In this configuration, the substance to be crystallized is dissolved in an under-saturated solution located at the feed side of the membrane, as depicted in Figure 1. According with the general working principle of a membrane crystallizer, described in section 3, the membrane must be prevented to be wet by the contacted solutions, because mass exchange has to occur only in the vapor phase. To avoid wetting, hydrophobic membrane materials are preferred for aqueous solutions in currently used MCr; theoretically, the principle can be reversed and hydrophilic membranes can be potentially used for oleophilic liquids in the crystallization of nonvolatile species soluble in organic medias. In the most common arrangement, the distillate side of the membrane consists in a condensing fluid (often the pure solvent)sin the case of thermal activation of the driving forcesat a lower temperature than the feed side, or in a stripping hypertonic solution of inert salts (NaCl, CaCl2, etc.), in the case of the isothermal configuration. The gradient of vapor pressure


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Figure 1. General principle of a membrane crystallizer: volatile molecules (solvent or antisolvent) move through the membrane by a mechanism of evaporationmigration-condensation. Not-volatile solute molecules concentrate on the feed side thus achieving the thermodynamic condition for crystallization.

between the two subsystems induces a mechanism of evaporation of the solvent at the first interface on the feed side, the migration of the solvent in vapor phase through the porous membrane, and, finally, its recondensation at the second interface on the distillate (Figure 1). The continuous removal of solvent from the feed solutions increases solute concentration thus generating supersaturation. As solvent evaporates from the feed, the establishment of the concentration polarization layers adjacent to the membrane face occurs. Accordingly, the solute concentration in the polarization layer close to the membrane surface, cm, is higher with respect to the bulk solute concentration, cb, on the feed sides. According to eq 9, this concentration polarization layer is related to the transmembrane flux J:54 cm J ) exp cb k

()

(9)

where k is the mass transfer coefficient. In MCr usually low fluxes (in the order of a few liters per hour square meter) are used to control gently the supersaturation. Therefore, concentration polarization does not represent a limiting factor to the driving force, as it is for example in RO. Due to the change of the physical state of volatile component (solvent) at the interface between the solutions and the membrane, heat is absorbed by vaporized molecules on the feed side and released on the distillate side after condensation, so that temperature polarization also exists across the membrane. Although temperature polarization generally represents the major limiting factor in MD,55 in the case of MCr both concentration and temperature polarization might affect locally the degree of supersaturation and the mechanism of nucleation can proceed in a different way close to the membrane with respect to the bulk. The crystals nucleated and grown on/near the membrane might display particular characteristics due to these phenomena.61 4.2. Antisolvent Membrane Crystallizer (AMCr). The system operates according to the two schemes depicted in Figure 2. In solvent/antisolvent demixing configuration (Figure 2a), a certain solute is dissolved in an appropriate mix of a solvent

and an antisolvent, whose composition is chosen in such a way that the solute remains indefinitely in solution in the original conditions. When a gradient of vapor pressure is generated between the two sides of the membranes by a temperature difference, the solvent, which is supposed to have at the same temperature a higher vapor pressure than the antisolvent, evaporates at higher rate thus producing a certain solvent/ antisolvent demixing. As the amount of solvent in the mixture decrease, the lower solubility of the solute generates supersaturation and a phase separation occurs when the antisolvent exceeds a certain volume fraction. The requirements for this configuration are that (i) the antisolvent and the solvent are miscible; (ii) the solute is under its solubility limit in the initial solvent/antisolvent mixture; (iii) the solvent evaporates at higher velocity than the antisolvent; (iv) the solvent and the antisolvent do not form azeotropes or, if they do, solution supersaturation needs to occur before the azeotropic composition point. This configuration might be particularly indicated for the crystallization of mixtures of species recovered by aqueous/organic solvent extraction combinations. In the antisolvent addition configuration (Figure 2b), a solute is dissolved in a solvent and then an antisolvent is gradually evaporated from the other side of the membrane by applying a gradient of vapor pressure. As the antisolvent mixes with the solvent, the solute dilutes for the increase of total volume but, at the same time, the composition of the mixture changes. Above the solubility limit in the solvent/antisolvent mixture, the excess of antisolvent creates supersaturation and solute crystallization. This configuration requires that the antisolvent and the solvent are miscible. In this case, the specie to be crystallized can be soluble in aqueous solutions and poorly soluble in organic, low boiling, liquids. In AMCr, a certain amount of solvent might be present initially in the distillate/retentatesdepending on the configurationsto modulate the rate of solvent removal in demixing configuration or to avoid wetting of the membrane, when using the pure antisolvent, in antisolvent addition, respectively. This is the case when using ethanol, which it is known to wet a wide

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Figure 2. Principle of an antisolvent membrane crystallizer: (a) solvent/antisolvent demixing and (b) antisolvent addition configurations. Tf feed temperature; Td distillate temperature.

compilation of membrane materials, both hydrophilic and hydrophobic, when used as pure. A mixture of water/ethanol, in which ethanol has a volume fraction below 35% v/v, might be useful to avoid wetting of polypropylene membranes.54 Furthermore, also in the case of antisolvent membrane crystallizer, hydrophilic membranes can be potentially used in a reversed process, depending on the character of the contacted solutions, provided that wetting of the membrane is avoided. 5. Control of Supersaturation 5.1. Effect on Crystal Morphology and Purity. Crystals’ morphology reflects the balance between the extent of nucleation and crystal growth rates in the crystallization kinetics. Usually, a low level of supersaturation (inside the metastable zone) favor the growth process, with the production of a limited amount of larger crystals, while a high level of supersaturation supports an excess of nucleation and the formation of a huge number of small particles. In MCr, parameters like solute concentration, concentration of the precipitating agent (if any), concentration of the stripping agent (for the isothermal MCr), solution velocity (for the dynamic system), nature and concentration of the antisolvent (for the AMCr), crystallization solution temperature (Tcry), distillate temperature (Td) (for the thermal system), and the transmembrane temperature gradient (∆T) contribute to establish the initial working point. When using a membrane as precise dosing device to modulate crystallizing solution com-

position, the specific patch which leads, starting from the undersatured solution, to crystallization depends on the evolution of the parameters above, giving rise to different results for the diverse routes followed. The effect would be the variation of the rate and the extent of nucleation over crystal growth with the possibility to generate a broad set of trajectories, that are not readily achievable in conventional crystallization formats, and which would lead to the production of specific crystalline morphologies and structures. Some variations rely on the state of the retentate and are therefore directly related to the solubility of the species to be crystallized. In this case, variations aiming to increase supersaturation in the feed will stimulate excessive nucleation at the expenses of crystal growth, with the appearance of a shower of smaller crystals. On the other side, variation of conditions exclusively related to the distillate would influence only transmembrane flux but not the solubility of the compound. All the variations exclusively related to the distillatese.g. addressed to decrease the transmembrane fluxsare associated with a reduced supersaturation generation rate and hence to a slower crystallization kinetics. This generally translates in longer elapsed time for crystals appearance and to the encouragement of crystals growth over nucleation, with the production of fewer larger particles.30,34 Changes which affect these two opposite aspectssthe transmembrane flux (kinetic) and the solubility (thermodynamic)shave to be carefully balanced during the


design of the crystallization process to achieve the desired final crystals morphology. In the case of hen egg white lysozyme (HEWL) crystallization by MCr, when increasing the initial protein concentrationswhile keeping other conditions constantsa reduced transmembrane flux and its steeper decrease with the time was observed. This would have favored the production of few big crystals. Although the reduction of flux, the increased solute concentration enhanced supersaturation, leading to the undesirable excess of nucleation with the production of a huge amount of small crystals. A similar behavior was observed when increasing precipitant (NaCl) concentration or decreasing crystallization temperature, due to the reduced solubility of HEWL.31,33 Control of transmembrane flux has also an influence on the purity of the products. Normally, crystal purity might be reduced by the high local level of supersaturation which generates a growth rate higher than the critical threshold value which separates regions of impurity inclusion and the growth of more pure crystals. For supersaturation above this critical value, inclusions will more probably occur, whereas at lower growth velocities the tendency to grow purer crystals will rise and inclusions will be less effective. In MCr, the possibility to act on the transmembrane flux, by changing the driving force of the process, allows operating on the proper growth conditions, thus achieving more pure crystals. In the case of sodium chloride crystallization from a NaCl/KCl solutions, low and gentle supersaturation generation rate led to small and well-controlled growth rates and hence to the production of purer crystals in one step.25 5.2. Influence on Polymorphism. Many substances can exist in solid crystalline state as several phases, a phenomenon named polymorphism. Each polymorph is characterized by its specific physical properties, like solubility, dissolution rate, thermal and mechanical stability, optical properties, etc. Each form represents a specific, patentable, material. Among the different phases, the relative stability in a specific condition is ruled by thermodynamics, as described by the classical nucleation theory (CNT).62 However, the phase that will be effectively obtained depends on kinetics.63 This is because a competition between the thermodynamic and kinetic control of the nucleation phase can affect the final outcome of the process. According to the CNT concepts, the stationary rate of nucleation N, can be described by the following equation: N ) A exp

( ) -W* kB T

(10)

where kB is the Boltzmann’s constant, A is a pre-exponential kinetic parameter, and W* is the nucleation work. In the approximation of spherical particles, the nucleation work in the exponent is defined as W* )

16πυ02γ3 3(kBT)2 ln2 S

(11)

where ν0 is the molecular volume and γ is the interfacial energy. This equation shows that the degree of supersaturation might govern the occurrence in the nucleation of the different forms of the same substance. Let us to consider, for the sake of simplicity, a dimorphic system, with the two polymorphs A and B having a different solubility with the stable polymorph A having the lowest at a specific temperature. According to eq 11, the height of the nucleation barrier that separates the stable and the metastable phases is increased by a large difference in

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Figure 3. Different pathway in crystallization of stable and metastable phases in a dimorphic molecular system for which ∆G *A > ∆G *B.

solubility and interfacial energy between the two forms. This can be seen in a typical energy-reaction coordinate diagram, as that showed in Figure 3, where it is displayed the free energy variation ∆G of a solute in a supersaturated fluid which transforms, by crystallization, into one of two crystalline products A or B. Associated with each reaction pathway is a transition state and an activation free energy which is implicated in the relative rates of formation of the two structures. As A is the more stable (less soluble), its supersaturation is always higher than that of form B: SA > SB. However, three situations might occur: (1) γA < γB, so that the activation energy for the stable polymorph is lower than that of the kinetic form (∆G*A < ∆G*B); (2) γB , γA, so that the difference of interfacial energy in eq 11 overcomes the difference in supersaturation with the final consequence that the activation energy for the stable polymorph is higher than that of the kinetic form (∆G*A > ∆G*B); (3) the solubility and the interfacial energy for the two phases are very close to each other so that ∆G*B ≈ ∆G*A. In the first case, the formation of the stable form A is thermodynamically favored and it will be obtained. In this situation, if the metastable phase is the desired product, a variation in solute solubility and/or in interfacial energyse.g. by changing solution composition in antisolvent crystallizationscan favor the formation of the phase B. In the second case, not necessarily the most stable form is the first to appear and a scenario as that depicted in Figure 3, in which two different paths can be followed, can develop. This arises since such systems are subject to the issue of the growth of one form over another, which is described by Ostwald’s rule of stages, which states that “when leaving a metastable state, a given chemical system does not seek out the most stable state, rather the nearest metastable one that can be reached without loss of free energy”.63 Although it is generally known that this rule is not a physical law and that more stable phases can form

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directly as said above, it appears obvious that polymorphism adds a kinetic dimension to crystal growth. Crystallization mechanism involves an activated state related to a collection of self-assembled molecules which exist as a new separate solid phase. The phase boundary is associated with an increase in free energy of the system which must be offset by the overall loss of free energy. For this reason, the magnitudes of the activated barriers are dependent on the size (i.e., the surfaceto-volume ratio of the new phase) of the supra-molecular assembly (crystal nucleus). According to Volmer,64 the critical size n* which an assembly of molecules must have in order to be stabilized by further growth is given by the following equation: n* )

32πυ02γ3 3(kBT)2 ln3 S

(12)

The higher the operating level of supersaturation, the smaller this size is (typically a few tens of molecules). Although the supersaturation with respect to B is lower than that for A, if the critical size is lower for B than for A, for a particular solution composition, then the nucleation work is WA*> WB* according to eq 11 and ∆G*A > ∆G*B, so that kinetics will favors form B, following an “Ostwald’s behavior”. The direct formation of the stable phase A will only occur if the system is able to overcome the activation barrier for the thermodynamic form. In any case, eqs 11 and 12 display as the supersaturation degree is the determining factor in this case. In the third situation, the activation free energy for the two phases differs only slightly, so that the probability of the two forms to nucleate concomitantly is very high and the nucleation of both polymorphs occurs. In this last case are the relative growth rates of the diverse forms with respect to the rate of conversion of the kinetic product into the stable one that will influence the final outcome of the process. The competitiveness of all these effects to the reduction of the nucleation work, the critical nucleus size, and the relative growth/dissolution velocities of the two phases will affect the polymorphic form that will be effectively obtained.65 Therefore, while the degree of supersaturation states the thermodynamic tendency toward the formation of a specific form, the phase that will actually be obtained depends on the rate at which a certain level of supersaturation is generated with respect to the relative nucleation and growth/dissolution rates. From this example it appears clear that the control of supersaturation and the rate of its variation would represent a tool to impact on the thermodynamic/kinetic balance during the crystallization of a polymorphic system, with the consequent possibility to address the growth of a specific phase. In a membrane crystallizer, this kind of control can be achieved by controlling the composition of the crystallizing solution through the management of the transmembrane flux. This provides an opportunity to systematically affect the degree and the rate of variation of the supersaturation which, in turn, affects the polymorphic composition of the precipitate. As this control can be produced very precisely, by fine-tuning the operating conditions and/or by choosing the opportune membrane properties, selective polymorphs crystallization is an important possibility available to operators using MCr. Evidence of this possibility is reported in the selective crystallization of either the R or γ polymorph of the amminoacid glycine,66 the phases I and II of paracetamol,61 or the forms R and β of L-glutamic acid.67 Namely, when the least stable structure (or a mixture of nuclei of the different polymorphs) forms, following an Ostwald-

like behavior, the relative growth rates of the different phases with respect to the supersaturation generation rate will fix which form will effectively be grown. When the rate of variation of supersaturation is low, due to the low evaporation rates through the membrane, if nuclei of the more stable structure have time to grow at the expense of the less stable forms, via solventmediated transfer of solute, a “thermodynamic control” occurs and the more stable polymorph will selectively (or prevalently) be obtained. For higher evaporation rates, the increase in the metastable zone width induces nucleation at higher values of supersaturation. In this situation, the conversion from the metastable to the stable phase could not be fast enough with respect to the growth of the former, so that the kinetic form (metastable), which might be also the first to appear according with the Ostwald rule, is observed. In this case, the overall process is “kinetically controlled”. The same mechanism can be exploited to address the polymorphic composition of the precipitate in antisolvent membrane crystallization processes. The fine dosage of antisolvent in the crystallizing of the aminoacid L-histidine allowed to modulate the amount of the stable and the metastable phases by acting on the transmembrane flux.68 6. Heterogeneous Nucleation Assisted by the Membrane Two molecules that have to form a crystalline contact are brought together by translational diffusion. In order to increase the chance to establish the proper positioning leading to aggregation, molecules need to be adjusted spatially by a subsequent rotational diffusion. This is the ideal situation for what has been defined as homogeneous nucleation, which takes place fundamentally inside extremely pure solutions. The random rotations of molecules, which even slows down very fast with larger molecules like proteins, leads to a reduced chance for the effective molecular interaction. As a consequence, in many crystallization experiments, because the free-energy barrier to homogeneous nucleation is relatively large (of the order of 100 kBT or more), the required saturation levels are not reached, so that nucleation does not occur. To create an environment that favors nucleation, the use of nucleation-inducing (nucleant) surfaces has been attempted for several years.69 Such nucleants could help to enhance the chances of any single trial to produce crystals by facilitating the proper molecular orientation, leading to the formation of crystalline clusters with well-ordered internal organization. Substrate-molecule interactions would reduce the surface tension of the growth units and hence will lower the activation energy for nucleation allowing the crystallization to occur in conditions which would not be adequate for spontaneous nucleation; this effect is termed heterogeneous nucleation.70 A first reason for the attractiveness of heterogeneous nucleation is that nucleation induced at lower degree of supersaturation can occur inside the metastable zone. This is because growth in the metastable zone affords kinetic advantages that often lead to the production of larger and better-ordered crystals than those grown at higher supersaturation. The mechanisms of heterogeneous nucleation might arise from both physical and chemical interaction between the solute molecules and the nucleant. Different surfaces may induce heterogeneous nucleation by different ways: (i) introduction of spatial characteristics related to the crystalline lattice;71 (ii) modification of the supersaturation profile near the surface due to the concentration polarization and/or adsorption of the solute onto the surface by specific interactions;72 (iii) the presence of a surface microstructure, like, e.g., roughness or porosity,


( 21 - 43 cos R + 41 cos R)

∆G*het ) ∆G*hom

Figure 4. Reduction in the free energy of the nucleation barrier due to heterogeneous nucleation as a function of the water contact angle with the polymeric surface (CA cellulose acetate; PAN polyacrylonitrile; PC polycarbonate; PEI polyetherimide; PP polypropylene; PSf polysulfone; PTFE polytetrafluoroethylene; PVDF polyvinylidenefluoride).

conducive to facilitate nucleation.73,74 Although heterogeneous nucleation has been attempted by using several substrates,75–79 none have proved to be generally applicable as a “universal nucleant”. In a membrane crystallizer, the crystallizing solution is in direct contact with the membrane surface, therefore a solutemembrane interaction is likely to occur, depending on the fluidynamic regime. This effect can be due to both the structural and chemical properties of the membrane surface: (1) the porous nature of the surface might supply cavities where solute molecules are physically entrapped leading, locally, to high levels of supersaturation; (2) the nonspecific and reversible chemical interaction between the membrane and the solute can allow to concentrate and orient molecules on the surface without loss of mobility, thus facilitating effective interaction proper for crystallization. In the case of complex molecular systems, like proteins, the different interaction mechanism is dependent on the patches which are available on the molecular surface. Hydrophobic and hydrophilic spots, positively and negatively charged functional groups, and hydrogen bonding moieties are known to provide affinity for almost any kind of nonbiological surface.80 Furthermore, preferential solute-membrane interaction can facilitate specific solute-solute interaction pathways which would lead to the formation of particular crystal structures as in the case of HEWL.81 The energetics of nucleation concerns mainly the work to create a surface. Quantitatively, the free energy required for the formation of two-dimensional nuclei, when it is lowered by the presence of an appropriate substrate, is described by the following equation:82 ∆G*het ) φ · ∆G*hom

3

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(14)

The contact angle is determined by the interactions between the surface and the molecules in the nucleus. Attractions between the surface and the molecules that are stronger than those between the molecules in the nucleus will lead to a small angle R as the nucleus spreads into a thin droplet to maximize its contact area with the surface. If the surface tends to repel the molecules, then the nucleus is pushed away from the surface, resulting in a contact angle R > 90°. Figure 4 shows graphically the above expression for different polymeric materials used as heterogeneous nucleants. If the nucleus wets the substrate completely (R ) 180°), ∆G*het ) ∆G*hom; when the contact angle is 90° (limit between hydrophobic and hydrophilic behavior), * ) 1/2∆Ghom * , and the smaller the contact angle R, the ∆Ghet smaller the value of the activation energy for nucleation, which turns out to be zero for R ) 0. The effective interfacial energy γeff (eqs 11 and 12) for heterogeneous nucleation is reduced by a factor 0 < φ < 1 compared to the interfacial energy γ for a pure homogeneous process: γeff ) φ1/3γ. Because γeff < γ, the work of formation for heterogeneous nucleation is substantially reduced compared to that for a homogeneous process. Furthermore, the preexponential kinetic parameter Ahet in the eq 10, is much smaller than the homogeneous value: Ahet ≈ 1015-1025 , Ahom ≈ 1035. Therefore, heterogeneous nucleation on a substrate is generally

(13)

where φ is the ratio between the heterogeneous and the homogeneous nucleation contribution. Considering the interaction between solute and substrate in terms of the contact angle R that the nucleus forms with the ideally smooth and chemically homogeneous substrate, the reduction of the activation energy for nucleation by heterogeneous activation is given by the equation:

Figure 5. Schematic illustration of protein crystallization on irregular surfaces: (a) molecules dispersed in solution first adsorbed on the surface; (b) the irregular structure which may physically block the lateral migration of the adsorbed protein molecules into the concaves; (C) the trapping of molecules on the surface which may result in a relatively higher local supersaturation, which would increase the possibility of aggregation.

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Figure 6. Well-faceted porcine pancreas trypsin crystals grown on the surface of a macroporous hydrophobic polypropylene membrane.

energetically less demanding than the homogeneous case because of the lowering of the surface energy of the nucleus on the substrate upon interfacial contact.83 When using membrane crystallization, eq 14 is no longer applicable because nucleation takes place on a porous substrate. In this case, a modified version of the equation which takes into account the porous structure of the surfaces has to be considered:84

[

]

∆G*het 1 (1 + cos R)2 3 ) (2 + cos R)(1 - cos R)2 1 - ε ∆G*hom 4 (1 - cos R)2 (15) where ε is the overall surface porosity, defined as the ratio of the total pore areas on the whole geometrical surface. If ε ) 0, eq 15 reduces to the form reported in the literature for heterogeneous nucleation on nonporous surfaces. Figure 5 shows a possible heterogeneous nucleation mechanism generated by an irregular surface topography as that above a porous membrane. In this scheme, molecules dispersed in solution are first adsorbed on the surface by means of nonspecific attractive interactions. The irregular structure may physically block the lateral migration of the adsorbed protein molecules into the concaves, so that they are forced to be packed into compact aggregates. The trapping of molecules on the surface may result in a relatively higher local supersaturation, which would increase the possibility of nucleation compared with that on an ideally flat surface. Here, nucleation will follow with the formation of critical clusters comprising molecules forming suitable bond angles with their neighbors, while the molecules in a randomly packed compact structure may form a fractal cluster, which cannot work as a nucleus for crystal

growth. Critical clusters then grow into crystals while the fractal clusters grow into larger clusters. Figure 6 depicts a crystal of porcine pancreas trypsin crystallized above the surface of a polypropylene membrane. From the figure is apparent, the perfectly faceted shape of the crystal embedded inside the pores where macromolecular aggregation started. From a technological point of view, the control of surface porosity in producing membranes can be achieved easily, so that specific membranenucleants, having the desired value of porosity which might be used to achieve the desired ∆G*het/∆G*hom ratio, can be produced. 7. Current Limitations of MCr and Perspectives When using MCr technology, the interfacial area for solvent removal or antisolvent addition per unit of crystallizer volume is constant and very highsespecially in the case of hollow fibers membrane modules (more than 20.000 m2/m3 of module85)swhile the removal/addition points are distributed over the whole extension of the membrane (pores). Accordingly, supersaturation gradients can be substantially reduced (and anticipated) when designing a crystallization plant. This possibility is not available in the case of conventional thermal evaporators. The establishment of the conditions suitable for crystallization (supersaturation generation) assisted by the membrane, and at the same time, the crystallization phenomenon which withdraws from the solution small particles that might foul the membrane represents a particular synergic combination, useful to increase durability of the membranes itself. On laboratory scale, even in the case of heterogeneous nucleation induced by the membrane, the shear stress generated in dynamic membrane crystallizer is sufficient to avoid crystal deposits, thus preserving


the membrane functionality. If considering potential industrial application of MCr, working over longer time, operations like membrane cleaning would be surely advisible, as it is for every membrane operation. In the case, on the other side, of static MCr, crystals immobilized above the membrane can be easily recovered and characterized, as it is e.g. for the single crystal X-ray diffraction analysis of proteins. The process has been successfully utilized in the crystallization of inorganic salts from multicomponent systems, like the retentates of NF and/or RO stages in seawater desalination.21,24 Fractionation of the component, by controlling finely the operating conditions, has been proven to be a useful tool to crystallize selectively the different component from complex mixtures like concentrated seawater. MCr differs from other MAC processes because mass transfer assisted by the membrane, does not occur by size exclusion effect, but by a mechanism of evaporation-migration-condensation. This mechanism, occurring in the vapor phase, allows a finer control over the transmembrane flux and, hence, on supersaturation. Low-pressure microfiltration membranes, with nominal pore sizes on the order of a few hundreds of nanometers, are completely utilizable for this purpose. Therefore, not volatile solute molecules, having molecular size much smaller than the pores’ size, can be crystallized while keeping suitable trans-membrane fluxes (productivities) associated to null (or very low) pumping energy input (recirculation at atmospheric pressure). A fundamental point relies on the energetic aspects in MCr operations. In this process, the evaporation step requires an obligatory energy input, consisting of the latent heat of vaporization associated with the phase changes.55 This aspects makes MCr comparable with evaporator crystallizers in terms of energetic cost. In this respect, MAC using RO membranes has been proposed by Kuhn et al.39 as an alternative to reduce the total energy consumption. However, the same authors, demonstrated experimentally and theoretically that RO-MAC, which requires high pumping energy duty (to generate around to 40 bar), becomes economically most suitable with respect to thermal evaporation for substances with moderate solubility, larger molecular weight, and a strong dependence of their solubility on temperature.42 Otherwise, RO-MAC will be limited by concentration polarization phenomena, which will cause a reduction of the driving force for mass transport across the membrane and, eventually, solute precipitation above the membrane with consequent loss of selectivity. For highly soluble and low molecular weight substances, the osmotic pressure of the solution, that in RO has to be overcome to achieve suitable productivities (transmembrane fluxes), would be so high that the pumping energy required would make the process unlikely or the pressure would exceed the maximum admitted limit. Nevertheless, substances displaying a flat solubility curve would require so high an amount of heat to warm the solution before the RO stage, to avoid scaling above the membrane, so that the thermal consumption will make the process economically unfeasible. Dynamic MCr does not generally suffer of limitations linked to concentration polarization or to the osmotic pressure. Temperature polarization, which usually impacts MD operations, is not so effective in MCr as a temperature as high as 30-40 °C is enough to produce the transmembrane flux suitable to generate supersaturation (and comparable with RO-MAC).26,86 Furthermore, if on the other hand, the development of new membranes with reduced thermal conductivity would allow us to reduce further the heat lost through the membrane and thermal polarization phenomena, on the other side, the higher energetic

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duty of MCr with respect to RO-MAC might be counterbalanced by the increased control of the process, which translates in the increased added-value and quality of the product obtained. In addition, a MCr unit can be operated by using waste heat when coupled with solar energy or utilizing low-grade heat sources,87–89 thus increasing substantially its energetic efficiency. All these aspects together, combined with the general advantages offered by membrane operations, like operational simplicity, compatibility between different membrane operations in integrated systems, good robustness and stability under operating conditions, environment compatibility, easy control and scale-up, and large operational flexibility make MCr technology an interesting option for the rationalization of industrial crystallization, leading to significant innovation in both processes and products. The main concerns about MCr relies on the membrane behavior. In fact, the process completely collapses as the membrane is wet by one of the contacted solution, with the direct dispersion of one phase into the other. While this aspect has been resolved for aqueous solutions when operating with moderate transmembrane fluxes (on the order of a few liters per hour square meter), by using highly hydrophobic membrane materials (polypropylene, polytetrafluoroetylene, polyvinylidene fluoride), the problem may still exists in AMCr or when considering the reverse process, in which it is required to crystallize hydrophobic molecules soluble in organic solvents. In this case, the development of new membranes which are resistant to, and will not be wet by, organic media would be extremely advisible for exciting future applications, ranging from single crystal semiconductors crystallization from organic solvents to the production of inorganic (photo)catalysts for heterogeneous processes and so on. Literature Cited (1) Margolin, A. L.; Navia, M. A. Protein Crystals as Novel Catalytic Materials. Angew. Chem., Int. Ed. 2001, 20, 2204. (2) Falkner, J. C.; Al-Somali, A. M.; Jamison, J. A.; Zhang, J.; Adrianse, S. L.; Simpson, R. L.; Calabretta, M. K.; Radding, W.; Philips, G. N.; Colvin, V. L. Generation of Size-Controlled, Submicrometer Protein Crystals. Chem. Mater. 2005, 17, 2679. (3) Llina`s, A.; Goodman, J. M. Polymorph control: past, present and future. Drug. DiscoVery Today 2008, 13, 198. (4) McPherson, A. Crystallization of biological macromolecules; Cold Spring Harbor Laboratory Press: Cold Spring Harbor, USA, 1999. (5) Tavare, N. S. Micromixing limits in an MSMPR crystallizer. Chem. Eng. Technol. 1989, 12, 1. (6) Drioli, E.; Curcio, E.; Di Profio, G. State of the Art and Recent Progresses in Membrane Contactors. Chem. Eng. Res. Des. 2005, 83, 223. (7) Boerlage, S. F. E.; Kennedy, M. D.; Bremere, I.; Witkamp, G. J.; Van der Hoek, J. P.; Schippers, J. C. Stable barium sulphate supersaturation in reverse osmosis. J. Membr. Sci. 2000, 179, 53. (8) Tomaszewska, M. Concentration of the extraction fluid from sulfuric acid treatment of phosphogypsum by membrane distillation. J. Membr. Sci. 1993, 78, 277. (9) Gryta, M. Concentration of saline wastewater from the production of heparin. Desalination 2000, 129, 35. (10) Gryta, M.; Tomaszewska, M.; Grzechulska, J.; Morawski, A. W. Membrane distillation of NaCl solution containing natural organic matter. J. Membr. Sci. 2001, 181, 279. (11) Gryta, M.; Grzechulska-Damszel, J.; Markowska, A.; Karakulski, K. The influence of polypropylene degradation on the membrane wettability during membrane distillation. J. Membr. Sci. 2009, 326, 493. (12) Van de Lisdonk, C. A. C.; Rietman, B. M.; Heijman, S. G. J.; Sterk, G. R.; Schippers, J. C. Prediction of supersaturation and monitoring of scaling in reverse osmosis and nanofiltration membrane systems. Desalination 2001, 138, 259. (13) Azoury, R.; Garside, J.; Robertson, W. G. Crystallization processes using reverse osmosis. J. Cryst. Growth 1986, 79, 654.

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ReceiVed for reView February 25, 2010 ReVised manuscript receiVed May 28, 2010 Accepted June 1, 2010 IE100418Z

Supersaturation Control and Heterogeneous Nucleation in

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