On the Influence of Hydrogen Bond Interactions in Isothermal and

Jun 22, 2013 - To verify and quantify these effects, experiments were conducted and the Fokker–Planck modeling equations were used to obtain the ...
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On the Influence of Hydrogen Bond Interactions in Isothermal and Nonisothermal Antisolvent Crystallization Processes G. Cogoni,† R. Baratti,*,† and Jose A. Romagnoli‡ †

Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Università di Cagliari, Cagliari, Italy Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA

‡

ABSTRACT: The effect of the temperature on the Crystal Size Distribution (CSD) in antisolvent crystallization operation, for systems where the solubility is weakly dependent on the temperature, is analyzed. The hydrogen bonding properties of the solvents used that influence the supersaturation of the solution and consequently the growth and the nucleation dynamic can explain this effect on the CSD. To verify and quantify these effects, experiments were conducted and the Fokker−Planck modeling equations were used to obtain the quantifying parameters (growth velocity, the asymptotic mean size, and the diffusivity). Results are provided through investigations into the nonisothermal antisolvent crystallization of sodium chloride (NaCl), in which the solubility is practically independent of temperature for the range of operating conditions considered.

1. INTRODUCTION Crystallization is a widely used technology for solid−liquid separation in the process industry. It is extensively used in the production of pharmaceuticals to separate the drug from the solvent mixture, as well as to ensure that the drug crystals conform to size and morphology specifications. The crystal size in crystallization processes is one of the most important variables, since it influences, among others,1−8 factors such as filtration rate, dewatering rate, dissolution rate, and bioavailability. The driving force in crystal formation is supersaturation. The trend of supersaturation generation during the crystallization process has a direct and substantial impact on crystal characteristics such as size, morphology, and purity. There are a number of ways to control supersaturation including temperature and evaporation. In the past decade, the salting-out method has drawn significant attention in crystallization research and literature. In this method, which is also known as solventing-out or drowning-out or quenching, a substance known as antisolvent (or precipitant) is added to the solution with the goal of reducing the solubility of the solute in the original solvent and consequently achieving supersaturation. This technique is regarded as an energy-saving alternative to evaporative crystallization, provided that the antisolvent can be separated at low (energy) costs. Also, in cases where a solute is highly soluble or its solubility does not change much with temperature, antisolvent crystallization is an advantageous method.9−15 Considering the antisolvent crystallization, it has been found that the supersaturation is directly proportional to the concentration and amount of antisolvent introduced in the crystallizer and inversely proportional to the operating temperature. It is also known that at, low supersaturation, crystal growth is predominant over nucleation, resulting in larger crystal size. On the other hand, at higher supersaturation, crystal nucleation dominates crystal growth, ultimately resulting in smaller crystals.16 Recently, cooling has been combined with antisolvent crystallization for several systems.7,14 Organic systems such as paracetamol and acetyl-salicylic acid, used in © 2013 American Chemical Society

aforementioned publications have solubilities that change significantly with temperature. In these cases, the effects and the benefits of incorporating cooling with antisolvent crystallization are clear because it can significantly increase the crystallization yield. However, for crystallizing systems where solubility is weakly dependent on temperature, the effect of temperature is not straightforward. It was shown recently17 that for this kind of systems temperature also influences the supersaturation, which is enhanced at low temperatures and becomes weaker as the temperature increases. Consequently, the supersaturation is directly proportional to the antisolvent feed rate and concentration of the antisolvent and, inversely proportional to the temperature. Although the effects of temperature on antisolvent crystallization operation were shown numerically and experimentally, even for a system where the solubility is weakly dependent on temperature, there is still no clear explanation for these effects. One reason for this enhancement caused by the temperature and also by the amount of antisolvent used can be explained through the interactions between the solvent and the antisolvent. The antisolvent interacts strongly with the solvent, mostly through hydrogen bonding caused by the intrinsic polarity of the solvents used, increasing its strength so that the system is forced to crystallize.18 The temperature influences the hydrogen bond strength while the number of the hydrogen bond interactions is proportional to the amount of antisolvent in the system and therefore to the antisolvent feed rate. In order to investigate the solvent−antisolvent and solvent− solute interactions and study the influence of hydrogen bonding on the supersaturation of the solution, in this paper, we have considered three different antisolvents using the same volume concentration but under different operating conditions. Received: Revised: Accepted: Published: 9612

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The three antisolvents differ by polarity index (PI), which is related to the hydrogen bond strength with higher polarity implying stronger hydrogen bonds.19,20 It is hypothesized that, under the same conditions, smaller crystals can be obtained using a highly polar antisolvent, since the hydrogen bond effect is strong. In order to study the effect of temperature on the enhancement or inhibition of hydrogen bonding, an antisolvent with average polarity was used on a system whose solubility was weakly dependent on temperature. Additionally, the experimental runs were conducted to investigate the hydrogen bonding strength, by changing the operating conditions and choosing the antisolvent with the optimal PI, in order to obtain the maximum and the minimum supersaturation limits. We then compared the results obtained under the same operating conditions while using a medium polarity antisolvent. A recently proposed stochastic modeling approach based on the Fokker−Plank equation (FPE)21−24 is used to quantify the different effects, such as CSD dispersion (parameter D), growth velocity (r), and asymptotic mean size of crystals in logarithmic scale (K). Results are provided through investigations in the nonisothermal antisolvent crystallization of sodium chloride (NaCl), where the solubility is practically independent of temperature for the range of operating conditions considered.

Figure 2. Hydrogen bonds between water (H2O) and different organic polar molecules, respectively: (a) within water; (b) alcohols; (c) ketones/aldehydes; and (d) carboxylic acids.

of the solvent, the probability that these polar groups can establish hydrogen bonds with the solvent diminishes. The strength of the hydrogen bonds is also influenced by temperature, pressure, and concentration, specifically increasing at lower temperatures, higher pressures, and higher concentrations.20,26 Hydrogen bonds are directional and relatively weak, with energy between 10 and 40 kJ/mol, but they are strong enough to define the structure and properties of water, proteins, and many other materials. The competition between these two interactions, ion−dipole and hydrogen bonds, affects the supersaturation of the antisolvent crystallization processes and consequently influences the shape of the Crystal Size Distribution (CSD), the growth and the nucleation rates, and the morphology of the crystals.25 Supersaturation is represented as the difference between the concentration of the system and the equilibrium concentration of the solute in the liquid phase.27 The equilibrium concentration depends on thermodynamic aspects, of which the most important is the activity coefficient that is influenced by the polarity of the compounds considered. Consequently, hydrogen bonds have an important role on the solubility of the system, therefore influencing supersaturation. The growth and nucleation rates are both directly proportional to the supersaturation, so that when supersaturation increases, the nucleation and growth rates rise as well. For higher values of supersaturation, the nucleation process dominates, yielding crystals with smaller mean sizes. Concerning the antisolvent crystallization processes, the influences of the antisolvent feed rate and temperature have been studied in previous works.17,20−24,28,31 It was shown that increasing the antisolvent feed rate and/or decreasing the temperature increases the supersaturation of the system, favoring the nucleation mechanism and inducing a large number of nuclei in the initial stages of the process, consequently yielding a wider CSD. Physically, increasing the antisolvent feed rate and/or decreasing the temperature increases the number of hydrogen bonds in the solution and their strength, therefore enhancing the supersaturation and favoring the nucleation of new crystals, consequently increasing the dispersion of the crystal sizes. A similar effect can be induced by changing the secondary solvent, in particular, using ones that have a higher polarity index or by changing the antisolvent concentration. It is hypothesized, regarding antisolvent crystallization processes, that higher hydrogen bond strength generates higher

2. SOLVATION, HYDROGEN BONDING, AND SUPERSATURATION In this section, after recalling the concepts of solvation, hydrogen bonding, and supersaturation, we will propose a hypothesis to explain the influence of the temperature on the CSD even when the temperature, as in the present case, weakly influences the solubility. Solvation, also called dissolution, is the process of attraction and association of solvent molecules with molecules or ions of a solute. As ions dissolve in a solvent, they spread out and become surrounded by solvent molecules (Figure 1). This is a

Figure 1. Na+ and Cl− ions surrounded by water molecule evidencing the ion-dipole interactions; the other water molecules completing the solvation sphere have been omitted for sake of clarity.

typical ion-dipole interaction, which involves charged ions and polar molecules such as water. The magnitude of the interaction energy is between 40 and 600 KJ/mol and depends upon the ionic charges, the dipole moment of the molecule and the square of the distance between the center of the ion and the midpoint of the dipole. Hydrophilic solvents, such as water, ethanol, and other solvents with hydroxyl groups, can establish hydrogen bonds within their molecules or other similar hydrophilic molecules (Figure 2). The hydrophilic nature of a solvent is proportional to the polarity index25 and represents how strong the separation of charges is in a molecular structure, leading to the hydroxyl groups interacting with other similar molecules through hydrogen bonds. Hydrogen bonds are stronger when the polarity index is higher. Diminishing the hydrophilic nature 9613

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antisolvents: 190 proof ethanol (EtOH), 95% vol. acetic acid (AcOH), and 95% vol. iso-propanol (2-PrOH). The experimental setup and procedure are described in the following sections. Experimental Setup. The experimental rig is made up of a one liter, jacketed, cylindrical glass crystallizer connected to a heating/cooling bath controller. The system is continuously stirred using an axial propeller agitator connected to an electric motor where 500 rpms were kept constant during all the experimental run and the same for all the set of experiments. The temperature in the crystallizer is measured using an RTD probe that is wired up to a slave temperature control system capable of heating and cooling. In similar fashion, the antisolvent addition is carried out by a slave peristaltic pump. The master control is performed by a computer control system that is wired up to the slave temperature and feed rate controllers respectively. The desired set-points are set by the master controller. All relevant process variables are recorded. Along the operation, about 8 mL samples were taken in an infrequent fashion. Samples were then vacuum-filtered over filter paper and then dried in an oven overnight with a constant temperature of 50 °C before additional visual inspection.21−24 Crystal Size Measurement. Light microscopy was used to measure the size of the crystals. A stereo light microscope (Wild-Heerbrugg, Switzerland) connected to a digital camera (Amscope Model MD500, United States) was used. Several images were taken with the camera for each sample and analyzed using the AmScope software (iScope, United States). The software allows for the measurement of the length and/or area of particular crystals in pixels units. Using a supplied calibration slide, these lengths and areas can be converted to a micrometer length scale. The number of crystals measured varied for each sample and was selected by a stabilization criterion of ±2.5% of the mean. Experimental Procedure. During start up, the crystallizer was loaded with a saturated aqueous solution of sodium chloride made up with 34.2 g of NaCl in 100 g of distilled water, which is a saturation criterion valid for a range of temperatures from 10 to 30 °C, for which the percent change in solubility is 1.1%.29 To study the influence of polarity of different solvents with different polarity indices, we have considered a first set of experiments keeping a constant temperature of 20 °C and a constant antisolvent feed rate equal to 1.5 mL/min for each antisolvent that comprises: acetic acid (most polar), ethanol (medium polarity), and iso-propanol (least polar). Then, a second set of experiments was conducted using an antisolvent with a medium polarity index (ethanol) with a constant antisolvent feed rate equal to 1.5 mL/min and using three different temperatures, respectively 10, 20, and 30 °C. Every run on these two sets of experiments lasted from 4 to 8 h allowing the system to reach the asymptotic conditions. In order to enhance the hydrogen bond effect, a third set of experimental runs was made, one run using acetic acid, with a constant feed rate of 3.0 mL/min at a constant temperature of 10 °C, and a second run using iso-propanol, with a constant feed rate of 0.7 mL/min and a constant temperature of 30 °C. Both of these runs were compared, under the same operating conditions, with ethanol as the antisolvent. The antisolvents used in these experimental runs are acetic acid, with a PI equal to 4.8; ethanol, with a PI of 4.3; and iso-propanol, with the lowest PI, equal to 3.9. Polarity indexes, feed rates, and temperatures used in the three sets of experimental runs are summarized in Table 2.

supersaturation due to their statistical dominance on ion-dipole interactions, consequently influencing the nucleation rate and the growth velocity. The effects of supersaturation on the mean size of crystals, the nucleation-and the growth rates are qualitatively summarized in Figure 3.16 From Figure 3 we can

Figure 3. Effects of supersaturation on the crystal size (solid black line), growth rate (dashed black line), and nucleation rate (solid gray line).

observe that the crystal size increases up to a maximum following that it starts to decrease as the supersaturation increases. This happens when the nucleation mechanism is dominant. Note that the functionality of the nucleation and the growth rates are always monotonically increasing/decreasing functions, but the behavior can be different from the one illustrated in Figure 3. A qualitative summary of the hypothesized effects of hydrogen bonding is shown in Table 1, considering the physical aspects that we have discussed so far. Table 1. Qualitative Effects of Increasing the Antisolvent Feed Rate, Temperature, and Using and Antisolvent Polarity Index on the Asymptotic Mean Size, Dispersion, and Growth Velocity increasing

asymptotic mean size

dispersion

growth velocity

antisolvent feed rate temperature polarity index

↓ ↑ ↓

↑ ↓ ↑

↑ ↓ ↑

In order to verify and quantify these effects, a set of experimental runs, carefully selected, was conducted and is discussed in the next sections. Furthermore, the FPE equation modeling approach was used to fit the data and to obtain the quantifying parameters: the growth velocity (r), the asymptotic mean size (K), and the diffusivity parameter (D).21−24

3. EXPERIMENTAL PROGRAM AND MODELING APPROACH A set of experiments was carried out in order to study the polarity effects on the supersaturation of crystallization processes. The experiments were carried in a bench scale crystallizer that was kept at a fixed temperature and used a constant antisolvent feed rate. We have used purified water, reagent grade sodium chloride (99.5%), and three different 9614

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asymptotic CSD can be obtained analytically using the approach reported by Tronci,31 which leads to the following expression for the stationary solution of 1:

Table 2. Polarity Indexes, Antisolvent Feed Rates, and Temperatures Used in the Three Sets of Experimental Runs set 1

set 2

set 3

PI

q [mL/min]

T [°C]

duration time [h]

final vol. [m3]

3.9 4.3 4.8 4.3 4.3 4.3 4.8 3.9 4.3 4.3

1.5 1.5 1.5 1.5 1.5 1.5 3.0 0.7 3.0 0.7

20 20 20 10 20 30 10 30 10 30

8 8 8 8 8 8 4 8 5 8

820 × 10−6 820 × 10−6 820 × 10−6 820 × 10−6 820 × 10−6 820 × 10−6 820 × 10−6 436 × 10−6 1000 × 10−6 436 × 10−6

y2

m

log(L(yi , t j ; θ )) =

(1)

(2)

∂Ψ(y , t ) lim =0 y →+∞ ∂y

(3)

y →−∞

⎡ (y − μ )2 ⎤ 1 0 ⎥ exp⎢ − 2 ⎢⎣ σ0 2π 2σ0 ⎥⎦

y3

(6)

(7)

Ψ(y , t ) exp(y)

where

L = exp(y)

(8)

(9)

4. RESULTS AND DISCUSSION As hypothesized in section 2, it is expected that the hydrogen bonds influence the supersaturation of the solution; in particular, as hydrogen bonds become stronger (using an antisolvent with high PI or decreasing the temperature or increasing the antisolvent feed rate or its concentration instead), the supersaturation becomes higher as well, thus decreasing the solubility and obtaining crystals with a smaller mean size and a narrower CSD. Here, three sets of experimental runs were selected in order to validate the hypothesis. Considering the first set of experimental runs using different antisolvents with different polarities, where all the runs were conducted at 1.5 mL/min and 20 °C, we can observe from Figure 4 the behavior of the crystals at the end of the run (8 h), considering the same image format and the same magnification factor for the microscopic analysis. We notice (from right to left) that as the antisolvent PI increases, the crystals, at asymptotic conditions, become smaller as we expected. The higher polarity of the antisolvent used induces stronger

(4)

In which the function h(y,t,θ) is a logistic model defined as y⎞ ⎛ h(y , t ; θ ) = ry⎜1 − ⎟ ⎝ K⎠

y2

nj

∑ ∑ log(Ψ(yi , t j ; θ))

⎛ σy2 ⎞ ⎟ μL = exp⎜⎜μy + 2 ⎟⎠ ⎝

and the initial conditions, hereafter assumed as a Gaussian distribution21−24 Ψ(y , t0) =

+∞

∫−∞ er / D( 2 − 3K )

where yi is the value in logarithmic scale of the nj-th experimental observation for the crystal size (j = 1, ..., m), m is the number of experimental runs carried out by varying input parameters, tj is the sampling time used for the m experimental runs, and θ is the vector of parameters r, K, and D. Furthermore, the CSDs and the mean sizes (logarithmic scale) can be transformed into linear scale by applying the following nonlinear transformations: Ψ(L , t ) =

∂Ψ(y , t ) =0 ∂y

1

j=1 i=1

along with the boundary conditions30

lim

NS =

The parameters (r, K, D) are then inferred by maximizing the log-likelihood function considering all the experimental data collected at different operating conditions:

Modeling Approach. In order to characterize quantitatively the behavior of the systems using different antisolvents with different polarities and/or temperature, a model based on the Fokker−Planck Equation (FPE)30 has been used. The FPE approach has been proposed in previous papers21−24 to describe the dynamic behavior of a crystallization process, as a valid alternative to the classical population balance equations. The FPE, in logarithmic scale, is stated as ∂ 2Ψ(y , t ) ∂Ψ(y , t ) ∂ =D − [Ψ(y , t )h(y , t ; θ )] 2 ∂t ∂y ∂y

y3

ψ (y) = NS er / D( 2 − 3K )

(5)

The parameters of the FPE are defined as follows: r is the growth velocity of the mean size of crystals, K is the asymptotic mean size in logarithmic scale, and D is the diffusivity of the Fokker−Planck equation30 that represents how much the frequency distribution will spread out along the time domain. One of the advantages of this modeling approach is that the

Figure 4. Asymptotic images taken at the end of the experimental runs using three different antisolvents: (a) acetic acid, (b) ethanol, and (c) isopropanol. 9615

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increasing the temperature, we have weaker hydrogen bonds that has a similar effect to using an antisolvent with lower polarity, and consequently, a lower supersaturation rate is obtained. The low values of diffusivity at higher temperatures can be explained by the dissolution of crystals that generates narrower CSDs. These last results are also reported in terms of CSDs and mean sizes, in order to highlight the asymptotic and dynamic behavior of the system under temperature changes using an antisolvent with medium polarity and a constant feed rate. This behavior observed is analogous to that observed in Figure 5, confirming that as the temperature increases the supersaturation and the nucleation rate decrease, allowing the crystals to grow indefinitely according to the mass of solute introduced on the initial solution. Similar behaviors with the temperature have been obtained for different systems, using polar solvents.17,21−24,28,31 Again we can see that both temperature and polarity play an important role in antisolvent crystallization processes due to the influence of hydrogen bonding (see Table 1). Indeed, in using an antisolvent with a higher polarity index and keeping constant the antisolvent feed rate and temperature, we are favoring, from a statistical point of view, the number of hydrogen bonds in the system. On the other hand, considering only one antisolvent and keeping a constant antisolvent feed rate while adjusting the temperature, we have a similar effect since at lower temperatures we are increasing the strength of hydrogen bonds, thus increasing the number of hydrogen bonds in the solution, and consequently increasing the supersaturation of the solution. To emphasize the temperature, the feed rate, and the polarity effects and their influence on the supersaturation of the system, we have considered a third set of experimental runs composed of two runs under extreme conditions. In the first set of runs, we used isopropanol at high temperature (30 °C) and low antisolvent feed rate (0.7 mL/min); it was expected, according to Table 1, that the biggest crystals would be formed for this set among all the experimental runs. We performed the second experiment using acetic acid at low temperature (10 °C) and with a high antisolvent feed rate (3.0 mL/min) to obtain the maximum supersaturation possible within the range of temperatures and antisolvent feed rates considered. The results are shown and compared with the data collected using ethanol at the same operating conditions in Figure 7. In the case of the acetic acid (the most polar antisolvent), when compared with the results obtained using ethanol at the same operating conditions, we can see a slight difference in terms of the asymptotic CSDs and mean size of the crystals, with a smaller mean size for the acetic acid according to Table 1. The same small differences have been obtained for the dispersion and the growth rate of the system. This fact can be explained by the high supersaturation of the system, which likely reached a saturation point due to the high hydrogen bond strength and prevalence. This result is characterized by an explosive increase in the rate of nucleation in the early stages of the run, in which the crystals grow slightly, limited by the amount of solute introduced at the beginning of the experimental run, ultimately obtaining similar CSDs at the end of the run using both antisolvents. In the second experiment, at lower extreme of the supersaturation conditions (Figure 8), we can see that the asymptotic CSDs are extremely different between mean sizes for both antisolvents. This effect is explained by the very small nucleation rate, so that the growth mechanism is dominant, resulting in a limited amount of nuclei in the first stage of the experimental run and allowing the crystals to grow bigger.

hydrogen bonds and consequently a higher supersaturation, favoring the nucleation of crystals and reducing their asymptotic dimension. To describe quantitatively the influence of different antisolvents on the dynamic- and the asymptotic behavior of the crystal size distribution (CSD), the parameters of the FPE have been estimated using the Maximum Likelihood method, as described in the previous paragraph. The estimated FPE parameters and the PI of the antisolvents used are summarized in Table 3. Table 3. Polarity Index (PI) for Each Antisolvent Used, Related to the FPE Parameters for First Set of Experimental Runs T = 20 °C and q = 1.5 mL/min antisolvent

acetic acid

ethanol

iso-propanol

PI r (growth velocity) K (asymptotic dimension) D (diffusivity)

4.8 1.421 4.895 0.326

4.3 1.403 4.930 0.216

3.9 0.429 5.429 0.090

The FPE parameters in Table 3 represent respectively the growth velocity (r), the asymptotic mean size in logarithmic scale (K) and the diffusivity of the FPE (D), proportional to the CSD dispersion. Observing the overall behavior of the parameters, they follow the trend expected according to the polarity index and hypothesized in Table 1. The greater the PI, the smaller is the asymptotic mean size of crystals (smaller K), reaching quickly the asymptotic conditions (higher r). Furthermore, in order to visualize these effects, we have plotted the CSDs (asymptotic conditions) and the dynamic mean size evolutions obtained using each antisolvent together with the FPE model predictions. We can observe that the mean size of crystals, when an asymptotic behavior is reached, is inversely proportional to the polarity index of the antisolvent used. The same trend can also be observed for the dispersion of the CSDs, which becomes wider (considering the asymptotic conditions) as polarity increases (FPE diffusion D). Considering the temperature effect, a similar behavior was observed during the second set of experimental runs, see Figure 6. In this case, ethanol was used as the antisolvent at different temperatures, keeping constant the antisolvent feed rate. Observing the values of the FPE parameters reported in Table 4, we could notice the analogy, in terms of temperature Table 4. Temperature Effects Related to the FPE Parameters for the Three Antisolvents Considered PI = 4.3 and q = 1.5 mL/min ethanol r (growth velocity) K (asymptotic dimension) D (diffusivity)

10 °C

20 °C

30 °C

1.934 4.858 0.373

1.403 4.930 0.216

1.103 5.049 0.171

changes, with the data observed in the previous set of parameters obtained using different antisolvents with varying polarities. The growth velocity decreases as the temperature increases, the same for the diffusivity, while the opposite trend has been obtained for the asymptotic mean size of crystals. This behavior can be explained in terms of the hydrogen bond strength, which is a function of the temperature. Indeed, when 9616

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Figure 5. Experimental results fitted with the FPE for the runs using (a) acetic acid, (b) ethanol, and (c) iso-propanol, in isothermal conditions and keeping constant the antisolvent feed rate. The results represent both the asymptotic conditions and the dynamic behavior of the system.

Specifically, when using iso-propanol as the antisolvent, with its low polarity index, the hydrogen bond effect is relatively weak, generating a small supersaturation, and inhibiting the nucleation of new crystals. Consequently, the CSD does not reach asymptotic behavior, growing indefinitely (limited by the amount of solute mass in the system) after 8 h, using all the antisolvent available for the experiment. Summarizing, the overall behavior shows that the crystal size increases by increasing the temperature or decreasing the antisolvent feed rate or using an antisolvent with a low polarity index. Temperature and polarity index are correlated to the hydrogen bond strength by physical aspects, thus decreasing the temperature causes the hydrogen bonds to become stronger,20,26 while an opposite effect is observed when the polarity is decreased. This, in turn, increases the supersaturation, enhancing the nucleation rate, and obtaining at the end smaller crystals. The same effect can be obtained keeping a constant temperature, using an antisolvent with a higher polarity index or using a high antisolvent feed rate since this statistically increases the number of hydrogen bonds in the solution. From a physical point of view, we have first hypothesized and then confirmed that there exists a correlation between the hydrogen bond strength and the supersaturation of the solution, thus influencing the nucleation and the growth rates. Although hydrogen bonds are weaker than ion-dipole interactions, they are able to reduce the number of water molecules (or in general solvent/antisolvent molecules) that surround the solute ions, favoring the crystallization of the solute. The hydrogen bond strength is directly proportional to

the polarity of the solvent/antisolvent considered and also depends on pressure and temperature.20 It should be noted that the results were obtained for a system whose solubility is weakly dependent on temperature. Using different antisolvents with different polarities, we can obtain different results influencing the supersaturation and, as a consequence, obtaining different asymptotic and dynamic behaviors of the CSD.

5. CONCLUSIONS In the present work, we have studied the influence of different antisolvents on the antisolvent crystallization processes in nonisothermal conditions, regarding the behavior of the asymptotic and dynamic evolution of the CSDs. We have found that there exists a direct correlation between hydrogen bond strength and the supersaturation. The hydrogen bond strength is influenced by pressure and temperature or by changing the nature of the antisolvent, with regards to their polarity index. The hydrogen bond effect can be also be adjusted by changing the amount of antisolvent in the system, adjusting the antisolvent feed rate or its volume concentration. The results obtained are congruent with the hypothesis we have made, showing that the asymptotic mean size of crystals is inversely proportional to the hydrogen bond strength, while the growth velocity and the dispersion of the CSD are directly proportional. The results obtained using different antisolvents, different temperatures and feed rates, and considering the hydrogen bond influence on the solution supersaturation can be extended further to optimize the process and to find optimal operational 9617

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Figure 6. Experimental results fitted with the FPE for the runs using ethanol, keeping constant the antisolvent feed rate and varying the temperature from 10 to 30 °C. The results represent both the asymptotic conditions and the dynamic behavior of the system.

Figure 7. Experimental results fitted with the FPE for the runs using ethanol and acetic in the upper extreme condition, when temperature is kept constant at 10 °C and the antisolvent feed rate at 3.0 mL/min.

Figure 8. Experimental results fitted with the FPE for the runs using ethanol and iso-propanol in lower extreme conditions, when temperature is kept constant to 30 °C and the antisolvent feed rate at 0.7 mL/min. 9618

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policies. These include controlling the crystal mean sizes and/ or CSD dispersion, by manipulating the antisolvent feed rate and temperature, as well as finding the best antisolvent to use. The latter, however, should include other economic aspects as well as issues related to the separation/recovery of the antisolvent from the solvent used.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +39 070 6755056. Fax: +39 070 6755067. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

J.A. Romagnoli kindly acknowledges the financial support by the National Science Foundation through the Award No. 1132324 and Regione Sardegna for the support, through the program “Visiting Professor 2012”

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dx.doi.org/10.1021/ie303414b | Ind. Eng. Chem. Res. 2013, 52, 9612−9619