pubs.acs.org/Langmuir © 2009 American Chemical Society
Solvent-Modulated Nucleation and Crystallization Kinetics of 12-Hydroxystearic Acid: A Nonisothermal Approach† Michael A. Rogers*,‡ and Alejandro G. Marangoni§ ‡
Department of Food and Bioproduct Sciences, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N5A8, and §Department of Food Science, University of Guelph, Guelph, Ontario, Canada N1G2W1 Received October 27, 2008. Revised Manuscript Received February 22, 2009
The solvent type strongly affects the nucleation behavior of 12HSA and therefore strongly influences the peak nucleation rate, fiber length, spatial distribution of mass, and degree of branching. Using nonisothermal kinetic models, a correlation was established among the activation energy of nucleation, fiber length, and induction time of 12HSA nucleation in different solvents. However, there was no correlation between any measurable parameter and solvent polarity. Activation energies varied from 2.2 kJ/mol in methyl oleate to 15.8 kJ/mol in glycerol. Nucleation behavior and structure were strong functions of the cooling rate, with distinct regions observed above and below 5-7 C/min for fiber length, induction time, rate constant, and peak nucleation rate. The abrupt changes in the rate of nucleation, crystal growth rate constant, and degree of branching around this cooling rate are related to whether the nucleation and crystal growth processes are governed by mass transfer or thermodynamics. Furthermore, the Avrami equation accurately predicted several structural features of the fibrillar network such as fiber length and, to a lesser extent, induction time.
Introduction The microscopic and mesoscopic diversity of organogels makes them interesting soft materials for numerous applications with potential novel industrial applications within the food, pharmaceutical, cosmetic, and petrochemical industries.1 The aggregation of gelator molecules (i.e., 12-hydroxystearic acid (12HSA)) requires specific interactions that build the primary structures often termed “crystal-like” that are induced by preferential 1D growth into rods, tubes, or sheets. The primary structures associate to create 3D network structures (secondary structure) via noncovalent interactions (i.e., hydrogen bonding, van der Waals interactions, π-π stacking, and metal coordination bonds).2,3 The microstructure of 12HSA organogels can vary depending on the solvent and can be modified from a random highly branched network to a highly ordered linear fibrillar networks with limited fiber branching.4,5 It has been well documented that each type of network has very different physical properties (i.e., macroscopic hardness, oil binding capacity and degree of crystallinity).4,5 Solvent-gelator interactions play a key role in mediating organogel formation, which ultimately determines the macroscopic properties of the gel.6 Organogel formation is strongly influenced by the type of solvent used. In general, proper gelation is achieved by using a solvent that has limited interactions with the gelator molecules.6 When the gelator and the solvent are unable to interact via hydrogen bonding, thin, entangled fibers form.6 Conversely, if the solvent interacts strongly with the gelator molecule, then thick and often highly clustered fibers arise.6 † Part of the Gels and Fibrillar Networks: Molecular and Polymer Gels and Materials with Self-Assembled Fibrillar Networks special issue. *Corresponding author. E-mail:
[email protected]. Tel: + 306 966 5028. Fax: + 306 966 8898.
(1) Terech, P.; Weiss, R. G. Chem. Rev. 1997, 97, 3133. (2) Terech, P.; Furman, I.; Weiss, R. G. J. Phys. Chem. 1995, 99, 9558. (3) Suzuki, M.; Nakajima, Y.; Yumoto, M.; Kimura, M.; Shirai, H.; Hanabusa, K. Langmuir. 2003, 19, 8622. (4) Rogers, M. A.; Wright, A. J.; Marangoni, A. G. Curr. Opin. Colloid Interface Sci. 2009, 14, 33–42. (5) Rogers, M. A.; Wright, A. J.; Marangoni, A. G. J. Am. Oil Chem. Soc. 2007, 84, 899. (6) Zhu, G.; Dordick, J. S. Chem. Mater. 2006, 18, 5988.
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Complicating the matter, it has also been documented that the cooling rate used for gelation also influences fiber morphology.7 If the organogelator-solvent system was transferred to low temperatures, spherulitic structures developed whereas at elevated temperatures longer fibers were formed.7 Much work has been carried out on the isothermal nucleation and crystallization of organogels.8-11 There is a general consensus among these authors that self-assembled fibrillar networks form via a nucleationgrowth-noncrystallographic branching mechanism.8-11 However, very little information exists on the nonisothermal nucleation and growth behavior of organogels.12 Crystallization typically occurs under nonisothermal conditions (i.e., the temperature changes as the material crystallizes) in industrial processes. Nonisothermal nucleation and crystallization induce different macroscopic properties such as crystallinity, mechanical strength, and oil-binding capacity.4 In part, nucleation and crystallization change because of modified heat- and mass-transfer conditions. The importance of the nucleation behavior is of great importance because of its strong effects on structural features including fiber size and morphology and the spatial distribution of the crystalline mass.13 Industrially, the application of organogels to be utilized as novel soft materials has been extremely limited even though there is tremendous potential. The inability to modify or predict the microstructure of these complex systems systematically and the long-term storage not being well understood are the limiting factors for many industrial applications.14,15 Alterations in solvent type, gelator concentration, and cooling rate can alter the (7) Huang, X.; Terech, P.; Raghavan, S. R.; Weiss, R. G. J. Am. Chem. Soc. 2005, 127, 4336. (8) Huang, X.; Raghavan, S. R.; Terech, P.; Weiss, R. G. J. Am. Chem. Soc. 2006, 128, 15341. (9) Li, J. L.; Liu, X. Y.; Strom, C. S.; Xiong, J. Y. Adv. Matter 2006, 18, 2574. (10) Tan, G.; John, V. T.; McPherson, G. L. Langmuir 2006, 22, 7416. (11) Liu, X. Y.; Sawant, P. D. Appl. Phys. Lett. 2001, 79, 3518. (12) Rogers, M. A.; Marangoni, P.; Raghavan, A. G. Cryst. Growth Des. 2008, 8, 4596–4601. (13) Marangoni, A. G.; McGauley, S. E. Cryst. Growth Des. 2003, 3, 95. (14) Wang, R.; Lui, X-Y.; Xiong, J.; Li, J. J. Phys. Chem. B 2006, 110, 7275. (15) Rogers, M. A.; Marangoni, A. G.. J. Phys. D. 2008, 41, 215501.
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oil-binding capacity and may affect the crystallinity and spatial distribution of the supramolecular network. Thus, it is the purpose of this study to examine how 12HSA crystallizes in different solvents under nonisothermal crystallization conditions, specifically, how the affects of cooling rate influence nucleation behavior, fiber growth, and crystal morphology.
Methods Sample Preparation. DL-12HSA (99% pure) was obtained from NuCheck Prep (Elysian, MN). Triolein oil was obtained from NuCheck Prep (Elysian, MN), and methyl oleate, light mineral oil, and glycerol were obtained from Sigma-Aldrich (Oakville, ON, Canada) and used as received. Samples of 12HSA (2 wt %) in each solvent were prepared by heating the mixture to 85 C for 30 min. Brightfield Light Microscopy. Samples for microscopy were placed on a 25 75 1 mm3 glass slide (Fisher Scientific, Pittsburgh, PA) after being heated to 80 C. In an attempt to prevent a constrained environment and reduce the surface effects, no coverslip was applied. The slide was transferred to a thermostatically controlled microscope stage (model LTS 350, Linkam Scientific, Surry, U.K.) and cooled at 1-15 C/min from 80 to 5 C. Samples were imaged on a Leica microscope (Leica Microsystems, DM-RXA2/CTR-MIC, Richmond Hill, ON, Canada) with a 40 objective lens (N.A. 0.85) using fully cross-polarized light. A cooled CCD camera (Q-Imaging: Retiga 1300, Burnaby, BC, Canada) acquired images as uncompressed 8-bit (256 greys) grayscale TIFF files with a 1280 1024 spatial resolution. Image J was used for the analysis of the fiber length and the number of crystals. Images taken during nucleation and crystal growth were recorded in triplicate and were analyzed by counting the number of individual nuclei on each micrograph and the length of the fibers using Image J (Bethesda, MD). Differential Scanning Calorimetry. HSA solvent (1012 mg of a 2 % solution) was added to Alod-Al hermetic DSC pans and was then held for 30 min at 80 C. The DSC chamber (Q2000, TA Instruments, New Castle, DE) was continually flushed with nitrogen (0.5 mL/min) and cooled and heated at 2 C/min to determine the peak melting temperatures. Non-Isothermal Nucleation. The isothermal model addresses situations where the temperature remains constant during the reaction and the temperature drop from the melting temperature, Tm, to the set crystallization temperature, Tset, is instantaneous (Figure 1A). As well, it is assumed that crystallization occurs only when Tset is reached, not prior to this. For the isothermal case, time zero is assumed to be the start of the experiment with the temperature at the beginning of the experiment assumed to be Tset. This model is suited to the study of systems that are not heat-transfer-limited. Under isothermal conditions, the crystallization process can be characterized by an induction time (ti), which is the time required for the appearance of the first solid nuclei at Tset under the influence of a thermal driving force. The induction time ti is proportional to the degree of supersaturation (solutions) or the degree of supercooling or undercooling (melts), ΔT, which is the difference between the equilibrium melting temperature of the material (Tm) and the set crystallization temperature (Tset), Tm - Tset. Experimental realities limit the speed at which a system can reach the set temperature. Limitations in heat transfer will result in a gradual reduction in temperature (Figure 1B) as opposed to the instantaneous drop observed in Figure 1A. These conditions can be considered to be near-isothermal. It is assumed, in this case, that crystallization does not begin until after some time the set crystallization temperature has been reached. For a nearisothermal case, then, it is still possible to determine an induction time of nucleation and treat the crystallization process as if it was taking place under isothermal conditions. For this case, it is Langmuir 2009, 25(15), 8556–8566
Figure 1. Temperature and crystallization profiles for materials crystallizing under isothermal (A), near-isothermal (B), and nonisothermal (C) conditions. Reproduced with permission from ref 16. Copyright 2006, Elsevier. important to remember that time zero corresponds to the time when the system reaches Tset. The induction in this case is the time interval between the attainment of the set crystallization temperature and the time of the first appearance of solid nuclei. In the industrial manufacture of crystalline products, crystallization takes place under nonisothermal conditions. Under these conditions, crystallization occurs prior to attaining the set crystallization temperature Tset (Figure 1C). For this situation, both the nonisothermal induction time of nucleation (tc) and the undercooling at nucleation (ΔTc) have different meanings than for the isothermal case. The crystallization behavior and structure of these materials under such conditions is extremely sensitive to heat- and masstransfer conditions. The crystallization regime will ultimately affect the mechanical strength, flow behavior, and sensory texture. Of particular interest is the nucleation behavior of such systems as important structural features such as the crystallite number, size, and morphology as well as the spatial distribution of mass, which are a direct consequence of the nucleation behavior. However, no good theoretical tools exist to model the nucleation behavior of these complex organic mixtures under nonisothermal conditions. In this section, a new approach to the modeling of nonisothermal nucleation systems will be presented.
Formulation of the Time-Dependent Supercooling Parameter. To model nonisothermal nucleation, a new quantity or parameter that defines the driving force for nucleation has to be defined. This parameter will be shown to embody the dynamics (16) Marangoni, A. G.; Tang, D.; Singh, A. P. Chem. Phys. Lett. 2005, 419, 259.
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Figure 2. Bright-field images of 2 wt % 12HSA in methyl oleate (A, B), mineral oil (C, D), triolein (E, F), and glycerol (G, H) gels during cooling at 1 C/min taken at 70 C (A, C, E), 50 C (B, D, F) 45 C (G), and 35 C (H). Magnification bar = 100 μm.
Figure 3. Bright-field images of 2 wt % 12HSA in methyl oleate (A, B), mineral oil (C, D), triolein (E, F), and glycerol (G, H) gels during cooling at 10 C/min taken at 60 C (A, C), 40 C (B, D, E, G), and 20 C (F, H). Magnification bar = 100 μm.
of the system. It was previously mentioned that the induction time of nucleation and undercooling at nucleation have different meanings for the isothermal versus nonisothermal cases. The first step, therefore, in the formulation of a nonisothermal model is the redefinition of these parameters. Upon examination of Figure 1C, one can see that it is not the temperature differential, ΔT, that is the driving force for nucleation. Instead, it is the time that the system has been exposed to a particular temperature differential. In other words, the supercooling of the system is a dynamic quantity as opposed to being a static quantity as for the isothermal case: ΔT is changing in time as the material crystallizes and changes composition. Thus, a supercooling time exposure has to be defined. This corresponds to the exposure of the system to supercooling until the initiation of nucleation. This is calculated as the area under the supercooling-time trajectory from the time when the system crosses the melting temperature, Tm, to the time where the first crystal nuclei appear (tc). The temperature at which the first crystal nuclei appears is called the crystallization temperature, Tc. Notice that Tc 6¼ Tset and therefore [ΔT = (Tm - Tset)] 6¼ [ΔTc = (Tm - Tc)]. If the cooling rate is assumed to be constant, then the supercooling-time exposure (β) at the onset of nucleation can thus be defined as
Another important parameter in the characterization of a nonisothermal system is the cooling rate. A linear cooling rate is defined as ΔT φ ¼ ð2Þ Δt
1 β ¼ ΔTc tc 2 8558 DOI: 10.1021/la8035665
ð1Þ
As previously discussed, at the crystallization temperature Tc, t = tc. At the melting temperature Tm, t0 = 0. Substituting these into eq 2 gives ðTm -Tc Þ ΔTc ¼ φ ¼ ð3Þ tc tc -0 Substituting ΔTc/φ for tc in the expression for the supercooling-time exposure at nucleation (eq 1) gives the following expression: β ¼
1 ðΔTc Þ2 2 φ
ð4Þ
The parameter β corresponds to the triangular area under the curve for the supercooling-time curve (Figure 1C). This parameter takes into consideration the amount of supercooling in time required for nucleation to start. It is important to realize that the parametrization of the data relative to temperature as well as time is necessary for a proper description of nucleation under nonisothermal conditions. The supercooling-time exposure, β, incorporates a thermodynamic component in the Langmuir 2009, 25(15), 8556–8566
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Figure 4. Number of nuclei counted on bright-field micrographs as the sample was cooled nonisothermally for 12HSA in methyl oleate (A, B), mineral oil (C, D), triolein (E, F), and glycerol (G, H). form of the supercooling at nucleation (ΔTc) and a kinetic component in the form of the nonisothermal nucleation induction time (tc). Finally, the square root of β corresponds to the effective supercooling experienced by the system at nucleation, namely, pffiffiffi ΔTc β ¼ pffiffiffiffiffiffi 2φ
ð5Þ
This effective supercooling is a linear function of the chemical potential difference between the melt and the crystalline solid (Δμ). This chemical potential difference is related to ΔTc as Δμ = ΔHf (ΔT/Tf), where ΔHf is the enthalpy of fusion of the crystalline material, Tf is the temperature of fusion, and ΔT Langmuir 2009, 25(15), 8556–8566
corresponds to the degree of undercooling (T - Tf) at nucleation. Thus, the effective supercooling is√related to the chemical √ potential difference at nucleation as β = TfΔμ/ΔHf (2φ). In this treatment, the relationship between the nucleation rate under nonisothermal conditions and the chemical potential difference at nucleation will be modeled in a statistical fashion using an exponential probability density function. This approach is in contrast to the Gibbs-Thompson approach, where an estimate of the interfacial energy of the crystal nucleus is required. A long-standing issue in the area of surface science is the determination of the interfacial energy. The statistical approach presented here allows for the determination of the nucleation free energy without the need to determine the crystal-melt interfacial energy and requires only the determination of DOI: 10.1021/la8035665
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Figure 5. Rate of nucleation determined by the change in the number of nuclei per unit time for 12HSA in methyl oleate (A, B), mineral oil (C, D), triolein (E, F), and glycerol (G, H). a supersaturation-related term, the effective supercooling at √ nucleation ( β).
Probabilistic Approach to Modeling Non-Isothermal Nucleation Kinetics. In previous work by our group, we determined that the normalized √ nucleation rate (J/Jmax)) had an exponential dependence on β, where Jmax corresponds to the maximum nucleation rate. This observation raised the possibility of modeling nonisothermal nucleation kinetics statistically, in a similar fashion as for the kinetic theory of gases, using an exponential probability density function. To develop this argument logically, we must revisit the basic premises of kinetic theory. The rate of reaction (v) is a function of the concentration of molecules with sufficient energy to overcome an energy barrier to the particular reaction (N*), and thus v = k[N*], where k is the rate constant for the reaction and N*corresponds to the concentration of molecules in the activated state. In the kinetic theory of gases, the molecules in the activated state are those 8560 DOI: 10.1021/la8035665
molecules with sufficient energy, and in the proper orientation, to undergo the chemical reaction. For the case of nucleation reactions, N* would correspond to the concentration of molecules in the metastable state, just prior to the nucleation event. The proportion of molecules in the appropriate state to undergo a reaction (from energetic and conformational considerations) will be given by (N*) = p(x)(NT), where NT is the total concentration of reactant and p(x) corresponds to the probability density function (pdf) that describes the frequency distribution of the particular event. √ Following this line of reasoning, the effective supercooling β was assumed to be distributed in an exponential fashion, with an √ exponential pdf, p( (β); k), of the form 8 9 pffiffi < ke -k β ; pffiffiffi pffiffiffi βg0 = pffiffiffi pð β; kÞ ¼ ð6Þ :0 ; β < 0; Langmuir 2009, 25(15), 8556–8566
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Figure 6. Variation of the nucleation rate (J) vs the supercooling-time exposure (β) for 2% 12HSA in methyl oleate (A), mineral oil (C), triolein (E), and glycerol (G) and Jmax, the maximum nucleation rate, which is a fitted parameter that is a function of the cooling rate for 12HSA in methyl oleate (B), mineral oil (D), triolein (F), and glycerol (H). Circles represent cooling rates greater than 5 C/min, and squares represent cooling rates less than 5 C/min.
The parameter k is called the rate parameter. The rate parameter has to satisfy the condition k > 0. This pdf applies to values √ of the randomly distributed variable belonging to the set β ∈ [0; ¥). The scale parameter (μ) is simply the inverse of the rate parameter and represents the mean, or expected √ value, of an exponentially distributed random variable, E[ β] = μ = 1/k. Thus, this pdf is appropriate to model our situation where our random variable always has to be greater than zero and the mean is fixed. Exponential distributions are used to model memoryless Poisson, or stochastic, processes that take place with constant probability per unit time or distance. This is the reason that exponential pdf’s are extensively used to model random processes such as Brownian motion and diffusional processes. In the case of Brownian motion, the future position of a molecule is independent of its current position. In our case, we assume that our nucleation phase-transition initiation event takes place with Langmuir 2009, 25(15), 8556–8566
a constant probability per unit effective supercooling (β), possibly not unreasonable considering the constant cooling rates used. Another interesting property of an exponential pdf is that among all continuous pdf’s, with support [0;¥), the exponential pdf with μ = 1/k has the highest entropy. Many physical systems tend to move toward maximal entropy configurations over time (principle of maximum entropy). Considering all of the above, the rate of the nucleation reaction (J) will thus be given by pffiffi pffiffi J ¼ kp NT ke -k β ¼ Jmax ke -k β ð7Þ
Determining the Energy of Activation for a Non-Isothermal Process. By combing eqs 5 and 7, the relative nucleation rate can be expressed as an exponential function of the inverse of the DOI: 10.1021/la8035665
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Rogers and Marangoni undercooling (ΔT ≈ 0) and/or with very short induction times (ti ≈ 0). To determine the energy of activation using this expression, we√can use the same arguments as earlier. Replacing √ β with ΔTc/ (2φ) and ΔTc with Qm/Cp, we obtain ΔTc Qm ¼ k -k2 pffiffiffiffiffiffi ¼ k -k2 pffiffiffiffiffiffi ð14Þ Jmax 2φ Cp 2φ √ plot corresponds to√k2. The slope of the J/Jmax versus β √ From the slope of the J/Jmax versus 1/ φ plot, s = k2Qm/( 2) Cp, Qm can be determined from pffiffiffi s 2 Cp ð15Þ Qm ¼ k2 J
Figure 7. Calculated activation energy vs static relative permittivity.
square root of the cooling rate, namely, J Jmax
¼ ke
ΔTc ffiffiffi -kp
ð8Þ
2φ
Using this model, it is possible to determine the energy required to initiate the nucleation process. Consider that from Tm to Tc no phase change has taken place. Thus, up to this point, strictly specific heat Qm has been removed from the system (Qm = CpΔT), where Qm is the specific heat removed from the system upon cooling per gram of material and Cp is the specific heat (heat capacity) of the material. Substituting Qm/Cp for ΔT in eq 8 leads to the expression J Jmax
¼ ke
mffiffiffi - Qp Cp
2φ
¼ ke
mffi - Qp Z
φ
¼ ke
-pXffi
φ
ð9Þ
where Qm is proposed here to represent the energy of activation for nucleation per unit mass (J/g) and Z [J g-1 K-1/2 s1/2] is defined as Z ¼
pffiffiffi 2 Cp k
ð10Þ
Thus, from a knowledge of k (eq 7) and Cp, Z can be calculated using √ eq 10. Moreover, from the nonlinear fit of J/Jmax versus 1/ φ data, the constant X can be obtained. It is then possible to determine the energy of activation for nucleation as Qm = Z*X (J/g). This quantity can then be multiplied by the average molecular weight of the triacylglycerols (MW, g/mol) to obtain the molar energy of activation for nucleation (QM), QM = ZXMW (J/mol). Special Case When β Is Very Small. As shown in eq 7, the nonisothermal expression has the form J Jmax
pffiffi ¼ ke -k β
ð11Þ
The first two terms of the Taylor expansion of this function are J Jmax
pffiffiffi ¼ ke -ka -k2 e -ka ð β -aÞ
ð12Þ
For the case where a = 0, this expression reduces to J Jmax
≈k -k2
pffiffiffi β
ð13Þ
Thus, √ for the case where the effective supercooling at nucleation ( β) is in the vicinity of a = 0, the exponential probability density function can be approximated by a linear function. This situation would apply to processes with very small metastable regions that nucleate at very small degrees of supersaturation or 8562 DOI: 10.1021/la8035665
Results and Discussion Nucleation Kinetics. The crystallization behavior of 12HSA organogels is sensitive to the cooling rate that modifies the macroscopic structure influencing oil mobility, crystallinity, and elasticity.4 The fiber morphology and number of nuclei differ depending on which solvent is employed during gel formation. Each of the four solvents was capable of forming an organogel with 12HSA. 12HSA formed very long thin fibers in triolein and mineral oil at slow cooling rates (Figure 2), whereas in methyl oleate small strands were formed. Interestingly, 12HSA managed to gel glycerol, even though it caused the 12HSA to phase separate macroscopically into large, very complex structures at slow cooling rates. However, a continuous network structure was still maintained during gelation. At a fast cooling rate of 10 C/min (Figure 3), 12HSA in mineral oil (Figure 3C,D) and triolein (Figure 3E,F) still produced relatively long fibers. The fiber growth of 12HSA in methyl oleate (Figure 3A,B) and glycerol (Figure 3G,H) was limited, and it could be observed by microscopy that the network was predominantly composed of small crystals similar in size to those observed at the onset of nucleation. Faster cooling rates (i.e., above 5-7 C/min) lead to higher rates of nucleation, resulting in a decrease in crystal size and an increase in the number of nuclei (Figure 4). At faster cooling rates, lower onset temperatures of nucleation were observed, indicating a higher degree of undercooling/supercooling at the moment of nucleation, which led to the creation of a larger number of smaller crystals.16 It is obvious that 12HSA in methyl oleate produced the most nuclei (Figure 4A,B) and had the shortest fiber length. Conversely, 12HSA in triolien and mineral oil produced the longest fibers and the smallest number of nuclei (Figure 4C-F). To quantify the nucleation process, the number of crystals (N) was counted and plotted as a function of time (t) for each cooling rate (Figure 4), and the first derivative of this curve was taken, which corresponds to the rate of nucleation. Further analysis will use the peak nucleation rate (Jp) (Figure 5). A simple inverse relationship between the rate of nucleation and the cooling rate was found to represent three of the four solvents, including mineral oil, triolein, and glycerol (eq 15), which is similar to that observed during SAFiN crystallization. 12HSA in methyl oleate had a similar relationship to that observed for spherulitic crystals between the peak nucleation rate and the supercooling trajectory. If we compare the molecular constituents of spherical crystals with its melt and 12HSA with methyl oleate, then distinct similarities are observed. For spherulitic crystals, the liquid and crystalline molecules have very similar molecular structures, hence during nucleation they have the potential to interact with one another. 12HSA interacts with other 12HSA Langmuir 2009, 25(15), 8556–8566
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Figure 8. Fiber length as a function of the time/temperature supercooling trajectory measured using image J on bright-field micrograph for 12HSA in methyl oleate (A,B), mineral oil (C,D), triolein (E,F) and glycerol (G,H).
molecules via both hydrogen bonding and London dispersion forces. In mineral oil, triolein, and glycerol, 12HSA can interact only via London dispersion forces with mineral oil and triolein and by hydrogen bonding with glycerol. However, 12HSA in methyl oleate has a similar molecular structure (i.e., they both have polar head groups and hydrophobic tails) and may interact noncovalently both via hydrogen bonding and London dispersion forces in a very similar fashion to 12HSA-12HSA interactions. For methyl oleate, it seemed to follow an exponential function (eq 9), which may be explained by increased solvent gelator interactions. Two dissimilar regimes with differing sensitivities to the cooling rate were observed between Jp and the cooling rate and Jp and the β parameter (Figure 6C-H). Cooling rates of less than than 5-7 C/min did not significantly affect the rate of nucleation whereas cooling rates greater than 5-7 C/min showed a dependence between the rate of nucleation and the cooling rate. The nucleation rate was significantly affected by the supercooling time Langmuir 2009, 25(15), 8556–8566
exposure for rapidly cooled samples (p < 0.05). Slow cooling rates did not significantly affect the nucleation rate as a function of the β parameter (p > 0.05), implying that fast cooling rates lead to a time-dependent thermodynamic driving force and at slow cooling rates the nucleation behavior was a function of mass transfer. It is interesting that three of the four solvents (i.e., glycerol, mineral oil, and triolein) showed two distinct modes of assembly with the linear response of the peak nucleation rate versus the β parameter and cooling rate. Methyl oleate is the only solvent that does not behave in a similar fashion with regard to the peak nucleation rate versus the β parameter and cooling rate (Figure 6A,B). This may be due to the abundant ability of interactions to occur between the polar head and the hydrocarbon chain with the solvent. Figures 2 and 3 show very little fiber growth with 12HSA in methyl oleate; however, there were abundant nuclei. This may have been due to solvent being incorporated into the crystal lattice, which prevents 12HSA molecules from adhering to the growing crystal surface. DOI: 10.1021/la8035665
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Figure 9. Rate constant, K (A,D,G,J), maximum fiber length, Ymax (B,E,H,K) and induction time Xo (C,F,I,L) as a function of the time/ temperature supercooling trajectory measured using image J on bright-field micrographs (Figures 1 and 2) for 12HSA in methyl oleate (A,B,C), mineral oil (D,E,F), triolein (G,H,I), and glycerol (J,K,L).
Using eqs 13 and 15 for mineral oil, triolein, and glycerol and the slopes obtained (Figure 6C-F), we can calculate the molar energy of activation for nucleation. For methyl oleate, eqs 7 and 9 were used to calculate the molar energy of activation for nucleation (Figure 6A,B). For 12HSA (MW = 300 g/mol), we determined the energy of activation for the nucleation of 12HSA/methyl oleate to be 2.2 kJ/mol, 12HSA/mineral oil to be 5.4 kJ/mol, 12HSA/triolein to be 10.6 kJ/mol, and 12HSA/ glycerol to be 15.8 kJ/mol. The activation energy for 12HSA in triolein (10.6 kJ/mol) corresponded well to previous work on 12HSA in canola oil (12.1 kJ/mol). The activation energies were plotted as a function of the static relative permittivity to determine if the activation energy was a function of the solution polarity (Figure 7). Originally, it was thought that because the static relative permittivity is a function of solvent polarity and the rates of phase separation and nucleation are a function of the difference between the solvent and gelator polarity then the quantifiable activation energy should be a function of the static relative permittivity. However, it is obvious that there is no quantifiable relationship between the polarity and the activation energy of nucleation (Figure 7) because methyl oleate and triolein both have static relative permittivities of 3.2 but their activation energies are 2.2 and 10.6 kJ/mol, respectively. This illustrates that the polarity of the solvent does not seem to be a dominating factor influencing the activation energy. It is logical to think that although polarity influences the activation energy 8564 DOI: 10.1021/la8035665
the ability of the solvent to interact with the gelator is more significant regarding the nucleation parameters. Recently, the self-assembly of nonamphiphilic foldamers was observed in both methanol and hydrocarbons.17 These authors reported that upon changing the solution polarity there was a modification in the mechanism of self-assembly from vesicle formation in methanol to organogel formation in hydrocarbons. This may be attributed to the ability of methanol to interact with the hydrogen bonding moiety of the nonamphiphilic foldamer, resulting in the solvation of the vesicle.17 Conversely, there will be a further driving force to minimize the contact between the hydrogen bonding moiety and the hydrocarbon solution, resulting in the formation of chain-extending organogels. Because a region of the 12HSA molecule is capable of hydrogen bonding and another one is capable of interacting via London dispersion forces, the argument for nonamphiphilic foldamer stacking is applicable to 12HSA stacking and explains the observed changes in crystallite morphology observed in different solvents. Crystal Growth Kinetics. The rate of crystalline fiber growth was determined by measuring the length of each fiber on the micrographs (Figures 2 and 3), and the data was fitted to a modified Avrami equation characterizing the crystal (17) Cai, W.; Wang, G-T.; Xu, Y-X.; Jiang, X-K.; Li, Z-T. J. Am. Chem. Soc. 2008, 130, 6936.
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Figure 10. Maximum nucleation rate (A), induction time (C), and maximum fiber length (E) as a function of the calculated activation energy. Maximum nucleation rate (B), induction time (D), and maximum fiber length (F) as a function of the static relative permittivity.
growth kinetics (Figure 9).18 The modified Avrami model had the form
where Y is the fiber length, Ymax is the maximum length of the fiber, kapp is the apparent rate constant of fiber elongation, x is the time, xo is the induction time, and n is the dimensionality of growth. The Avrami model, originally developed for isothermal conditions, is strictly incorrect in characterizing nonisothermal crystallization. An excellent fit to the data was observed, allowing it to be used as a characterization tool of the fiber growth kinetics.12 The Avrami index, n, was constrained to a numerical value of 2 because sporadic 1D growth was observed (Figures 2 and 3). Upon fitting the modified Avrami model to the experimental data (Figure 8), the constants for Ymax, xo, and kapp were determined (Figure 9). The calculated and experimentally determined Ymax corresponded very well, suggesting that the Avrami model is a good characterization tool for the nonisothermal SAFiN growth of 12HSA in different solvents. Furthermore, we observed a drastic difference in the final length of the fibers depending on the cooling rate. Cooling rates greater than 5-7 C/min produced short fibers as a result of the greater number of nuclei initially formed, and thus less crystal growth occurred. The calculated and experimental induction times did not correspond as well as the maximum fiber length. It has
previously been shown that the addition of small amounts of solvent molecules, capable of interacting with the growing SAFiN, may modify the micro- or nanostructure of the network.19 This is partially due to the method by which the onset of crystal growth was determined using the first visible signs of crystalline mass with bright-field microscopy. Nevertheless, the same general trends were followed for both the nuclei observed on the micrographs and calculated values. Interestingly, all 12HSA/solvent systems seemed to have different nucleation conditions centered between 5 and 7 C/min, although each had different final lengths. This suggests that within this range of cooling rates there is a different mode of assembly for 12HSA regardless of the solvent employed. The Avrami constant, K, followed the same trends as the peak nucleation rates (Figure 9A, D,G,J), again indicating that two different mechanisms of selfassembly are present that modify the rates of nucleation and crystal growth. The time-dependent thermodynamic driving force at fast cooling rates leads to greater rates of both crystal growth and nucleation. This regime of nucleation would be similar to that described by Wang, et al. in relation to their proposed nucleation-growth-noncrystallographic branchinggrowth mechanism.14 If we compare our micrographs, samples that cooled faster and slower than 5-7 C/min indicate significant differences in the morphology of the SAFiN network (Figures 2 and 3). Slow cooling rates develop fewer nuclei with very little branching and fiber lengths of several hundred
(18) Rousset, P. In Physical Properties of Lipids; Marangoni, A. G., Narine, S. S., Eds.; Marcel Dekker: New York, 2002.
(19) Liu, X. Y.; Sawant, P. D.; Tan, W. B.; Noor, B. M.; Pramesti, C.; Chen, B. H. J. Am. Chem. Soc. 2002, 124, 15055.
n
Y ¼ Ymax ð1 -e -kapp ðx -xo Þ Þ
Langmuir 2009, 25(15), 8556–8566
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DOI: 10.1021/la8035665
8565
Article
micrometers. This type of system would not effectively entrain liquid oil and would exhibit syneresis.4 Conversely, in the regime where nucleation is a strong function of the supercooling-time exposure, significantly more nucleation takes place, leading to the creation of a highly branched network that entrains oil more effectively.4 Therefore, to engineer the oil binding capacity and hardness/elasticity of an organogel, external fields such as heat and mass transfer could be modified to achieve a specific energy of nucleation. The external fields would not only dictate the number of nuclei present but would also define the degree of branching and fiber length of the SAFiN network. Future work should define those critical ranges of nucleation behavior. Peak nucleation rate (Jpeak), induction time (Xo), and maximum fiber length (Ymax) were plotted both as a function of activation energy (Figure 10A,C,E) and polarity or static relative permittivity (Figure 10B,D,F). It becomes obvious that none of these parameters follow any significant relationship with respect to solvent polarity. However, the peak nucleation rate for nonisothermal growth (Figure 10A) seems to be exponentially related to the activation energy of nucleation. At low activation energies, there are numerous nuclei that form; however, as the activation energy increases, it reaches a steady state with regard to the number of nuclei that form. Furthermore, both the induction time and maximum fiber length were linearly related (r2 > 0.95) to the nucleation activation energy (Figure 10C,E). The fact that these parameters are well correlated with nucleation activation energy suggests that specific
8566 DOI: 10.1021/la8035665
Rogers and Marangoni
solvent-gelator interactions play a significant role in selfassembly, which has also been observed in the modification of self-assembly from the formation of vesicles to organogel depending on the solvent for foldamers.
Conclusions This study suggests that solvents strongly affect the nucleation behavior of 12HSA and that structural parameters in organogels such as fiber length and induction time are a strong function of the energetics of nucleation, as determined from the energy of activation of nucleation. Nucleation behavior and structure was a strong function of the cooling rate, with distinct regions observed above and below 5-7 C/min. The abrupt changes in the rate of nucleation, crystal growth rate constant, and induction time around this cooling rate are related to whether the nucleation and crystal growth processes are governed by mass transfer or thermodynamics. At slow cooling rates, below 5-7 C/min, nucleation and crystal growth are functions of how quickly 12HSA molecules can diffuse to the growing surface. Conversely, above 5-7 C/min there is a linear relationship between the number of nuclei and crystal length as a function of dynamic supercooling, and hence the limiting factor of 12SHA molecules being integrated into the growing crystal is thermodynamically restricted. Using the models developed and adapted in this work, we could establish a correlation between the activation energy of nucleation and fiber length and the degree of branching of 12HSA SAFiN’s in different solvents.
Langmuir 2009, 25(15), 8556–8566
