Kinetics of 12-Hydroxyoctadecanoic Acid SAFiN CrystallizationRationalized Using Hansen Solubility ParametersMichael A. Rogers* and Alejandro G. Marangoni

Department of Food Science, University of Guelph, Guelph, Ontario, Canada N1G 2W1

*S Supporting Information

ABSTRACT: Changes in solvent chemistry influencedkinetics of both nucleation and crystallization of 12-hydroxyoctadecenoic, as determined using differential scanningcalorimetry and applying a modified Avrami model to thecalorimetric data. Altering solvent properties influencedsolvent−gelator compatibility, which in turn altered thechemical potential of the system at the onset of crystallization,the kinetics of gelation, and the resulting 12HOA crystal fiberlength. The chemical potential at the onset of crystallizationwas linearly correlated to both the hydrogen-bonding Hansen solubility parameter and the solvent−gelator vectorial distance inHansen space, Ra. Our work suggests that solvent properties can be modulated to affect the solubility of 12HOA, which in turninfluences the kinetics of crystallization and the self-assembly of this organogelator into supramolecular crystalline structures.Therefore, modulation of solvent properties during organogelation can be used to control fiber length and thus engineer thephysical properties of the gel.

■ INTRODUCTION

Self-assembled fibrillar networks (SAFiNs), comprised of lowmolecular mass organogelators (LMOGs), have garneredremarkable attention for recovery of spilled oil,1 controlleddrug release,2−4 antibacterials,5 and use as edible oleogels.6

Despite the rapidly growing body of literature devoted tomolecular gels,7 new LMOGs are still, more often than not,discovered serendipitously and it remains challenging topredict, a priori, the structure of potential gelators or toforesee solvents that may gel by a known gelator.8−11 Designchallenges result from the antagonistic parameters that promotecrystal growth, while limiting solubility to form hierarchicalone-dimensional (1D) architectures. In other words, a gelatormust be sufficiently soluble to be compatible with the solventand at the same time sufficiently insoluble for self-assembly tooccur.12 Okesola et al. illustrate the point further by accuratelystating that most LMOGs sit on a knife edge between solubilityand precipitation.12 To impair rational design even further,there is no universal gelator capable of gelling all solvent classesand per se both the gelator and solvent chemistry need to beconsidered.7,8

Molecular gels, unlike polymer gels, are formed by smallmolecules, typically less than 3000 Da, and require a zero-dimensonal (0D) to 1D conversion driven by noncovalentinteractions between LMOGs. LMOG assembly develops froma multistep process where a sol is cooled and subsequentlysupersaturation drives aggregation via stochastic nucleation.The nucleation event requires highly specific interactions (i.e.,hydrogen-bonding,13,14 π−π stacking, electrostatic interactions,and van der Waals interactions15) that promote preferential 1Dgrowth. The resulting fibers are described as “crystal-like”, and

the extended crystalline aggregates, comprised of monomersheld together by noncovalent bonds, act in a manner similar tothat of polymer chains in polymeric gels to immobilize thesolvent. This 1D growth results in the formation of crystallinenano- or microfibers, which become entangled and formjunction zones, thus resulting in a three-dimensional (3D)network. The solvent is trapped within this 3D network of self-assembled fibrils, resulting in the formation of a gel matrix.16

Solvent plays a key role in this assembly process.17−28 Chemicalprocesses taking place in solution, including aggregation orcrystal growth, are affected by solution properties,29 and sinceself-assembly is influenced by both specific solvent−soluteinteractions and bulk solvent properties, such as viscosity,density, and polarity, it is almost impossible to pinpoint whichsolvent parameters will influence self-assembly.29

It is unrealistic to consider a solvent as a macroscopiccontinuum characterized by a single physical property, andunfortunately not one solvent parameter accounts for allinteractions. Katrikzky et al. stated that “...the simple concept ofpolarity as a universally determinable and applicable solventcharacteristic is a gross oversimplification”.30 An accuratemeasure of solvation accounts for solvent−solute interactionsand separates them quantitatively according to whether theinteractions are nonspecific or specific. Self-assembly ofmolecular gels requires the same solubility considerations asthose for polymer gels. Also, there must be consideration foradditional factors pertaining to how solvents affect intermo-

Received: September 21, 2016Revised: October 29, 2016Published: November 3, 2016

Article

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© 2016 American Chemical Society 12833 DOI: 10.1021/acs.langmuir.6b03476Langmuir 2016, 32, 12833−12841

lecular, noncovalent interactions between gelator molecules. Asan example of the solvent−gelator interplay, two solvents mayshare a similar bulk physical parameter, but the functionalgroups of the solvent may alter the nature of gelator−solventinteractions. Thus, LMOGs may not be similarly amenable togelation by a common gelator, and their gels may exhibit verydifferent mechanical properties. To illustrate, both 3-pentanoneand 1-butanol have static relative permittivities of ∼17,31 only3-pentanone is gelled by 12-hydroxyoctadecanoic acid(12HOA); a solution is obtained in 1-butanol under otherwiseequivalent conditions.22,32,33 For this reason, detailed evalua-tions of how different solvent parameters alter or influencegelation are direly needed.Due to the interplay between solvent and gelator, solvent

parameters have been closely linked to gelation abil-ity.8,17−19,23,24,26,28,32−40 Raynal and Bouteiller used Hansensolubility parameters (HSPs) when evaluating the gelationbehavior of numerous LMOGs.34 Their meta-analysis revealedthat the gels all had solvents with similar HSPs with only a fewexceptions.34 In a refinement of Hildebrand’s theory onsolubility parameters, HSPs are semiempirical decompositionsof the original Hildebrand solubility parameters (HiSP) intodispersive (d), polar (p), and hydrogen-bonding (h) solubilityparameters;41 namely,

δ δ δ δ= + +Hi2

H,d2

H,p2

H,h2

(1)

Readers are directed to Hansen’s original contribution in1967 for a clear explanation of how solvents and polymers wereassigned a solubility parameter, whose values can be found instandard reference tables.41 These three parameters can betreated as coordinates for a point in three dimensions alsoknown as the Hansen space. The nearer two molecules, e.g.,solvent and gelator, are in this 3D space, the more likely theyare to dissolve into each other. To determine if the parametersof two molecules are within range, a value called the interactionradius (Ra) is given to the substance being dissolved. This valuedetermines the radius of the sphere in Hansen space, and itscenter is the three Hansen parameters. To calculate thedistance (Ra) between Hansen parameters in Hansen space, thePythagorean theorem in 3D for spherical geometry is used:

δ δ δ δ δ δ= − + − + −R 4( ) ( ) ( )a2

d2 d12

p2 p12

h2 h12

(2)

where δd2 is the dispersive HSP for the gelator and δd1 is thedispersive HSP for the solvent. The HSPs for HOA wereestimated using the group contribution method42 and werefound to be δd = 16.59 MPa1/2, δp = 2.86 MPa1/2, and δh = 6.77MPa1/2.The objective of this study is to explore the relationship

between gelator solubility in different solvents, of differingHSPs, and correlate this solubility to kinetics of gelation andmicrostructure of the resulting organogel. Therefore, 12HOAwas selected from the plethora of gelators due to its broadgelation ability, and it has been extensively studied in numeroussolvents43−49 and in complex fluids such as mixed solventsystems, gelled microemulsions, and lamellar phases.50−56

■ METHODSSolvent selection criteria were maintained as simply as possible withthe aliphatic chain being linear and saturated and the functional grouplocated in the primary position, and the solvent must be in a liquidstate between up to 90 °C when placed in hermetically sealed DSCpans (TA Instruments, New Castle, DE, USA). The only exceptions tothese selection criteria were ketones where the functional group was

located in the middle of the molecule. All solvents (hexane, heptane,octane, decane, dodecane, tetradecane, hetanthiol, heptanthiol,octanthiol, decanthiol, nonanenitrile, decanal, dodecanal, octylamine,decylamine, and 5-nonanone) and D-12-hydroxyoctadecanoic acid(12HOA) were obtained from Sigma-Aldrich (Cherry Hill, NJ, USA)with purity greater than 0.95%. 12HOA was dispersed at 2 wt % in 2mL of solvent in 4 mL glass vials capped with PTFE lined lids (VWR,Randor, PA, USA). After 12HOA was dispersed in each solvent andcapped, the vials were placed in a hot water bath set at 90 °C for 20min. After the sol appeared clear, it was removed and stored for 24 h at20 °C.

Differential Scanning Calorimetry. Samples of 10 mg each of 2wt % 12HOA in various organic solvents were transferred into Alod-Alhermetic DSC pans. The DSC chamber (Q2000, TA Instruments) wasprecooled to 20 °C before the sample was placed into the chamber andcontinually flushed with nitrogen (0.5 mL min−1). The samples wereheated to 90 °C and cooled to 20 °C at 2 °C min−1, undernonisothermal conditions, to determine the peak crystallizationtemperature and then were heated to 90 °C at 2 °C min−1 to decidethe melting temperature. Kinetics of crystallization was monitoredusing a running integral of the crystallization peak obtained duringcooling. Samples were run in triplicate, and the mean and standarddeviation were plotted.

Microscopy. The supramolecular structure of 2 wt % 12HOA inthe solvents were imaged using a Linkham imagining station(Linkham, Surrey, England) equipped with a Q imagining 2560 ×1920 pixel CCD camera (Micropublisher, Surrey, Canada) and a 10×Olympus lens (0.25 N.A.; Olympus, Tokyo, Japan). Samples wereplaced on a glass slide, and a coverslip was placed on top of the sample.The slide was transferred onto a Peltier temperature control stage(LTS120, Linkham) using a water reservoir as the heat sink. Thesamples were heated to 90 °C and cooled at 2 °C min−1 to 20 °C toobserve fiber formation using nonpolarized light. Light micrographswere calibrated with a 100 μm micrometer. Fiber length was measuredusing ImageJ (Bethesda, MD, USA) and was reported as a mean ±standard deviation of 10 different crystals on three separatemicrographs for a total of 30 crystals per solvent.

X-ray Diffraction. The X-ray diffraction (XRD) or wide-angle X-ray scattering (WAXS) patterns of 12HSA gels in different solventswere obtained by use of a Bruker HiStar area detector and an Enraf-Nonius FR571 rotating anode X-ray generator equipped with a RigakuOsmic mirror optic system (∼0.06° 2q nominal dispersion for Cu Kα;l = 1.5418 Å) operating at 40 kV and 40 mA. All of the data werecollected at room temperature over a period of about 300 s. Thesample to detector distance was 10.0 cm, and the standard spatialcalibration was performed at that distance. Scans were 4° wide inomega (ω) with fixed detector, or Bragg, angle (2q) of 0°, and fixedplatform ( f and c) angles of 0° and 45°, respectively. In all cases, thecount rate for the area detector did not exceed 100,000 cps.

■ RESULTS AND DISCUSSIONSolvents were selected based on their ability to be gelled by 2wt % 12HOA; all solvent−gelator combinations resulted in gelswith the exception of octylamine and decylamine; both formedviscous solutions.57 Depending on the solvent, the melting andcrystallization profile (i.e., profile shape and onset and endtemperatures) for 12HOA differed. The difference between12HOA thermograms, in assorted solvents, included theamount of crystalline mass (i.e., solubility), the degree ofundercooling (Tm − Tc) at the onset of crystallization, or thetemperature difference between the onset of melting/fusion(Tm) and the onset of crystallization (Tc) (Figure 1A,B). Alower degree of undercooling required to initiate crystallizationsuggests that the gelator is not as soluble in the solvent and ittends to crystallize more readily from solution. This, of course,will be a strong function of the solubility of the gelator in eachsolvent. HSPs were devised to overcome the limitations of theHildebrand solubility parameter that do not include the effects

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of specific intermolecular interactions such as polar andhydrogen bonding.58 HSPs are ordinarily used to selectsolvents for dissolving polymers.59−61 However, the importanceof HSPs in new fields has been rapidly emerging and wasrecently introduced to the field of molecular gels by Raynal andBouteiller.34 HSPs for each solvent are easily obtained using theHSPiP software (4th edition version 4.1.07) via the simplifiedmolecular-input line-entry (SMILE) input function. Neither δpnor δd correlate to the degree of undercooling required toinitiate crystallization. However, the degree of undercooling isstrongly and significantly correlated to both δh and Ra (Figure2C,D). It has previously been shown that many gelationparameters are correlated to δh and Ra

8,9,22,32,33

When the difference between δh for the solvent and 12HOA(δh = 6.77 MPa1/2) decreases, the degree of undercoolingrequired to initiate gelation increases. Hence, a high degree ofundercooling is required when the solvent and gelator are morecompatible with one another. Likewise, when Ra decreases,undercooling increases; i.e., as chemical dissimilarity betweenthe solvent and gelator increases (i.e., Ra between two solventsincreases), the degree to which the solution needs undercooledto initiate crystallization decreases.This decrease may be attributed to the difference in chemical

potential at the onset of crystallization, Δμc,

μΔ =Δ

ΔH

TTc

m

m (3)

where ΔT = (Tm − Tc) is the effective undercoolingexperienced by the solution at the onset of crystallization,while ΔHm and Tm are the melting enthalpy and the onset ofmelting temperature determined experimentally by DSC. Thisform of the chemical potential for a solution is only valid if thesolution is ideal (see below). The chemical potential, Δμ, wasplotted as a function of the HSPs (Supporting InformationFigure S1), and the correlations to δh and Ra were very strong.This is not surprising since chemical potential is stronglycorrelated to the degree of undercooling (Figure S2),suggesting ideality in solution behavior. Thus, as thesolvent−-gelator chemical nature becomes more dissimilar(i.e., a greater Ra), the chemical potential required to initiateself-assembly increases.Earlier work correlating activation energies, determined using

an effective supercooling parameter, due to nonisothermalcooling and a probability density function found no correlationswith solvent polarity assessed using the static relativepermittivity of the various solvents.35 Originally, it was thoughtthat because the static relative permittivity is a function ofsolvent polarity and the rates of phase separation andnucleation are a function of the difference between the solvent

Figure 1. DSC melting and crystallization profiles for 12HOA innonane (A) and nonoanitrile (B).

Figure 2. Degree of undercooling determined by the temperature difference between the onset of crystallization and melting as a function of HSPsand Ra.

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and gelator polarity, then the quantifiable activation energyshould be a function of the static relative permittivity. With ournew understanding of HSPs, the data were re-examined and astrong correlation between the activation energy and δd or Ra

was observed (Figure 3). These findings are in line withobservations made for the chemical potential (Figure S1) andundercooling (Figure 2). As the solvent and gelator move apartin Hansen space, the dissimilarity of the gelator and solventincreases causing the chemical potential required to initiate self-assembly to increase, which in turn causes an increase in theactivation energy.The effects of gelator solubility characteristics in different

solvents on 12HOA crystallization kinetics were also explored.

The amount of crystalline mass formed in time was estimatedusing DSC. The area under the melting endotherm, at differenttimes/temperatures, was assumed to be proportional to theamount of crystalline mass formed. Panels A and B of Figure 4show a typical crystallization profile determined in this fashion.The profiles were, in turn, fitted to a modified Avrami model,adapted for nonisothermal crystallization, in order to determinean apparent crystallization rate constant (kapp). The index ofcrystallization is a function of both the dimensionality ofcrystalline growth and the type of nucleation (sporadic vsinstantaneous).35,62

= − −Y Y (1 e )k x zmax

( )napp (4)

Figure 3. Activation energy, determined using an effective supercooling parameter and a probability density function, as a function of Hansensolubility parameters. Data were originally presented in Rogers and Marangoni35 and were reanalyzed as a function of HSPs.

Figure 4. DSC profiles and their corresponding running integrals for nonane (A) and nonoanitrile (B). Rate constants (C, D) for nucleation andcrystallization determined from the modified Avrami model as a function of δh and Ra.

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where ymax is the phase volume upon completion ofcrystallization, z in the induction time, and n is the Avramiexponent. A nonlinear regression of the model to the data wascarried out using Graphpad Prism 5.0 (GraphPad Software, LaJolla, CA, USA) where Ymax was confined to 100%, because all

data sets were normalized to their maximum value, and n wasconfined to 2, since 1D crystals and sporadic nucleation wereobserved using polarized light microscopy;35 kapp and z werenot confined. Correlations between z and the variousparameters were not done because the values for z provided

Figure 5. Bright-field micrographs of 2 wt % 12HOA in various solvents. Scale bar in bottom right is 100 μm.

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the same information as the degree of supercooling (Figure 2).The rate constants were not correlated to δp or δd, but a strongfunction with δh and Ra was observed (Figure 4C,D).An increase in the rate constant of crystallization, suggests

that as the solvent and gelator become further apart in Hansenspace, the degree of undercooling and chemical potentialrequired to initiate self-assembly decrease. Numerous studieshave tried to link the driving force for crystallization to themicrostructure of the corresponding gel network in varioussolvents.13,63,64 The growth dimensionality of a molecular gelnetwork becomes closer to 1 when experiencing low drivingforces for crystallization (i.e., very slow cooling rates or highisothermal crystallization temperatures). Conversely, at high

cooling rates, under higher driving forces for crystallization, thisdimensionality increases, indicating more spherulitic crystalgrowth patterns. These increases have been attributed tocrystallographic mismatch branching (CMB), leading to theformation of shorter fibrils and more highly branchednetworks.65−67 Highly branched networks tend to have ahigher elastic modulus and improved solvent holdingcapacity.68 Recent work by Rohner et al. has eloquentlyshown that the rate of gelation is controlled by the solubility ofthe gelator, in their case an acid−amine complex, whichmediates the initial nucleation step required for gel assembly.69

This initial nucleation step is observed in our study by thediffering degrees of undercooling.

Figure 6. Fiber length, determined using polarized light microscopy, as a function of HSPs and Ra.

Figure 7. X-ray diffractograms of the WAXS region for a typical orthorhombic and triclinic polymorphic subcell (A). Domain size, calculated usingthe full width at half-maximum from the X-ray diffraction spectra and the Williamson Hull equation, as a function of the chemical potential (B).SAXS (C) and WAXS (D) peak positions versus chemical potential.

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It is clear from this work that the morphology of the SAFiNnetwork is strongly affected by the nature of the solvent used,varying from very fine thin fibers to coarse short fibers (Figure5). In an attempt to quantify the length, a total of 30 fibers (10fibers on three different micrographs (Figure S3) weremeasured using ImageJ.70 For 12HOA in different solvents,SAFiN length was linearly correlated with Ra (Figure 6). Asstated before, as Ra increases, the degree of undercoolingrequired to initiate crystallization decreases (Figure 2D), and asa result, the driving force for crystallization diminishes. CMBtheory states that at low degrees of undercooling, the fibersgrow one-dimensionally with little branching.63,64 At lowdegrees of undercooling (i.e., elevated crystallization temper-atures), the crystallographic mismatch nucleation barrier is veryhigh, favoring 1D fiber growth with a corresponding largecorrelation length or fiber length. When the crystallizationtemperature decreases (i.e., increased undercooling), there is anincrease in supersaturation causing the crystallographicmismatch barrier to be significantly reduced increasing thefiber tip branching.71 The highly branched fibers (i.e., short fiberlength) create gels with smaller pore sizes and of higherelasticity.27

By understanding the inter-relationship between HSP,undercooling, chemical potential, and fiber length, the physicalproperties (i.e., elasticity and solvent binding) of molecular gelsmay be precisely controlled. What is remarkable about thesefindings is that using the more simplified measure of solubility,the Hildebrand solubility parameter, there are poor correlationswith the undercooling, chemical potential, rate constant, andfiber length (Figure S4). This suggests that the interactionleading to these changes is not simply a difference in thesolubility of the gelator in a particular solvent. Instead, it is themagnitude of the hydrogen-bonding solubility parameter andthe distance in Hansen space that govern these changes instructure and gelation capacity.It has been previously reported that, in the polymorphic

forms of the 12HOA/solvent gels, at low δh, the wide-anglespacing was at 4.3 Å, corresponding to a hexagonal subcellspacing. As δh increases, a transition from a hexagonal to atriclinic parallel subcell (strong peak at 4.6 Å, and two weakpeaks at 3.9 and 3.8 Å) was observed.33 Herein, it is clear thatthe polymorphic form is correlated to changes arising in thechemical potential difference (Figure 7). It is clear that there isan increase in the long space (Figure 7C) with increasingchemical potential difference and at low chemical potentials anorthorhombic polymorphic form results while at high chemicalpotentials a triclinic polymorph persists (Figure 7D). The fullwidths at half-maximum from the X-ray diffraction spectra wereused to calculate the domain size using the Williamson−Hullequation:72

θ λ θ× = + × ×SK

FW( ) cos( )size

(4 strain sin( ))(5)

where FW is the full width at half-maximum, θ is the diffractionangle, K is the Scherrer constant, and λ is the X-ray wavelength.Since few diffraction peaks were observed, we had to assumethat the strain was zero. Since the strain was zero, the domainsize is calculated from the y-intercept when plotting FW(S) ×cos(θ) vs sin(θ). In this case, the domain size could becalculated from

λ= ‐kx ysize ( )/( intercept) (6)

This allows the calculated domain size, from theWilliamson−Hull equation, to be plotted against chemicalpotential. It is apparent that as the chemical potential increases,there is a reduction in the domain size of the lamellar spacing.

■ CONCLUSIONSIt is clear that changes in solvent chemistry affect nucleationand crystal growth events that define the physical properties ofa SAFiN network, which are highly dependent on LMOG fiberlength. The nature of a solvent will change solvent−gelatorcompatibility, affecting the degree of undercooling, chemicalpotential, kinetics of gelation, and fiber morphology. Theseparameters are all inter-related and linearly correlated to boththe hydrogen-bonding Hansen solubility parameter as well asRa, the difference in the chemical nature between the solventand gelator. This work provides evidence that the properties ofSAFiN networks are not solely altered by the incorporation ofsolvent molecules into the SAFiN fibers, causing crystallo-graphic mismatches but also by the kinetics of self-assemblydriven by changes in chemical potential and undercooling.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.6b03476.

Chemical potential as a function of HSPs (Figure S1),undercooling, as determined using differential scanningcalorimetry versus the chemical potential difference atnucleation (Figure S2), a bright-field micrograph of 2 wt% 12HSA in octylamine to demonstrate how fiber lengthwas measured (Figure S3), and undercooling, chemicalpotential, rate constant of crystalline growth and fiberlength as a function of Hildebrand solubility parameters(Figure S4) (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: mroger09@uoguelph.ca. Phone: 519-824-4120, ext.54327.NotesThe authors declare no competing financial interest.

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