pubs.acs.org/Langmuir © 2009 American Chemical Society
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Small-Molecule Diffusion through Polycrystalline Triglyceride Networks Quantified Using Fluorescence Recovery after Photobleaching† Stephanie Marty,‡ Melanie Schroeder,§ Kenneth W. Baker,§ Gianfranco Mazzanti, and Alejandro G. Marangoni*,‡ )
‡ Department of Food Science, University of Guelph, Guelph, Ontario, Canada, §Ken Baker Associates, Acton, Ontario, Canada, and Department of Process Engineering and Applied Science, Dalhousie University, Halifax, Nova Scotia, Canada
Received January 20, 2009. Revised Manuscript Received March 13, 2009 Fluorescence recovery after photobleaching (FRAP) has been used to quantify Nile red diffusion through five different triglyceride crystal networks composed of pure peanut oil (PeO), pure chemically interesterified fully hydrogenated palm oil (IHPO), two blends of PeO and IHPO blended in different mass ratios (70:30 and 30:70%, w/w), and pure cocoa butter. Calculated components from FRAP experiments (effective diffusion coefficient (Deff) and mobile fraction (Mf)) were correlated with crystal network structural characteristics (crystalline mass fraction and permeability coefficient) and illustrated that Deff can be predicted using this tool. Higher-permeability coefficients found for higher fractal dimensions, lower volume fraction of solids, and larger average particle sizes were significantly correlated to higher Deff.
Introduction 1,2
Developed in the seventies, fluorescence recovery after photobleaching (FRAP) is a technique that has been constantly evolving to measure the translational mobility of fluorescent molecules in many kind of systems. Meyvis et al.3 have reviewed several of its applications, especially in drug delivery studies and, biological cell and tissue research. FRAP is a versatile technique which allows both the qualitative and quantitative analysis of labeled molecules dynamics in vivo and in vitro. FRAP can be used to characterize binding properties of labeled molecules to cell membranes, transmembranous and intracellular transport or more generally small molecule diffusion (e.g., drugs) in macromolecular networks (polymer solutions, gels and solids).3-7 This technique consists of two steps. (1) Within a well-defined area, fluorophores are first irreversibly photobleached with a high intensity laser beam. (2) Fluorescence recovery is then measured (using a much lower intensity light beam) as unbleached molecules diffuse from the surroundings into this bleached region. The effective diffusion coefficient (Deff) and mobile fraction (Mf) are parameters commonly determined from FRAP experiments.1,8
† Part of the Molecular and Polymer Gels; Materials with Self-Assembled Fibrillar Networks special issue. *Corresponding author. Tel: (519) 824-4120, ext 54340. Fax: (519) 8246631. E-mail:
[email protected].
(1) Axelrod, D.; Koppel, D. E.; Schlessinger, J.; Elson, E.; Webb, W. W. Biophys. J. 1976, 16, 1055. :: (2) Peters, R.; Peters, J.; Tews, K. H.; Bahr, W. Biochim. Biophys. Acta, Biomembr. 1974, 367, 282. (3) Meyvis, T. K. L.; DeSmedt, S. C.; Van Oostveldt, P.; Demeester, J. Pharm. Res. 1999, 16, 1153. (4) Kappel, C.; Eils, R. Confocal Application Letter 2004, August, 2. (5) Pinte, J.; Joly, C.; Ple, K.; Dole, P.; Feigenbaum, A. J. Agric. Food. Chem. 2008, 56, 10003. (6) Karbowiak, T.; Hervet, H.; Leger, L.; Champion, D.; Debeaufort, F.; Voilley, A. Biomacromolecules 2006, 7, 2011. (7) Karbowiak, T.; Gougeon, R. D.; Rigolet, S.; Delmotte, L.; Debeaufort, F.; Voilley, A. Food Chem. 2008, 106, 1340. (8) Reits, E. A. J.; Neefjes, J. J. Nat. Cell Biol. 2001, 3, E145–E147. (9) Weiss, M. Traffic 2004, 5, 662. (10) Seiffert, S.; Oppermann, W. J. Microsc. 2005, 220, 20.
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However, the models used for quantification has lately been questioned3,9 and other approaches have been proposed.10-12 Constantly driven by our interest in better understanding food microstructure, microscopy techniques are now considered as an essential tool to study structure-function relationships in relation to processing effects, ingredients interactions, phase formation and transformation, product stability and so on.13,14 The large progress in confocal light scanning microscopy during the last 50 years has opened an area for rapidly analyzing food specimens with minimum sample preparation and higher resolution (both in space and in time). Nowadays, most of the confocal light scanning microscopes (CLSM) allow for volume reconstruction, various scanning modes (x,y - x,z - x,y,t - x,z,t, for examples) and fluorescence based experiments like FRAP. Alike many other materials, food products are composed of several different phases in contact with each other, and are usually in a thermodynamically unstable state that will tend to stabilize in time and thus structural, textural and visual modifications may occur.13 For example, the migration of oil in confections is usually followed by the apparition of a white film (bloom) at the surface of chocolate. This is a common phenomenon encountered in the food industry; however, still poorly understood.15,16 Chocolate matrices are complex media often described as a mixture of cocoa and sugar particles dispersed in a continuous liquid and solid triglyceride phase.17,18 Therefore, part of these mobile components (specific triacylglycerides and minor lipids) will be able to participate in post-manufacture events such (11) Starr, T. E.; Thompson, N. L. Biophys. Chem. 2002, 97, 29. (12) Lele, T. P.; Ingber, D. E. Biophys. Chem. 2006, 120, 32. (13) Aguilera, J. M.; Stanley, D. W. Microstructural Principles of Food Processing and Engineering; 2nd ed.; Aspen Publishers, Inc.: Gaithersburg, 1999. (14) Kalab, M.; Allan-Wojtas, P.; Miller, S. S. Trends Food Sci. Technol. 1995, 6, 177. (15) Ghosh, V.; Ziegler, G. R.; Anantheswaran, R. C. Crit. Rev. Food Sci. Nutr. 2002, 42, 583. (16) Lonchampt, P.; Hartel, R. W. Eur. J. Lipid Sci. Technol. 2004, 106, 241. (17) Aguilera, J. M.; Michel, M.; Mayor, G. J. Food Sci. 2004, 69, R167–R174. (18) Loisel, C.; Lecq, G.; Ponchel, G.; Keller, G.; Ollivon, M. J. Food Sci. 1997, 62, 781.
Published on Web 04/28/2009
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Table 1. Experimental Settings for Fluorescence Recovery Measurements in Peanut Oil Matrices (PeO 100), Blends of 30 and 70% IHPO in Peanut Oil (IHPO30 and IHPO70), 100% IHPO (IHPO 100), and 100% Cocoa Butter (CB 100) prebleaching
bleaching
postbleaching lapse
1
2
3 a
4
5
6
fat
laser intensity (%) scanning mode zoom factor
40 xyt 1
100 or 0 xyt 8
40 xzt 1
40 xyt 1
40 xyt 1
40 xzt 1
PeO 100 time interval (sec)
number of frames 1.635
5 1.635
30 1.635
1 3
20 14
10 1.635
1
IHPO 30 time interval (sec)
number of frames 1.635
5 1.635
30 1.635
1 3.5
25 30
15 1.635
1
IHPO 70 time interval (sec)
number of frames 1.635
5 1.635
30 1.635
1 5
30 40
30 1.635
1
CB 100 time interval (sec)
number of frames 1.635
5 1.635
30 1.635
1 5
15 25
15 1.635
1
10 5
30 140
1 1.635
IHPO 100
number of frames 5 30 1 time interval (sec) 1.635 1.635 1.635 a The laser intensity was set to 100% for bleaching the region of interest (ROI) and 0% outside the ROI.
as oil migration and fat recrystallization to more stable polymorphs.17 The nature and the process by which these events take place are still rather difficult to accurately explain because of the complexity of the chocolate matrix, and a general lack of microstructural information. For these reasons, the main goal of our study was to adapt FRAP for the study of structural basis of small molecule diffusion in model fat confectionery matrices, namely triglyceride crystal networks.
Experimental Section Test Solutions. The concentration range for which a linear relationship exists (Fluorescence or Intensity = f(dye concentration)) was determined using five test solutions of 500, 1000, 1500, 2000, and 2500 μmol/L, respectively. These concentrations have been tested in a locally purchased peanut oil (PeO) (Guelph, Canada) and a commercially available chemically interesterified :: fully hydrogenated palm oil (IHPO) (Noblee & Thorl, Hamburg, Germany). From this test, a final concentration of 1500 μmol/L was chosen. Specimen Preparation and Characterization. Five different triglyceride crystal networks composed of (1) pure peanut oil (PeO), (2) pure chemically interesterified fully hydrogenated palm oil (IHPO), (3 and 4) two blends of PeO and IHPO blended in different mass ratios (70:30 and 30:70%, w/w) and (5) pure cocoa butter were stained with nile red (Sigma, St Louis, MO, USA) at a final concentration of 1500 μmol/L. Blended and dyed mixtures were kept at 110 C for 30 min and vortexed every 10 min in order to obtain a complete dissolution of nile red. Fluorescence recovery experiments were performed on these stained fat matrices (about 15 μL) squeezed between a microscope slide and a coverslip. Three replicates were carried out for each sample. Samples were then crystallized at 20 C for 24 h prior to FRAP experiments. Sample Solid Fat Content (SFC) was measured by pulsed Nuclear Magnetic Resonance (pNMR) using a Bruker PC/20 series NMR analyzer (Bruker, Mississauga, Ontario, Canada). Melted samples were introduced into glass NMR tubes (n = 3) and stored in the same conditions as above (24 h at 20 C) prior to monitoring SFC. FRAP Equipment. FRAP experiments were carried out on a Confocal Laser Scanning Microscope (Leica, confocal, TCS SP2, Mannheim, Germany) equipped with an Ar/KrAr laser. The 488 nm line of this laser (15 μW) was combined with a reflection short Langmuir 2009, 25(15), 8780–8785
pass dichroic filter (RSP 500). The fluorescence signal was recorded between 600 and 750 nm. A 40X Ph, oil immersion, objective lens (Leica, Germany) with a numerical aperture of 1.25 was used. 8-bit images at a resolution of 512 512 pixels were obtained with a line scanning speed of 400 Hz and a beam expander of 3, in both xyt and xzt modes, xy- and xz-sections recorded at successive time intervals. The transmission light detector (polarized light mode) and the fluorescence detector were simultaneously activated for the purpose of (1) visualizing the effect of laser beam on fat crystal network during fluorescence recovery experiments, and (2) measuring network structural characteristics as fractal dimension and particle size. FRAP Experiments: Image Acquisition. Fluorescence recovery experiments were designed using the time-lapse tool available from Leica software. Table 1 summarizes the settings chosen for each sample. More flexible than the FRAP application also available from the software, this procedure allows for scanning in various modes, using different zoom factors and laser intensities (Figure 1). Bleaching was assessed by zooming (digital zoom factor of 8) at the center of the image and thus, a precise region of interest (ROI) was objectively defined with a radius r0 = 22 μm. Moreover, to minimize dye fading over scanning, the laser power intensity was kept to 40% for acquiring pre-bleaching and post-bleaching images. During bleaching, the laser power was at a maximum (100%) within the ROI and a minimum (0%) outside this region. Three series of FRAP experiments were performed on each of the replicates, giving a total of nine series for each sample.
FRAP Experiments: Processing of Fluorescence Intensity Data. Measurements of fluorescence recovery in post-bleach images were assessed in ImageJ software (Rasband, W., National Institute of Health, Bethesda, MD., USA, http://rsb.info.nih.gov/ij/) within a smaller area than the whole ROI (diameter of 10 pixels or 7.3 μm) in order to avoid edge effects. This is an important point to consider in these experiments. Assuming that this is a single, circularly constrained ROI, unmoving in the Z dimension, then the ‘volume’ of the ROI would be ultimately defined by the spot size and the numerical aperture of the objective used for both excitation and emission, which remains unchanged from one sample to the next. The circular ROI, as such, defines a rastered scan of photons (mechanically) constrained in the X-Y dimension. As the beam extends to the edges of the ROI it might occur that there is an “edge effect” as the raster scan of exciting illumination and the corresponding emitted fluorescence travel longer (and possibly more irregular) paths in and out of the specimen.5 Since Z was shifted repeatedly, with a known step size DOI: 10.1021/la900255u
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Marty et al. Figure 1. Example of images acquired during fluorescence recovery experiments of IHPO 70 using the fluorescence detector (A-G) and the transmitted light detector in polarized mode (H-N). The following images were acquired in xyt scanning mode: A and H are pre-bleaching images; B, I, C and J are the two first and two last images acquired during bleaching with an electronic zoom factor of 8; E, L, F and M are the two first and the two last of post-bleaching images. D, K, G and N are post-bleaching images when scanned in xzt scanning mode. Such images were only acquired after the bleaching (D and K) and at the end of the fluorescence recovery (G and N). The vertical (xz direction) and the horizontal (xy direction) magnification bars represent 15 μm. Table 2. Image Normalization and Data Fitting Procedure for Effective Diffusion Coefficient (Deff) and Mobile Fraction (Mf) Determinationa determination of: Deff model assumptions normalization
Mf 1
Axelrod et al.
Disk-shaped bleached 2D diffusion the intensity of the first post-bleached image according to: FnðtÞ ¼
FðtÞ -Fð0Þ Fð¥Þ -Fð0Þ
See Figure 2B component determination
Siggia et al.20
0:88ω 4t1=2
FnðtÞ ¼
FðtÞ Fi
See Figure 2C
data are fitted with an exponential function and the recovery half-time t1/2 is determined Deff is estimated from: Deff ¼
the average intensity projection of the prebleached images according to:
2
Mf is determined graphically
a Deff - effective diffusion coefficient; Mf - mobile fraction; F(¥) fluorescence at equilibrium (time ¥); F(0) - fluorescence of the first postbleach image (time 0); Fn(t) - normalized fluorescence (or intensity) at time t; F(t) - fluorescence at time t; F i - average intensity projection of pre-bleached images; ω - bleached area radius; t1/2 - recovery half-time.
and a known number of steps, then the same calculation applies and you have in fact defined a cylindrical volume. The use of a circular ROI mitigates this possible ‘edge effect’ and in fact results in relatively uniform bleaching from one sample to the next. In 8782 DOI: 10.1021/la900255u
turn, this ‘edge effect’ could be greater when using a rectangle of fixed dimension. Further to this, we have specifically limited this possible artifact by limiting the intensitometric measurements to the center of the circular ROI. The center of the bleached area was defined as the minimum intensity on the y- and x-axis using the first post-bleach image of each series. Data processing consisted in two steps: (1) Image normalization, and (2) Measurement of the averaged radial intensity profile within the region as defined above (total of 10 values for each time point) and using a custom multimeasure plugin program developed in our laboratory for the ImageJ software.19 Fluorescence recovery was evaluated using the average of the measured averaged radial intensity for each time point. In order to be able to compare several image series using Axelrod’s and Siggia’s approaches, it is necessary to normalize the intensity to 100%.4 The main differences (image normalization and data fitting) of these two approaches are highlighted in Table 2 and Figure 2. From Axelrod’s theory, effective diffusion coefficients (Deff) can be estimated from the exponential fits of the data. This model assumes only diffusion occurs, the bleached area is a disk and the diffusion occurs only laterally.1,6 In contrast, (19) Mazzanti, G. X-Ray diffraction study on the crystallization of fats under shear. Ph. thesis. University of Guelph, Guelph, ON, Canada, 2004.
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FRAP Experiments: Microstructural Components Analysis. The fractal dimension was determined using the boxcounting method and the Euclidean distance mapping (EDM) method. The Benoit 1.3 software (TruSoft International Inc., St Petersburg, USA, http://www.trusoft-international.com) was used to measure the box-counting fractal dimensions (Db) in thresholded polarized light, non inverted prebleached micrographs. A log-log plot of the number of occupied boxes and the size of these boxes gives a line with a slope equivalent to Db. The Euclidean distance mapping fractal dimensions (DEDM) was measured in thresholded polarized light, inverted prebleached micrographs using an algorithm proposed by J.C. Russ21 and available from Fovea Pro 4.0 plug-ins (Reindeer Graphics Inc., North Carolina, USA) in Adobe Photoshop CS2 version 9.0.2 (Adobe System Inc., San Jose, USA). In this method, each pixel is assigned to a gray scale value proportional to its distance to the nearest pixel of the background. DEDM is then given by the slope a log-log plot of the area of the band swept over by the circle and the circle radius.21,22 Particle equivalent diameters were obtained from thresholded inverted polorized light prebleached images using Fovea Pro 4.0 plug-ins (Reindeer Graphics Inc., North Carolina, USA) in Adobe Photoshop CS2 version 9.0.2 (Adobe System Inc., San Jose, USA). Statistical Analysis. Statistically significant differences between samples were determined using a one-way ANOVA from SAS program 9.1.3 for Windows (SAS Institute Inc., Cary, NC, USA).
Figure 2. n w Fluorescence recovery in IHPO 30 observed in nonnormalized intensity profile vs time (A) and, after normalization using the first post-bleached image intensity (F0) according to Axelrod’s theory (B) and the average intensity projection F i of prebleached images based on Siggia’s model (C). Mf represents the mobile fraction. This fluorescence recovery after photobleaching data was obtained from image analysis of fluorescence and polarized light micrographs acquired in time. The dynamics of the photobleaching events can be best appreciated in video clips created from images taken both in the x-y and x-z planes in time. video clip of the FRAP experiment in IHPO 30 viewed from the x-y plane video clip of the FRAP experiment in IHPO 30 viewed from the x-z plane In both movies the fluorescence micrographs are overlaid on the polarized light micrograph of the crystal network in order to simultaneously show the structure of medium through which diffusion of the Nile Red dye is taking place after photobleaching. mobile fractions (Mf) can be determined from Siggia’s model but numerical approaches would be required to estimate Deff.20 Data analysis and fitting was carried out using GraphPad Prism version 4.0 for Windows (GraphPad Software, San Diego California USA, http://www.graphpad.com). (20) Siggia, E. D.; Lippincott-Schwartz, J.; Bekiranov, S. Biophys. J. 2000, 79, 1761.
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Results and Discussion Fluorescence recovery in peanut oil and IHPO (30:70, w/w) matrices along xy- and xz-axis are shown in Movies 1 and 2, respectively. Movie 1 is a combination of images acquired with the fluorescence and the transmitted light (polarized mode) detectors and overlapped in a RGB color mode image with the fluorescence signal in the red channel and the signal from the transmitted light in both the blue and the green channels. Movie 2 represents images only acquired with the fluorescence detector. As it can be observed in these movies, the laser used for bleaching significantly reduced nile red fluorescence intensity without apparently melting the triacylglyceride (TAG) crystal network. However, partial local melting of these systems cannot be excluded. Moreover, these images suggest that the dye was not covalently bound to fat crystals but rather entrapped into the network and thus diffusing around the crystals. This set of experiments was designed to determine TAG crystal network effects on the effective dye diffusion coefficients (Deff) in 2-D. While the literature describing the different possible methods to calculate Deff (analytical vs numerical resolutions) is vast3,4,9,20,23,24 one of the simplest approaches is based on an analytical solution of Equation 1 as proposed by Axelrod et al.1 In Equation 1, the change in unbleached fluorophore concentration at position r and time t, C(r,t), due to 2-D dimensional diffusion process in a disk-shape bleached area is given by: DCðr, tÞ ¼ DΔCðr, tÞ Dt
ð1Þ
where D is the lateral diffusion coefficient. This equation relies on fundamental boundary conditions: (1) there is no fluorophore concentration gradient before bleaching, (21) Russ, J. C. In The Image Processing Handbook; 5th ed.; CRC Press and Taylor & Francis Group: Boca Raton, 2007; Chapter 8. (22) Berube, D.; Jebrak, M. Comput. Geosci. 1999, 25, 1059. (23) Lopez, A.; Dupou, L.; Altibelli, A.; Trotard, J.; Tocanne, J. F. Biophys. J. 1988, 53, 963. (24) Soumpasis, D. M. Biophys. J. 1983, 41, 95.
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Table 3. Crystal Network Structural Characteristics (Φ, a, and Db), Effective Diffusion Coefficients (Deff), and Mobile Fractions (Mf) of Different Fat Matricesa,b Axelrod’s model
Siggia’s model
TAG system Φ (%) ( SD n a (μm) ( SD n Db ( SD n DEDM ( SD n Deff (m2/s) ( SD n Mf ( SD n nd 9 nd 9 nd 9 (5.15 ( 0.44) 10-12a 9 0.21 ( 0.02a 9 PeO100 0.27 ( 0.14a 3 1.93 ( 0.16a 9 1.19 ( 0.08a 9 1.77 ( 0.12a 9 (3.39 ( 0.46) 10-12b 9 0.26 ( 0.02a 9 IHPO30 14.14 ( 0.12b 3 1.67 ( 0.24b 9 1.22 ( 0.05a 9 1.81 ( 0.09a,b 9 (1.29 ( 0.58) 10-12c 9 0.33 ( 0.06a 9 IHPO70 36.20 ( 0.87c 3 1.60 ( 0.11b 9 1.39 ( 0.09b 9 1.90 ( 0.03b 9 (1.32 ( 0.90) 10-13d 5 0.32 ( 0.15a 5 IHPO100 60.25 ( 1.30d 3 2.53 ( 0.34c 9 1.08 ( 0.12c 9 1.59 ( 0.11c 9 (2.89 ( 1.48) 10-12b 9 0.76 ( 0.23b 9 CB100 76.47 ( 0.40e 3 a Statistically significant differences between fat systems and for a specific parameter are shown with different superscript letters. b Φ - crystalline mass fraction; a - particle size; Db - box-counting fractal dimension; DEDM - fractal dimension based on Euclidean distance-mapping method; SD standard deviation; nd - not determined; n - number of replicates.
(2) the fluorescent molecules only move by a diffusional process (no flow) in an infinite medium, (3) the bleaching time is short compared to the recovery (square-well profile condition for the fluorophore concentration at t = 0), and r > r0 C ¼ C0 g at t ¼ 0 C ¼ 0 0 < r < r0 where t = 0 is the end of the bleaching step or the beginning of the recovery.Based on these assumptions, one can determine Deff by fitting the normalized intensity using an exponential function and calculating the recovery half-time (t1/2) as explained in Table 2. Deff is then given by Equation 2: Deff ¼
0:88ω2 4t1=2
ð2Þ
where ω is the bleached area radius.1,4 Unlike numerical approaches, it is believed that the Deff estimate obtained using Axelrod’s solution has a lower accuracy due to specific initial condition assumptions and data precision issues.3,23,24 However, this method requires significantly less data processing and results are still very close to those obtained using more sophisticated approaches when boundary conditions are fulfilled.4 Numerical approaches can be used and could lead to a more accurate estimation of Deff; however, one of the aims of this paper was to use simpler analytical solutions to the problem which still provide a reasonable estimate of Deff. In this work we did not explore numerical approaches to solving the problem. A similar approach has been taken by many authors, including Karbowiak et al.6,7 Here, fluorescence recovery is 4 to 85 times faster than photobleaching (∼50 s) (Table 1) and the fluorophore concentration is homogeneous (no compartments as in living cells). Furthermore, we assume that there are no molecular interactions with the matrix and thus mobile molecules are only subject to diffusion (Brownian motion). TAG crystal network structural characteristics (Φ, a, Db and DEDM) and values directly extracted from fluorescence recovery experiments (effective diffusion coefficients (Deff) and mobile fraction (Mf)) are reported in Table 3. Similar Mf values (∼0.2-0.3) are obtained for PeO, IHPO 30, IHPO 70 and IHPO 100. Moreover, the estimation of the fluorescence loss during scanning from the prebleaching images was estimated to be approximately 0.3% per scan, ranging from 10 to 20% depending on the specimen. On the contrary, cocoa butter’s Mf (∼0.8) is significantly higher than the Mf in PeO/IHPO matrices. This difference might be partly due to the very specific crystallographic behavior of cocoa butter (CB) and thus possible matrix modification in time.25,26 Depending on the crystallization conditions (25) Wille, R. L.; Lutton, E. S. J. Am. Oil Chem. Soc. 1966, 43, 491. (26) Vaeck, S. V. Manuf. Confect. 1960, June, 35.
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Figure 3. (A) Relationship between the effective diffusion coefficient (Deff) and the crystalline mass fraction (Φ) in the material. The filled circles correspond to the PeO/IHPO system while the open square corresponds to the CB system. (B) Effect of crystalline particle size (a) and box-counting fractal dimension (Db) on Deff . (C) Relationship between Deff and the permeability factor (P). The filled circles correspond to the PeO/IHPO system while the open square corresponds to the CB system. Values correspond to means and standard errors of nine replicates.
(dynamic vs static, cooling rate, degree of supercooling, etc.) metastable forms (i.e., γ, R and β’) may crystallize first and recrystallize later into stable β polymorph.27 Another explanation for this discrepancy is the determination of Mf based on Siggia’s method (Mf = F(¥) - F(0)). The fluorescence of the first postbleach image F(0) is different between samples (ranging from 0.2 for CB100 to 0.7 for PeO100). This observation might illustrate that the apparent degree of bleaching differs depending on the (27) Koyano, T.; Hachiya, I.; Sato, K. Food Struct. 1990, 9, 231.
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sample nature i.e. more bleaching occurs as the crystal network contains more solid. Here, it is suggested that the fluorescence recovery occurring during photobleaching is relatively faster in PeO100 or IHPO30 than in IHPO100 or CB100 and thus lower F(0) will be observed in the latter examples. In contrast, F(¥) is always the same for all the samples (∼0.9) and thus F(¥) - F(0) will vary between samples only due to F(0). Finally, it is worthwhile noting the standard deviation associated with Mf determination is increasing as the solid mass ratio is increasing and represents approximately 20% for IHPO100 and CB100. The possible heterogeneity of the crystalline network of IHPO100 and CB100 might explain this increased uncertainty. In addition, it is important to highlight that both Db and DEDM measurements show a comparable trend. In PeO/IHPO matrices, higher fractal dimensions are associated with higher Φ and smaller particle sizes. Thus, the rest of our discussion will be based only on the analysis and comparison of Db with the other parameters. Some interesting correlations between the structure of the materials and the diffusivity of the dye through this structure were observed (Figure 3). As expected, diffusion through materials with a higher amount of solids (crystalline mass fraction, Φ) was diminished, and thus resulted in a lower Deff (Figure 3A). Notice how the PeO/IHPO system yielded a continuous trend, while CB did not follow the same trend line. This suggests that the amount of crystalline mass plays an important role in the diffusion process; however, there are other structural effects that must also be taken into consideration. Two of these structural factors included the average size of crystalline particles (a) and the box-counting fractal dimension (Db). Their effects on Deff are shown in Figure 3B. Larger crystalline particle sizes were associated with a higher Deff, while a higher network Db was associated with a lower Deff. A larger particle size results in a network with a greater proportion of oil-filled pores, through which diffusion can take place. A higher Db, in turn, is associated with a more homogeneous and space-filling distribution of network mass, which would impede diffusion. Both structural effects have been previously reported by our group.28 The combined effect of all structural factors in the permeability coefficient on Deff was studied further using Darcy’s Law28 (eq 3) Q ¼
B 3 Ac ΔPr η 3 L
ð3Þ
where Q is the volumetric flow rate, B is the permeability coefficient, Ac is the cross-sectional area through which flow takes place, η is the viscosity of the permeating oil, Pr is the pressure drop over the distance L. Furthermore, on the basis of Bremer et al.’s work,29 a permeability coefficient related to net(28) Dibildox-Alvarado, E.; Rodrigues, J. N.; Gioielli, L. A.; Toro-Vazquez, J. F.; Marangoni, A. G. Cryst. Growth Des. 2004, 4, 731. (29) Bremer, L. G. B.; van Vliet, T.; Walstra, P. J. Chem. Soc., Faraday Trans. 1989, 85, 3359.
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work structural characteristics can be determined using eq 4 P ¼ a2 Φ2=ðD -3Þ
ð4Þ
where a is the particle size, Φ is the solids’ volume fraction, and D is the crystal network fractal dimension. Here, P = B*K, with B being the permeability coefficient and K being the tortuosity factor of the Kozeny-Carman equation. This model predicts a higher permeability coefficient with lower fractal dimensions, lower Φ, and larger average crystalline particle sizes. We calculated the permeability factor (P=B*K) using the values reported in Table 3. As expected, Deff increased with increasing network permeability (Figure 3C). As for the case of the mass fraction of solids’ effect on Deff (Figure 3A), the continuous trend line corresponds to the PeO/IHPO system, while CB did not fall exactly on this trend line. This could be because we could not determine whether there were differences in the Kozeny-Carman tortuosity factor between the two systems. It is quite plausible that the tortuosity of the diffusive path between these two systems is different, thus affecting the value of the permeability constant. Future work will include strategies to determine this factor. These results suggest that small molecule diffusion through TAG crystal networks is most probably not controlled by a single structural factor, but by a combination of factors.
Conclusions This work demonstrates the potential of FRAP in determining the effect of the TAG crystal network structure on the diffusivity of small lipophillic molecules through the medium. Although the analytical approach used to estimate Deff relies on some assumptions (pure lateral (i.e., 2D) diffusion and disk-shaped bleached area), strong correlations between Deff and crystal network structural characteristics were observed. Numerical approaches could lead to a more accurate estimation of Deff, but much more work would also be required to validate such simulations for a specific system. Comparisons between such solutions (analytical vs numerical) as well as the effect of polymorphism, for example, will be assessed in future work. Thus, these preliminary results based on relatively simple approaches suggest that this FRAP technique could prove to be a powerful tool to engineer smallmolecule permeability through complex matrices. Note Added After ASAP Publication. This article was published ASAP on April 28, 2009. The second equation in the paper has been modified. The correct version was published on May 1, 2009. Acknowledgment. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Ministry of Agriculture and Food (OMAF). Special thanks go to Edmund Co for sample preparation.
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