Effects of Structural Attributes and Phase Ratio on Moisture Diffusion

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Effects of Structural Attributes and Phase Ratio on Moisture Diffusion in Crystallized Lipids Sravanti Paluri, Dennis R. Heldman, and Farnaz Maleky Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b00552 • Publication Date (Web): 24 Jun 2017 Downloaded from http://pubs.acs.org on June 26, 2017

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Crystal Growth & Design

COVER PAGE Effects of Structural Attributes and Phase Ratio on Moisture Diffusion in Crystallized Lipids Sravanti Paluri1, Dennis R Heldman1,2, Farnaz Maleky2,* 1

Department of Food, Agricultural, and Biological Engineering, The Ohio State University, Columbus 43210, USA 2 Department of Food Science and Technology, The Ohio State University, Columbus 43210, USA *Corresponding author. [email protected] ABSTRACT The objective of this investigation was to study the effect of crystallization conditions and constituent phase ratio on moisture diffusion in lipids. Lipid samples were prepared by fast (13 °C/min) or slow (0.7 °C/min) cooling of binary trilaurin-triolein blends at 200 s-1 shear rate from 60 to 38 °C. Faster cooling at constant shear rate decreased crystal sizes and increased fractal dimensions (Dbox). Effective moisture diffusivities (Deff) were calculated as a sum of vapor (Dv,eff) and liquid phase (Dl,eff) diffusivities by using measured structural data in a diffusion model. Although no correlation was observed between overall Deff and crystallization conditions, the Deff values increased with triolein content, from 5.8-7.5 x 10-12 (no triolein) to 1.2-1.3 x 10-12 m2/s (40% triolein). Results showed that due to the large magnitude of water vapor diffusivity in air, the impact of structural variations, caused by varying cooling rates, on overall Deff was masked. However, there was a strong correlation between crystallization conditions and Dl,eff. Simulations of the diffusion model in the absence of voids revealed that Deff decreased as liquid oil decreased and Dbox increased. Reducing moisture diffusion may help in preservation of quality and shelf-life extension in lipids and lipid-based food products. Figure. Slower cooling at the same shear rate and chemical formulation increased moisture diffusivity in the liquid oil fraction due to larger fat crystals and lower fractal dimension. The magnitude of this influence of crystallization conditions on diffusion depends on the liquid oil content. Note-LLL/OOO is trilaurin/triolein w/w ratio in the lipid blends.

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ACS Paragon Plus Environment


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Effects of Structural Attributes and Phase Ratio

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on Moisture Diffusion in Crystallized Lipids

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Sravanti Paluri1, Dennis R Heldman1,2, Farnaz Maleky2,*

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1

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University, Columbus 43210, USA

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43210, USA

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*Corresponding author. [email protected]

Department of Food, Agricultural, and Biological Engineering, The Ohio State

Department of Food Science and Technology, The Ohio State University, Columbus

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ABSTRACT

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The objective of this investigation was to study the effect of crystallization conditions

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and constituent phase ratio on moisture diffusion in lipids. Lipid samples were prepared

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by fast (13 °C/min) or slow (0.7 °C/min) cooling of binary trilaurin-triolein blends at 200

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s-1 shear rate from 60 to 38 °C. Faster cooling at constant shear rate decreased crystal

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sizes and increased fractal dimensions (Dbox). Effective moisture diffusivities (Deff) were

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calculated as a sum of vapor (Dv,eff) and liquid phase (Dl,eff) diffusivities by using

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measured structural data in a diffusion model. Although no correlation was observed

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between overall Deff and crystallization conditions, the Deff values increased with triolein

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content, from 5.8-7.5 x 10-12 (no triolein) to 1.2-1.3 x 10-12 m2/s (40% triolein). Results

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showed that due to the large magnitude of water vapor diffusivity in air, the impact of 2


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structural variations, caused by varying cooling rates, on overall Deff was masked.

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However, there was a strong correlation between crystallization conditions and Dl,eff.

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Simulations of the diffusion model in the absence of voids revealed that Deff decreased as

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liquid oil decreased and Dbox increased. Reducing moisture diffusion may help in

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preservation of quality and shelf-life extension in lipids and lipid-based food products.

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KEYWORDS

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cooling rate, shearing, moisture diffusion, fractal dimension

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NOMENCLATURE

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Da

Molecular diffusivity of water vapor in air (m2 s-1)

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Dbox

Box-counting fractal dimension

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Dc

Diffusivity in the continuous liquid oil phase (m2 s-1)

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Deff

Effective diffusivity of moisture (m2 s-1)

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Dl,eff

Effective moisture diffusivity in the liquid oil fraction (m2 s-1)

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Dv,eff

Effective water vapor diffusivity in the void fraction (m2 s-1)

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LLL

Trilaurin

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OOO

Triolein

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SFC

Volume fraction of solid fat (solid fat content)

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WUR

Water uptake ratio

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ζ

Volume fraction of liquid oil

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θ

Empirical parameter accounting for pore structural attributes 3



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ν

Volume fraction of void spaces

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τ

Tortuosity of the diffusional path

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Φ

Solid fat content or SFC

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INTRODUCTION

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Lipids are uniquely described by their chemical composition, polymorphism, melting

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point, solid fat content, and crystal structure attributes. Their structural attributes are

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greatly influenced by several internal and external factors during crystallization.1 The

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external factors influencing crystallization include degree of undercooling, cooling rate,

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the presence of mechanical agitation or shear, and application of pressure.1,2 Among these

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crystallization conditions, the application of cooling and shearing rates to influence

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microstructure and water or oil diffusion in lipids has been generating a lot of interest.

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Limiting the diffusion of moisture decreases microbial growth and other undesirable

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changes in quality and sensory attributes during the storage of lipids and lipid-based food

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products.3 It has been shown that in lipids as well as other polymer matrices, shear

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controlled crystallization reduces interlocking and agglomeration of crystals and

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produces homogeneously distributed smaller crystals.4,5 When sheared lipid samples

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were put in contact with oil or moisture, a marked decrease in oil or water uptake

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compared to their non-sheared counterparts was reported.3,6,7 While the application of

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shear has been confirmed to decrease moisture diffusion, the impact of cooling rate with

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or without shearing on moisture diffusion remains nebulous. Several studies have shown

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that there is a strong effect of cooling rate on the shape and size of crystals in a fat 4


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network.8–11 It has been observed that generally, faster cooling decreases crystal sizes in

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lipids.8–13 Some researchers have studied the relationship between crystal size, domain

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size, lamellar spacing, fractal dimension, etc., and permeation of water vapor through the

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fat networks.9,14,15 For instance, lower water vapor permeability was reported in lipid

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networks with higher solid fat content and bigger domain sizes.15,16

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Besides the above structural parameters, the modification of crystallization conditions

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with shear processing has also been shown to affect porosity or void fraction thereby

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influencing diffusivity.17 Therefore, a diffusing molecule encounters solid fat, liquid oil,

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and void spaces in the lipid network. Generally in a porous matrix, the porosity, solid fat

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content, mass diffusivity, and tortuosity are used to calculate the effective diffusivity of

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oil or water in a lipid network.18 As per Marangoni et al., the network’s porosity can be

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defined as volume ratios of either oil to total volume (in absence of voids) or the effective

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volume available (anything but solid fat) to total volume.17 The above parameters can be

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measured experimentally except for the tortuosity which reveals information about

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variation in diffusional path caused by different structures. Hence, in order eliminate the

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need for storage studies by predicting oil or moisture diffusivity in lipids, it is necessary

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to express tortuosity as other measurable structural properties. , Due to absence of a

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structure-based model, the tortuosity parameter has been either ignored or speculated in

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the past correlations between structure and moisture permeability.15,19–21 As a result, the

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influence of crystallization conditions on moisture diffusivity calculated from models

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using structural properties (including tortuosity) as inputs is not yet clear.

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The objective of this investigation was to study the effect of cooling rate at a constant

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shear rate applied during lipid crystallization on the structural properties and moisture

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diffusion through the network during storage. For this purpose, lipid samples were

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prepared by cooling at two different rates with a constant shearing rate. The effect of

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crystallization conditions on structural attributes, such as solid fat content, void fraction,

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crystal sizes, and fractal dimension was analyzed. A correlation between structural

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attributes and moisture diffusivity was established by applying a diffusion model to

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moisture uptake data from nuclear magnetic resonance microimaging.

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MATERIALS AND METHODS

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Trilaurin of 99.2% purity, triolein of 95% purity, microbiology grade granulated agar

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powder were purchased from TCI America (OR, USA), Pfaltz & Bauer Inc. (CT, USA),

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and BD Difco Dehydrated Culture Media (NJ, USA), respectively. Three lipid blends

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were prepared by mixing trilaurin (LLL) and triolein (OOO) in 100/0, 80/20, 60/40 w/w

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ratios at 60 °C in a jacketed beaker connected to a water bath. These blends were held

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isothermally at 60 °C, well above the melting point of ̴ 47.5 °C, for 30 minutes to destroy

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all crystal memory. The melts were then cooled at fast (13 °C/min) or slow (0.7 °C/min)

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rates and 200 s-1 shear rate to 38 °C, about 10 °C below their melting point to ensure

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crystallization and transferred to glass sample vials 8 mm diameter x 40 mm height.

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Upon transfer, the samples were labeled with the nomenclature LLL%/OOO%/cooling

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rate as 100/0/fast, 100/0/slow, 80/20/fast, 80/20/slow, 60/40/fast, and, 60/40/slow and

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stored isothermally at 38 °C. 6


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Solid Fat Content

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The solid fat content (SFC) data for the samples was measured in triplicate at 38 °C using

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pulsed nuclear magnetic resonance (Minispec mq20 spectrometer, Bruker Optics Ltd.,

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ON, Canada) and reported in Table 1.

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Crystal Attributes

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The microstructure of lipid samples was observed under a Carl Zeiss polarized light

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microscope (PLM) (Carl Zeiss Microscopy GmbH, Germany) fitted with Axiovision Rel.

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4.8 camera and a heating stage. A small droplet of the sample was extracted after cooling

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to 38 °C, placed on a preheated glass slide and covered with a preheated glass cover slip.

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This slide was stored at 38 °C in an incubator for two days after which it was imaged in

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the PLM under 10x magnification at 38 °C as shown in Figure 1a. Images were

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thresholded on ImageJ (U.S. National Institute of Health, Bethesda, Maryland, USA) as

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shown in Figure 1b. Next, the crystal areas in the thresholded images were calculated

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using ImageJ as illustrated by the shaded region in Figure 1c. The thresholded images

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were formatted to BMP files on Adobe Photoshop, and the box-counting fractal

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dimension was calculated on BenoitTM software (TruSoft International Inc., FL, USA) as

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shown in Figure 1d. About forty such images from multiple replicates of each sample

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were analyzed.

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Void Fraction 7



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The void fraction in samples was measured using a Vereos Digital positron emission

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tomography/computed tomography (PET/CT) system from Philips, Cleveland, OH, USA.

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All the samples were crystallized in the jacketed beaker assembly, pipetted into glass

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vials (8 mm diameter x 40 mm height), and stored at 38 °C for 2 days before CT imaging

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at 120 kV. Three centrally located slices of 0.63 mm thickness with 61 x 58 microns2

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resolution in the sagittal plane were analyzed. The image processing and data analysis

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steps for one representative slice are shown in Figure 2. The slice from CT scan was a

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grayscale image consisting of pixels with varying intensities (Figure 2a). In 8-bit images,

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a pixel with an intensity of 0 appears black, 255 appears white, and all other intensity

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values in between are shades of gray. Since air voids are of present interest, the pixels of

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value 0 (black) were to be separated from all other pixel values. However in reality, due

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to discontinuous regions and complex boundaries in images, it is often difficult to

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delineate the area of interest (black pixels of value 0) from the background. To address

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this problem, segmentation or thresholding was performed to separate a segment of pixel

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values in the neighborhood of 0 from the rest of the image using ImageJ as shown in

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Figure 2b. Next, using MATLAB (R2013b, The Mathworks, Inc., Natick, MA, USA), the

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thresholded image was converted into a binary image of only black (value 0) and white

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(value 1) pixels (Figure 2c). The void fraction was calculated as the ratio of black pixels

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to total pixels in the image as illustrated in Figure 2d. Triplicates of samples were

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prepared to produce nine slices for analysis (three replicates x three slices). The measured

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void volume fraction in samples is reported in Table 1.

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The pulsed nuclear magnetic resonance (p-NMR) method used here only accounted for

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the volume fraction of protons present as solid (ϕ). The volume fraction present as liquid

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was 1-ϕ. Since voids or air spaces are devoid of protons, they are not accounted for in p-

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NMR measurements. The void fractions of samples measured using CT are reported in

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Table 1. Therefore, the total volume of all the phases in the sample was calculated as the

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sum of the volume fraction of solids (ϕ), liquids (1- ϕ), and voids (as measured by CT).

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The actual liquid oil fraction (ζ) and void fraction (ν) were calculated by dividing their

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respective measured values over the total volume and reported in Table 2.

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Moisture Uptake Measurements

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A 1.5% agar gel was prepared to use as a moisture source for studying moisture uptake in

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lipid samples. The gel was poured into glass tubes (10 mm diameter x 0.6 mm thickness x

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160 mm height) to about 15 mm high and stored for a day at 38 °C. Lipid samples were

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prepared as described previously and poured into glass vials and stored for two days at 38

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°C. The crystallized lipid samples were layered on top of the 1.5% agar gel layer by

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inverting the open-top 8 mm diameter vials filled with lipids and inserting them into the

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10 mm diameter tubes filled with agar gel. These two-layered samples were stored for

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nine weeks at 38 °C to mimic moisture diffusion in a multi-layered food system during

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storage. Moisture diffusion was measured in a Bruker Avance III HD Ascend 800 MHz

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nuclear magnetic resonance instrument equipped with a 5/10 mm Micro5 Imaging Probe

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interfaced to Paravision v6.0 (Bruker) software. The data was analyzed as per Paluri et

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al., and the moisture uptake values were calculated.3 9



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Statistical Analysis

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Data were processed using JMP®, Version 10 (SAS Institute Inc., Cary, NC). The

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reported values correspond to means and standard errors. Statistical analysis was

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performed by one-way ANOVA, student t- and Tukey tests at α=0.05. For regression

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coefficients, the analysis was performed with z-statistics and two-tailed p-values for

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differences in means (α=0.05).22,23

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RESULTS AND DISCUSSIONS

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Polarized light microscopy images for each sample are shown in Figure 3a-f. As seen in

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the figure, the crystals had varied morphologies (spherical or rod-like) depending on the

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sample. Therefore, for comparison of crystal sizes, the equivalent circle diameters for

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various shapes were calculated based on crystal areas computed using Figure 1 and

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reported in Table 1. Results of a two-way ANOVA test revealed that both crystallization

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conditions and LLL/OOO ratio had significant effects on crystal sizes. A statistical

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comparison of crystal sizes showed that the fast-cooled samples at 200 s-1 shear had

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significantly smaller crystal sizes compared to the slow-cooled samples made with the

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same LLL/OOO ratio. It has been previously reported that the increase in cooling rate8–11

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and the presence of shearing24–27 lead to a decrease in the size of crystals. The smaller

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size of crystals observed in samples cooled faster at the same shear rate of 200 s-1 (Table

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1) could be explained by the viscosity changes and nucleation rate of crystals under

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different cooling rates.28 It has been reported that in fast cooling, a large number of nuclei 10


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form instantly causing a fast increase in viscosity thereby hindering molecular movement

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and limiting crystal growth.8,10,11 On the contrary, Martini et al. found that under slow

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cooling conditions, the nuclei form after longer induction times and grow slowly under

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increased mass transfer rates and lower viscosity conditions to form bigger

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aggregates.29,30

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Although the overall effect of LLL/OOO ratio on the crystal sizes was significant, the

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crystal sizes of the 100/0 and 80/20 samples were similar (Table 1). However, both the

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fast and slow-cooled 60/40 samples had significantly larger crystals compared to all the

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100/0 and 80/20 samples. Comparing the fast-cooled samples containing 0% (100/0/fast)

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and 40% triolein (60/40/fast), the 60/40/fast samples exhibited crystal sizes nearly two

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times as that of the 100/0/fast samples (Table 1). This was attributed to the large fraction

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of liquid oil present in the 60/40/fast sample which facilitated better heat transfer

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conduction and increased molecular movement to cause the growth of larger crystals

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compared to the 100/0/fast sample.31 Similarly, the large fraction of liquid oil present in

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the 60/40 samples cooled at a slow rate is also expected to enhance the crystal growth in

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60/40/slow sample compared to the 100/0/slow sample. In fact, the crystal size

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differences were rather dramatic in the slow-cooled samples where the 60/40/slow

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sample had four times bigger crystals than the 100/0/slow sample (Table 1). Besides the

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presence of more liquid oil in 60/40/slow sample, this drastic increase in crystal sizes was

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also due to longer time for nucleation and crystal growth under slower cooling Therefore,

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due to the combined effects of slower cooling and the presence of more liquid oil

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increasing heat transfer and molecular mobility, the 60/40/slow sample had much larger 11



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crystals compared to the 100/0/slow sample. This information is interesting as previous

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studies have linked crystal sizes in lipids to the transport of water or oil through the

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network.15,19,32

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Another important structural property of lipid networks with respect to diffusion through

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the medium is the fractal dimension.19,20,32 Fractal dimension is a measure of self-

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similarity and spatial distribution or degree of occupancy of mass in the crystal

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network.8,33 Among the several types of fractal dimensions; box-counting, particle-

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counting, Fourier-transform, etc.; the box-counting fractal dimension has been reported to

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be more sensitive to crystal shape, size, and area fraction (number of pixels in the image

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occupied by crystals divided by the number of pixels in the whole image).34 Furthermore,

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since the box-counting fractal dimension is calculated on the basis of position and

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distribution of fat crystal mass in the micrographs, it is expected to influence the

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diffusional path of water in the fat matrix. A higher fractal dimension signifies a more

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ordered and homogeneous network.33 From fractal dimensions of the samples reported in

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Table 1, it was revealed that both crystallization conditions and LLL/OOO ratio had

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significant effects on fractal dimension. However, no particular trend was observed for

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the effect of LLL/OOO ratio on fractal dimension. All the fast-cooled samples (Figure 3a,

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c, e) exhibited significantly higher fractal dimensions compared to the slow-cooled

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samples (Figure 3b, d, f) prepared at the same shear rate. This is in agreement with the

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literature, wherein rapidly cooled lipid samples were found to display a more

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homogeneous spatial distribution and higher mass occupancy thereby exhibiting higher

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fractal dimensions.8,35,36 Moreover, the presence of shearing has also been reported to 12


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encourage homogeneous crystal size distribution and ordered structures leading to higher

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fractal dimensions.37,38

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As reported in Table1, the lipid samples had about 2%-7% volume void space (ν) when

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crystallized in the glass vial indicating that the presence of shearing during sample

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preparation introduced air bubbles in the melt. A two-way ANOVA test revealed that

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while the effect of LLL/OOO ratio on the void fraction was significant, the crystallization

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conditions did not affect the void fraction significantly. Results indicate that the void

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fraction in samples containing 100% LLL was significantly higher than samples with

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20% and 40% triolein that had much lower SFC. Indeed, it has been noted in the past that

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air bubbles incorporated during preparation are retained better in samples with higher

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SFC after the mixing is stopped.39 Hence, it is evident the crystallization conditions and

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compositional variations used in this study had a strong correlation with structural

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properties. Next, the effects of varying structural properties and LLL/OOO ratio on

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moisture diffusion through the lipid network were evaluated.

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Experimental water uptake ratios (WUR) have been computed by taking a ratio of the

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experimental water uptake values over the maximum water uptake value for all samples

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and plotted in Figure 4a-c.

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Effective moisture diffusivity in the lipid samples consisting of impermeable solids,

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liquid oil, and void spaces was correlated to the network structure by using a diffusion

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model based on fractal porous media theory.40 Tortuosity of the diffusional path is inbuilt

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in the model as a function of measurable attributes- liquid oil fraction and fractal

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dimension. The structural data from Table 1 were used as inputs to the model (Equation

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1) for predicting effective moisture diffusivities (Deff) in the lipid samples.

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Deff = Dv,eff + Dl,eff = ν θ Da + ζ Dbox / (2-Dbox) Dc

[1]

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where Dv,eff and Dl,eff are effective moisture diffusivities in the void and liquid fraction,

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respectively, ν is the void volume fraction, θ is an empirical parameter related to void

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structure, Da is molecular diffusivity of water vapor in air= 2.4 x 10-5 m2/s at 38 °C18, ζ is

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liquid oil volume fraction, Dbox is fractal dimension, and Dc is molecular diffusivity of

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water in liquid oil. Initial guesses were made for the unknowns, Dc, Deff, and θ, to

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generate predictions of water uptake ratios (WUR). To minimize the root mean squared

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error (RMSE) between experimental and predicted WUR profiles and obtain the optimum

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values of Dc, Deff and θ, a MATLAB program was written. Based on the minimum RMSE

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values, the molecular diffusivity of water in the liquid oil fraction (Dc) in all the samples

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was found to be 1.5 x 10-11 m2/s. This value is in the same order of magnitude as that

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reported by Bourlieu et al. in various lipids.41 The predicted WUR profiles of the samples

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are plotted alongside the experimental values in Figure 4a-c. As seen in the figure, there

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was a close agreement (RMSE 0.009-0.045) between the experimental and predicted

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curves of all the samples. This confirms that the structure-based model used (Equation 1)

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successfully captures moisture diffusion occurring in all the lipid samples.

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The diffusion model used here (Equation 1) presents the overall effective moisture

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diffusivity (Deff) as a sum of effective diffusivity in the void (Dv,eff) and liquid fractions 14


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(Dl,eff) as shown in Figure 5a. It was found that while the LLL/OOO ratio had a

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significant effect on overall Deff, the crystallization conditions did not influence the

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overall Deff values reported in Figure 5a. The samples with 15-16% SFC had significantly

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higher Deff values than those with 91-94% SFC. Moreover, individual contributions from

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vapor phase and liquid phase diffusion in overall diffusivity values were reported. For

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example, in 100/0 samples with 91-94% SFC and 6-7% void fraction (ν), vapor phase

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diffusion dominated due to the high molecular diffusivity of water vapor in air at 38 °C

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(Da= 2.4 x 10-5 m2/s). As the solid fat content decreased, the contribution from liquid

291

phase diffusion in overall diffusivity values increased. The average liquid oil fraction for

292

the two different crystallization condition at each LLL/OOO ratio are reported in Table 2.

293

As the ζ increased from an average of 7% in 100/0 samples to 83% in 60/40 samples, the

294

contribution of liquid phase diffusion increased to almost 45% of Deff (Figure 5a).

295

However, it seems that the predominant mode of mass transport remained to be vapor

296

phase diffusion in the void fraction. This was attributed to the overshadowing value of

297

molecular diffusivity of water in the air (Da ~ 10-5 m2/s) compared to liquid oil (Dc ~10-11

298

m2/s). This disparity in contributions from vapor and liquid phase diffusion to the overall

299

Deff most likely masked the effect of structural attributes on moisture diffusion in lipids.

300

Influence of LLL/OOO ratio and solid fat content on effective diffusivity. While

301

consistent trends were not observed for the effect of LLL/OOO ratio on the overall Deff,

302

the trends in effective diffusivities in the liquid oil fraction (Dl,eff) were found to be

303

consistent (Figure 5b). For example, diffusion in the liquid phase was significantly

304

influenced by constituent ratio when samples containing 100/0, 80/20, and 60/40 15



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Page 16 of 35

305

LLL/OOO ratio had ascending Dl,eff values of 10-16 – 10-15, 2 – 3 x 10-12, and 6 – 7 x 10-12

306

m2/s, respectively. As expected, the Dl,eff values of fast and slow-cooled samples

307

increased with the addition of triolein and the accompanying decrease in SFC. For

308

instance, when compared to the samples containing no triolein, the addition of triolein in

309

the liquid phase dramatically increased Dl,eff values from 10-16 – 10-15 in 100/0 samples to

310

10-12 m2/s in samples with 20%-40% by weight triolein (Figure 5b). This increase in

311

diffusivity values with increase in triolein weight fraction could be attributed to (i) the

312

relatively high polarity of unsaturated bonds in triolein, and (ii) the increase in liquid oil

313

fraction (ζ) from an average of 7% in 100/0 samples to 83% in 60/40 samples that

314

allowed for a marginally larger volume fraction of the system to be available for moisture

315

diffusion. This finding is in agreement with the work of Bourlieu et al. who reported that

316

moisture sorption and effective water diffusivity exponentially increases with an increase

317

in polarity and liquid content.42 Some other studies have also reported an increase in

318

water vapor permeability (WVP) in samples with lower SFC (higher liquid content).38,43

319

For example, in triolein-containing lipid films, water vapor transmission rate decreased

320

by 92% when SFC increased from 20 to 80% depending on film thickness.44 Ghosh et al.

321

reported a drastic decrease in WVP of about 87% when SFC from increased from 25% to

322

80%.45 While the increase in Dl,eff values found in this work is strongly related to SFC

323

and polarity of triolein, interestingly, the effect of polarity was muted when the samples

324

with the same LLL/OOO ratio were crystallized under different conditions (Figure 5b).

325

Influence of crystallization conditions on effective diffusivity. Moreover, this figure

326

(5b) documented the significant influence of crystallization conditions on Dl,eff. This is in 16


Page 17 of 35

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327

contradiction to the insignificant effects of structure on overall moisture diffusivity (Deff)

328

obtained from the sum of diffusion coefficients in the void (Dv,eff) and liquid oil fraction

329

(Dl,eff) (Figure 5a). This provides substantial evidence that the large magnitude of water

330

vapor diffusivity in void fraction had masked the impacts of structural differences created

331

by varying crystallization conditions (Table 1) on the overall Deff in the samples.

332

Furthermore, in samples with SFC < 40% (80/20/fast, 80/20/slow, 60/40/fast,

333

60/40/slow), the Dl,eff increased as the cooling rate at 200 s-1 shear decreased. This is not

334

in agreement with Franke et al.’s study where a minimum of 35% SFC was reported to be

335

necessary for the fat structure to influence moisture barrier property significantly.46 The

336

disagreement could be attributed to the thinner layers of fat, smaller moisture

337

concentration gradients, and an inferior gravimetric moisture measurement technique

338

used in their study. In support of the dependency of moisture diffusion on structural

339

attributes and the SFC, at very high SFC values (91-94%), structural differences in our

340

samples did not create significant differences in moisture diffusivities which in turn were

341

very low in magnitude (10-16-10-15 m2/s). This observation draws attention to the complex

342

relationships among SFC, structural attributes, and moisture diffusivity in lipids which

343

could be better understood through simulations.

344

While remarkable effects of structural attributes on liquid oil diffusivity (Dl,eff) were

345

reported in all the samples, a direct relationship of structure and overall Deff (Dl,eff +

346

Dv,eff) could not be established. As confirmed previously, this lack of relationship is

347

because the effective diffusivity in the void fraction (Dv,eff) masks the effect of structure

348

on the overall diffusivity. Although the creation of voids during experiments was 17



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Page 18 of 35

349

inevitable, the model in equation 1 allows for simulation of diffusion in solid-liquid

350

matrices in the absence of voids. Therefore, the individual effects of liquid oil fraction (ζ)

351

and fractal dimension (Dbox) on diffusivity values were evaluated using simulations with

352

the diffusion model by assuming negligible ν (and Dv,eff).

353

Simulations of moisture diffusion in lipids. Using equation 1, the model’s sensitivity

354

was tested through simple simulations in which one parameter was varied while the other

355

was held constant. In theory, the liquid fraction ζ in a lipid network ranges from 0 for the

356

presence of no liquid oil (SFC=1) to 1 for the absence of any solids (SFC=0). Fractal

357

dimension is a fraction 1.0 < Dbox < 2.0, used to describe fractals that have a mass

358

distribution between that of a line (Dbox = 1.0) and a two-dimensional plane (Dbox =

359

2.0).47 Hence, to isolate the influence of ζ on Deff predictions, the fractal dimension Dbox

360

was fixed at a value between 1.0 and 2.0. Figure 6a illustrates the variation of Deff as

361

predicted by the model with liquid oil fraction at Dbox = 1.1, 1.5, 1.9. It was observed that

362

overall, Deff increased with increase in ζ. Irrespective of Dbox values, the Deff values

363

reached a maximum of 15 x 10-12 m2/s equivalent to the molecular diffusivity of water in

364

oil when ζ=1. However, an increase in the amount of liquid oil fraction increased Deff at a

365

rate depending on the Dbox value. This is indicative of the important role of fractal

366

dimension (ζ) on moisture diffusion in lipids. The effect of fractal dimension on Deff in

367

lipids devoid of air fraction was also studied using simulations of the model (Equation 1).

368

Simulations were performed at measured ζ values of the samples used in this study

369

instead of using theoretical inputs of ζ. The Deff vs. Dbox curves at ζ values of fast and

370

slow-cooled samples from Table 2 were plotted in Figure 6b. Contrary to the impact of ζ 18


Page 19 of 35

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371

on Deff, an inverse relationship was observed between the predicted effective diffusivity

372

values and Dbox at any ζ. As mentioned previously, the crystal mass in a system with a

373

higher Dbox value is better distributed in the two-dimensional plane. This well-distributed

374

crystal mass (Dbox → 2.0), creates an increasingly tortuous path for moisture diffusion

375

around the relatively impermeable crystals. As a result, in Figure 6b, as Dbox → 2.0, the

376

Deff values drop below 10-12 m2/s irrespective of the liquid oil fraction (ζ). With a

377

decrease in Dbox, the Deff increased at different rates depending on the liquid oil fraction.

378

To compare the impact of changes in Dbox on Deff at a given liquid oil fraction (ζ), Deff vs.

379

Dbox curves were plotted at the three average ζ values (0.07, 0.59, 0.83) for fast and slow-

380

cooled samples of each LLL/OOO ratio (Figure 6b). The measured Dbox values of fast

381

and slow-cooled samples from Table 1 were marked on the average ζ curve for each

382

LLL/OOO ratio on the figure. The Deff vs. Dbox curves were found to exhibit drastically

383

different slopes depending on ζ values. A linear fit to the curves revealed that while the

384

slope was very low at ζ = 0.07 in 100/0 samples, it grew increasingly negative as ζ

385

increased. Due to the small slope (-0.6 x 10-12 m2/s) at ζ = 0.07 for 100/0/fast and

386

100/0/slow samples, different Dbox values created by changing cooling rates under

387

constant shear did not create significant differences in Deff values. This is reflected in the

388

small and statistically similar values of Deff =10-16 - 10-15 m2/s for these samples in Figure

389

5b. On the other hand, the slopes of Deff vs. Dbox curves were highly negative at -9.9 and -

390

14.4 x 10-12 m2/s at large values of ζ = 0.59 and 0.83 in the 80/20 and 60/40 samples,

391

respectively. The steep slopes of Deff vs. Dbox indicate that at larger base values of ζ in the

392

power law (Equation 1), the differences in Dbox values caused by varying crystallization 19



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Page 20 of 35

393

conditions might create significant changes in the Deff of samples. Indeed, the effect of

394

cooling rate at constant shear became prominent in the predominantly liquid (80/20 and

395

60/40) samples when different Deff values were obtained from statistically different Dbox

396

values (Figure 5b). Generally, slowly cooled samples at 200 s-1 shear exhibited lower

397

fractal dimensions and higher Deff values depending on the SFC. This was in agreement

398

with Dibildox-Alvarado et al. who reported higher permeability values for slowly cooled

399

samples with lower fractal dimensions.19 Therefore, it follows that the effect of

400

crystallization conditions (cooling rate and shearing) on Deff values depends on the SFC

401

and volume fraction of liquid oil in the sample. This concludes that in the absence of void

402

fraction, (i) Deff in a solid-liquid system is strongly correlated to Dbox and ζ values, (ii)

403

Deff increases with increase in ζ at rates depending on the magnitude of Dbox, and (iii) Deff

404

decreases with increase in Dbox depending on ζ values. Therefore, in lipid systems with

405

very low ζ, differences in Dbox values created by changing crystallization conditions

406

(cooling rate and shearing) may not influence Deff, whereas, at high ζ, changes in Dbox

407

have a significant effect on Deff values.

408 409

CONCLUSIONS

410

In this study, significant effects of LLL/OOO ratio and crystallization conditions (cooling

411

rate at constant shear) on the structural attributes of binary blends of monoacid

412

triacylglycerols, trilaurin and triolein were reported. Although specific relationships

413

among the LLL/OOO ratio, void fraction, fractal dimension, and crystal sizes of samples

414

were not observed; there was a direct correlation between the crystallization conditions 20


Page 21 of 35

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415

and structural attributes. An increase in cooling rate at constant shear rate was found to

416

significantly decrease crystal sizes and increase fractal dimensions in the samples.

417

Using a structure-based diffusion model, it has been established that the effective

418

moisture diffusivity in lipids containing relatively impermeable solids is a sum of

419

diffusivity in the void and liquid oil fractions. The model which required inputs of

420

measured void fraction (ν), liquid oil fraction (ζ), fractal dimension (Dbox) values, and an

421

empirical parameter (θ) related to void structure successfully predicted water uptake in all

422

the samples. Diffusion in void fraction dominated moisture transport in all the lipid

423

samples due to the large magnitude of molecular diffusivity of water vapor in the air

424

(~10-5 m2/s) as compared to water in liquid oil (~10-11 m2/s).

425

In solid-liquid mixtures, the importance of fractal dimension and liquid oil fraction in

426

moisture diffusion has been clearly demonstrated through simulations of the structure-

427

based model. Effective moisture diffusivities increased with an increase in liquid oil

428

fraction and a decrease in the fractal dimension of the lipid matrix. Faster cooling creates

429

a more tortuous diffusional path (Dbox →2) around the homogeneous and spatially well-

430

distributed mass of fat crystals in the lipid matrix. As a result, lipid layers and

431

components prepared with faster cooling at the same shear rate will be more resistant to

432

moisture transfer. In lipids with a high content of impermeable solids and low liquid oil

433

fraction available for diffusion, structural features have limited influence on moisture

434

diffusion. As liquid oil fraction increases, the changes in structural features begin to have

435

a significant influence on effective diffusivities for moisture migration through the lipid

21



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Page 22 of 35

436

network. This clearly establishes that the effects of fractal dimension and liquid oil

437

fraction on moisture diffusion in lipids depend on their relative magnitudes.

438 439

ACKNOWLEDGEMENTS

440

This work was supported by the USDA National Institute of Food and Agriculture, Hatch

441

project 232768, the Ohio Agricultural Research and Development Center, and the

442

Seiberling Endowment at The Ohio State University, Columbus. The authors would like

443

to thank Dr. Michael Knopp and Dr. Katie Binsell at the Wright Center for Innovation,

444

Department of Radiology, The Ohio State University, Columbus, for their help with

445

computed tomography.

446 447

22


Page 23 of 35

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448

FIGURES

449 450 451 452 453

Figure 1. A representative image depicting microstructure of lipid network. (a) Polarized light microscopy image at 10X magnification, (b) thresholded image generated in ImageJ and Adobe Photoshop, (c) ImageJ identified crystals as shaded regions of average crystal area of 63 microns2, (d) Benoit calculated the box-counting fractal dimension (Dbox) of this image to be 1.71.

454 455 456 457 458 459 460

Figure 2. Computed tomography (CT) of lipid samples for measuring void fraction. (a) A representative CT slice in the sagittal plane, (b) thresholded image of slice generated in ImageJ, (c) binary image consisting of only black and white pixels using MATLAB, (d) histogram depicting frequency of bins 0 (black pixels) and 1 (white pixels). Void fraction calculated as the ratio of black pixels to total pixels was found to be 0.088 or 8.8%.

461 462 463 464

Figure 3. Polarized light microscopy images at 10X magnification and 38 °C of slow (0.7 °C/min) or fast (13 °C/min) cooled sample (a) 100/0/fast, 91% SFC, (b) 100/0/slow, 94% SFC, (c) 80/20/fast, 40% SFC, (d) 80/20/slow, 38% SFC, (e) 60/40/fast, 15% SFC, (f) 60/40/slow, 16% SFC, under 200 s-1 shear.

465 466 467 468 469 470

Figure 4. Model predicted water uptake ratios for fast (solid lines) and slow-cooled (dashed lines) samples prepared at a 200 s-1 shear rate with (a) SFC 91-94%, 100/0, (b) SFC 38-40%, 80/20, (c) SFC 15-16%, 60/40 w/w ratios of trilaurin and triolein. Experimental ratios for fast and slow-cooled samples are displayed with filled square and open squares markers, respectively.

471 472 473 474 475 476 477

Figure 5. Predicted effective diffusivity values from proposed model for fast (solid pattern) and slow-cooled (striped pattern) samples prepared at a 200 s-1 shear rate. (a) Overall Deff as a sum of Deff in both vapor phase (Dv,eff, gray solid or gray striped) and liquid phase (Dl,eff, black solid or black striped). (b) Predicted diffusivity in only the liquid phase (Dl,eff) of the fast-cooled (black solid) and slow-cooled (black striped) samples.

478 479 480 481 482

Figure 6. Simulation of moisture diffusion in lipids in the absence of voids. (a) Deff versus liquid oil fraction (ζ) plots at various input fractal dimension (Dbox) values. (b) Deff vs. Dbox plots at the individual (solid line) and average (dotted line) ζ values of samples made with different cooling rates at 200 s-1 shear. The measured Dbox values for fast 23



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Page 24 of 35

483 484 485

(triangles) and slow-cooled (squares) samples are plotted on the average ζ curve at each LLL/OOO ratio.

486

TABLES

487 488

Table 1. Measured structural attributes of samples prepared under fast (13 °C/min) or slow (0.7 °C/min) cooling rates with 200 s-1 shear. LLL/ OOO

SFC ϕ (Volume %)

Crystal Size (Equivalent Diameter) (µm)

Void Space (Volume %)

Fractal Dimension Dbox

w/w

Fast

Slow

Fast

Slow

Fast

Slow

Fast

Slow

100/0

90.5 + 1.1aα

93.9 + 0.2bβ

6.7 + 0.9Aα

7.4 + 0.9Aα

4.7 + 0.6Aα

6.1 + 0.8Bα

1.64 + .01Aβ

1.53 + .02Bε

80/20

40.3 + 1.0cν

38.2 + 0.4dδ

2.8 + 0.3iβ

2.7 + 0.7iβ

4.7 + 0.5iα

7.7 + 0.9iiα

1.57 + .01iνδ

1.54 +.01iiνε

60/40

15.1 + 0.2eε

16.4 + 0.3fω

1.2 + 0.2aβ

2.9 + 0.7bβ

8.4 + 1.2aβ

24 + 3.1bν

1.69 + .01aα

1.59 +0.01bν

489 490 491 492

Note – The superscript letters represent significant differences (α=0.05) under each property between two cooling rates (first letter) and between all samples (Greek alphabets).

493 494

Table 2. Calculation of liquid oil and void fraction from measured solid fat content and void fraction. LLL/ OOO

SFC (measured)

Void Fraction (measured)

Actual Liquid Fraction ζ

Actual Void Fraction ν

Average Liquid Fraction ζ

w/w

Fast

Slow

Fast

Slow

Fast

Slow

Fast

Slow

Average

100/0

0.91

0.94

0.07

0.07

0.09

0.06

0.06

0.07

0.07

80/20

0.40

0.38

0.03

0.03

0.58

0.60

0.03

0.03

0.59

60/40

0.15

0.16

0.01

0.03

0.84

0.81

0.01

0.03

0.83

495 24


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“For Table of Contents Use Only” Effects of Structural Attributes and Phase Ratio on Moisture Diffusion in Crystallized Lipids Sravanti Paluri1, Dennis R Heldman1,2, Farnaz Maleky2,* 1

Department of Food, Agricultural, and Biological Engineering, The Ohio State University, Columbus 43210, USA 2 Department of Food Science and Technology, The Ohio State University, Columbus 43210, USA *Corresponding author. [email protected]

Figure. Slower cooling at the same shear rate and chemical formulation increased moisture diffusivity in the liquid oil fraction due to larger fat crystals and lower fractal dimension. The magnitude of this influence of crystallization conditions on diffusion depends on the liquid oil content. Note-LLL/OOO is trilaurin/triolein w/w ratio in the lipid blends. SYNOPSIS Faster cooling (13 versus 0.7 °C/min) at 200 s-1 of trilaurin-triolein mixtures decreased crystal sizes and increased fractal dimensions in the samples. Overall, effective moisture diffusivity calculated as the sum of diffusivity in liquid oil and void fractions was not influenced by cooling rate. However, diffusion through only the liquid oil fraction decreased significantly in samples structured through faster cooling.

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Effects of Structural Attributes and Phase Ratio on Moisture Diffusion

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