Investigating the Role of CNP and CNP Aggregates in the Rheological Breakdown of Triglyceride Systems

: In many food applications, the mechanical properties of fats play a critical role in determining the processing performance of fat-rich products. In fact, fat crystal networks form a particular class of soft materials that exhibit viscoelastic properties. The uniqueness of the mechanical response is intricately linked to the hierarchical nature of the system, as fats possess a complex architecture encompassing features at different scale levels (i.e., length scales). Since the discovery of crystalline nanoplatelets (CNPs), it has been hypothesized that CNPs are the basic building blocks of lipid networks and that CNPs are the responsible units for the mechanical properties of fats. This hypothesis, however, has only been partially tested. In this article, we examine which units could be responsible (e.g., lamellae, CNP, CNP aggregates) for the mechanical breakdown of fat crystal networks, through Rheo-USAXS in beamline ID02 (ESRF, Grenoble, France). Time-resolved USAXS profiles were acquired during the three steps of a three-interval thixotropy test (3iTT), namely, pre-shear, shear and recovery. The results were then utilized to evidence which specific length scale is arranged (i.e., orientated) during rheological breakdown. The findings suggest that, at the tested shear rates, orientation is only visible from 250 nm onwards, suggesting that the rheological breakdown of triglycerides is primarily driven by the orientation, and possible disruption, of CNP aggregates. These results reveal the critical role of CNP aggregates in the mechanical properties of fats. In the longer term, we believe this study will steer future research toward a more focused understanding of CNP aggregation and disaggregation dynamics


Introduction
The mechanical properties of fats play a key role in many food applications, as they influence the processing performance of many fat-rich products, such as chocolate, margarine or dough, and greatly dictate the sensory experience of consumers during consumption [1].Although the nanoscopic tailoring of the mechanical properties of fats remains a highly distant goal, it represents a highly desirable future direction.Research efforts should strive towards the rational engineering of fat networks, allowing for the design of healthier fats with precisely controlled functionalities.
From a mechanical standpoint, fat crystal networks represent a distinct category of soft material, which exhibits interesting viscoelastic properties [1,2].The mechanical response is intricately linked to the hierarchical nature of the fat system.In fact, fats are hierarchical systems with a complex architecture, encompassing different structures at different scale levels (i.e., length scales).At the molecular level, triacylglycerols (TAGs) pack together in a specific three-dimensional arrangement, adopting distinct polymorphic forms (α, β ′ , β).These then form lamellae, which subsequently stack, forming crystalline nanoplatelets (CNPs).Notably, at the mesoscale, these CNPs further assemble into various higher-order Crystals 2024, 14, 566 2 of 19 structures, dictated by the processing conditions and the chemical composition of the triglycerides (TAGs) themselves [3,4].
Since the identification of CNPs [5], it has been hypothesized that CNPs are the basic building blocks of lipid networks [6][7][8] and that therefore, CNPs are the responsible units for the mechanical properties of fats.This hypothesis, however, has not yet been experimentally confirmed.In fact, despite prior efforts to correlate the nanoscale structure of triglycerides with their macroscopic behavior [3,4,6,[9][10][11], a more precise understanding of structure-function relationships remains elusive.We believe that one key question remains unanswered: at which specific length scales does rheological breakdown occur?In other words, which units (e.g., lamellae, CNP, CNP aggregates) are responsible for the mechanical properties of fat crystal networks?
In this article, we try to answer these questions, by evidencing which specific length scales are arranged (i.e., orientated) during rheological breakdown.Until now, shear experiments on fat crystal networks have only been used to study the effect of shear on crystallization, as a mechanism to accelerate specific phase transitions within the material, with little to no rheological information being obtained [6,9,12,13].A noteworthy study performed in 2003 by Mazzanti et al. [9] was the first to explore the concept of crystallite orientation during the crystallization process.Although their work specifically focused on understanding the influence of shear in the development of fat crystal networks, their experiments brought to light the possibility of inducing orientation by applying shear.In their work, high shear rates were used during crystallization, and for the first time, the development of orientation on SAXD (small-angle X-ray diffraction) profiles was reported (1440 s −1 ) [9].In our current understanding of shear-crystallization, increased shar rates can enhance primary nucleation by supplying the energy needed to overcome activation barriers.As a result, increased nucleation leads to smaller crystal formation, which usually translated into stronger fat crystal networks, depending on how the fat crystals aggregate [14].In the study of Mazzanti et al., CNPs are concluded to be the basic building block of triglycerides [6,9].However, their results suggest that only at very high shear rates was orientation achieved.In fact, no orientation was perceived when crystallizing samples at lower shear rates (90 s −1 ), thus suggesting that rheological breakdown at lower shear rates could not be explained in the SAXD range.Unfortunately, their research was limited to the SAXD and WAXD range, and no rheological data accompanied the results.
The study was later extended, and similar conclusions were obtained [6].Orientation was, in the work of Mazzanti, described as the sum between unoriented CNPs and oriented CNPs [6].The interplay between orientation and randomness was often quantified via the Peclet number (Pe).This dimensionless parameter captures the interplay between the forces exerted by shear flow and the randomizing effects of Brownian motion.Shear forces, on one side, tend to align the building blocks, promoting order within the network.On the other side, Brownian motion acts in opposition, introducing disorder [6].Whenever Pe > 10, shear forces dominate the system, and orientation effects become obvious.
In this article, we will build further on the concept of domain orientation.The novelty of this paper lies in the idea of finding a critical length scale, which upon orientation can be directly associated with the rheological breakdown of fats.For this, simultaneous thixotropy and ultra-small-angle X-ray scattering (USAXS) experiments were performed.Specifically, USAXS emerges as a fitting technique for studying CNPs and CNP aggregates [8,15,16], as it provides information between 25 nm and 3.14 µm [17].Orientation was quantified at various length scales for four different systems.Two 30% dilutions of pure monounsaturated fatty acids were used: tripalmitin (PPP) in triolein (OOO) and tristearin (SSS) in OOO.Additionally, two commercial sources of monounsaturated fatty acids were crystallized on a pilot scale scraped surface heat exchanger (SSHE).For this, a 10% dilution of fully hydrogenated rapeseed oil (FHRO) in high oleic sunflower oil (HOSO) and a 10% dilution of palm stearin (PS) in HOSO were used.

In Situ Sample Preparation
In this article, we refer to in situ sample preparation when the sample was crystallized in the same sample stage intended for subsequent thixotropy measurement.For this, two possible stages were utilized.Whenever rheology measurements were intended, the sample was first crystallized using an MCR Anton Paar 302 (Anton Paar, Graz, Austria) with a 25 mm sandblasted parallel plate geometry (PP25S).When the sample was prepared for X-ray scattering thixotropy measurement, a Linkam shear cell (CSS450, Linkam, Salford, UK) (Xenocs, Grenoble, France) was utilized for sample crystallization.The protocol was the same across the two different stages.First, the sample was heated to 80 • C for at least 15 min.The molten sample was then placed in the stage, and a gap of 1.5 mm was set.To erase crystal memory, the sample was molten to 80 • C for 15 min.A temperature ramp followed at 10 • C/min to 15 • C. The sample was then allowed 15 min of isothermal crystallization time at 15 • C before thixotropy measurement.

Pilot Scale Sample preparation
Samples crystallized on a pilot scale are meant to mimic industrially relevant shear and cooling rate conditions.For this, a benchtop system, consisting of a micropump and an SSHE of 29 mL, was used (Het Stempel B.V, Zwijndrecht, The Netherlands).For further specifications on the device, the reader is referred elsewhere [18].Two samples were crystallized at a pilot scale, a 10% FHRO dispersion in HOSO and a 10% PS dispersion in HOSO.At least 4 L was utilized per trial.The inlet temperature was set to around 73 • C, the flow rate was set to 5 Kg/h, and the SSHE rotation was set to 750 rpm.The outlet temperature was recorded to be around 15 • C. Samples were collected in the outlet point immediately after production and stored in margarine tubs in a thermostatic cabinet set at 15 • C, until being transported to the European Synchrotron Radiation Facility (ESRF) in a portable mini car refrigerator (also set at 15 • C) (Vevor, San Bernardino, CA, USA).Before thixotropy measurement, the samples were carefully scooped into the corresponding stage (already set at 15 • C).

Rheological Thixotropy Experiments
A controlled shear strain 3-intervals thixotropy test (3iTT) was performed using an MCR Anton Paar 302 (Anton Paar, Graz, Austria) with a 25 mm sandblasted parallel plate geometry (PP25S) at a gap of 1.5 mm.All measurements were performed at 15 • C. Samples were allowed to equilibrate for 5 min before measurement.In the first interval, a shear strain of 0.1% was applied at a constant frequency of 1 Hz for 2 min.In the second interval, a constant shear rate of 10 s −1 was applied for 2 min.Finally, in the recovery step, a low shear strain was applied for 5 min (the same settings as the first interval, a shear strain of 0.1%, and a frequency of 1 Hz).All measurements were performed in triplicate.
The percentual recovery of the 3-interval thixotropy test (3iTTr) was calculated following Equation (1), where η * r is the complex viscosity modulus at in the recovery interval (obtained at around 363 s), and η * pre is the complex viscosity modulus at the end on the pre-shear interval (obtained at around 108 s).
In situ thixotropy experiments were performed using a modified Linkam shear cell (CSS450, Linkam, Salford, UK) (Xenocs, Grenoble, France), in which the quartz windows were replaced by two Kapton windows (X-ray transparent).Samples were prepared according to Sections 2.2 and 2.3.Before measurement, the sample was allowed 5 min of relaxation time (at 15 • C), after which a first X-ray scattering profile was recorded (one-time acquisition of 0.1 s with 10 frames per acquisition).This measurement will be here referred to as "Static".
For the in situ thixotropy measurements, the Linkam shear cell was set to follow the same procedure as described in 2.2.During the pre-shear step, the sample was preconditioned at 1 Hz and a 0.1% strain for 2 min.In the second interval, the sample was sheared at a constant shear rate of 10 s −1 for 2 min.Finally, in the recovery step, the sample was subject to a constant shear strain of 0.1% at 1 Hz.The whole test was performed at 15 • C with a 1.5 mm gap.During the experiment, time-resolved X-ray scattering profiles were acquired every 16 s (10 different acquisitions in each cycle, each of 0.1 s of exposure time).
In each acquisition, two-dimensional patterns were recollected and normalized by transmission using standard procedures (flatfield, solid angle and transmitted intensity correction).The two-dimensional images were then transformed into two-dimensional azimuthal projections, where the signal was re-binned into polar coordinate systems [20].The azimuthal profile was then reduced to 1D profiles, following one of the three procedures, (1) full range reduction, (2) azimuthal average on reduced angular range or (3) azimuthal profile on reduced q-range.All data reduction was performed using SAXSUtilities [21].

Full Range Reduction
The full range reduction took all angular ranges [−180 • ; 180 • ] and all measured q-ranges [0.0021 nm −1 ; 0.24 nm −1 ] into consideration.Data were reduced into a single onedimensional pattern by means of an azimuthal integration.The ten frames per acquisition were then averaged.The contribution of the empty shear cell was then subtracted, to correct for the sample holder and background (empty beam, capillary and air gap).Each profile was then divided by the thickness of the sample (equivalent to a shear cell gap of 1.5 mm).
The results of the full range reduction were then dynamically re-binned using SAXSUtilities [21] to arrange the points homogeneously on a logarithmic q-scale.The data were then fitted following the model proposed by Penagos et al. (Equation ( 2)) [22].For further information on the model, the reader is referred elsewhere [23].The model assumes that CNPs can be approximated to a parallelepiped and that at a low q-range they aggregate, forming fractal networks.
In Equation ( 2), ϕ V is the volume fraction of the fat phase (proportional to the SFC), V P is the volume of the parallelepiped scattering units, and ∆ρ is the difference between the scattering length density of the solid TAGs and the corresponding dissolved fractions.It is assumed that most of the solid TAGs are composed of tristearin or tripalmitin, accordingly, while the liquid fraction is mostly composed of triolein.The form factor is assumed to be a polydisperse parallelepiped form factor function, ⟨ P PP ⟩ , (polydispersity = 0.3), and the aggregation at a low q can be modeled through a power law model, with B being a scale factor and P being the power law exponent.Interactions between CNPs are assumed to be limited to the formation of isotropic fractal aggregates in the model.

Azimuthal Average-I(q)
Azimuthally averaged profiles were used to find orientation within the sample.This reduction allowed one to obtain 1D profiles over a limited angular range.For this, the 2D azimuthal profile was partially integrated into one of four different angular ranges, namely [−15 Appendix A).The resulting one-dimensional profiles (I vs. q) were averaged, normalized, and corrected by sample thickness.

Azimuthal Profile-I(ψ)
Whenever orientation is found in a sample, azimuthal profiles allow one to identify orientation within a narrowed length scale.The reduction is thus performed in between two q-values (known as a q-crown) (see Appendix B).To do so, the 2D azimuthal profiles were reduced into one of the five q-ranges.The real-space length scale of these ranges is [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm].The obtained 1D profile (I vs. ψ) was averaged, normalized and corrected by sample thickness.

Statistical Analysis
All statistical analyses were conducted using Minitab Statistical Software.Mean values were compared using a Wilcoxon signed-rank test with a significance level of 0.05.For the post hoc analysis, the Dunn test was performed.

Rheological Results
Figure 1 presents the plot of the 3iTT results, highlighting three different moments (A, B and C), which correspond to the three intervals (pre-shear, shear and recovery).Table 1 presents the corresponding numerical values of those moments.In the first interval, a low strain (0.1%) is applied, aiming at obtaining the initial viscosity.This interval, also called the "low-shear phase", provides the reference value before a mechanical break.In this stage, contained between 0 and 120 s, no rheological breakdown is expected, as the shear forces remain minimal.As seen in Figure 1, the complex viscosity remains constant over this timeframe.Statically produced samples report a higher complex shear modulus (G*) than their pilot scale counterparts, attributed to the higher TAG concentration (Table 1).Interestingly, both pilot scale samples have a very similar initial G*.In the second interval, also known as the "high-shear phase", the sample is she at a constant shear rate (10 s −1 ), and due to the sample's shear-thinning behavior, a re tion in the complex viscosity modulus is observed.Traditionally, a loss in viscosity ca associated with the deformation or alignment of structures.This interval spans betw 120 s and 240 s, and the complex viscosity modulus progressively decays, reachin lowest values at the end of the interval.When compared to the initial viscosity values drop in viscosity is particularly high for the 30% PPP static sample, while the 10% FH pilot scale sample seems to have a moderate loss in viscosity.
Finally, in the last step, a low shear strain is applied (repeating the conditions u in the first interval).This allows one to measure sample recovery over time and struct regeneration.In this case, as seen in Figure 1, all samples recover only partially.Furt more, as evidenced in Table 1, after the cessation of shear, the 10% FHRO pilot scale s ple displayed a superior recovery capacity, while the 30% SSS statically produced had lowest recovery.This result is interesting, as it displays that, although the pilot scale s ple was prepared with a lower amount of solid fat (around 10%), it could retain struct integrity be er than the statically produced sample (30% SSS).In addition, this is no case for the palmitic samples, where both static and pilot scale samples have a rather recovery capacity.In the second interval, also known as the "high-shear phase", the sample is sheared at a constant shear rate (10 s −1 ), and due to the sample's shear-thinning behavior, a reduction in the complex viscosity modulus is observed.Traditionally, a loss in viscosity can be associated with the deformation or alignment of structures.This interval spans between 120 s and 240 s, and the complex viscosity modulus progressively decays, reaching its lowest values at the end of the interval.When compared to the initial viscosity values, the drop in viscosity is particularly high for the 30% PPP static sample, while the 10% FHRO pilot scale sample seems to have a moderate loss in viscosity.
Finally, in the last step, a low shear strain is applied (repeating the conditions used in the first interval).This allows one to measure sample recovery over time and structural regeneration.In this case, as seen in Figure 1, all samples recover only partially.Furthermore, as evidenced in Table 1, after the cessation of shear, the 10% FHRO pilot scale sample displayed a superior recovery capacity, while the 30% SSS statically produced had the lowest recovery.This result is interesting, as it displays that, although the pilot scale sample was prepared with a lower amount of solid fat (around 10%), it could retain structural integrity better than the statically produced sample (30% SSS).In addition, this is not the case for the palmitic samples, where both static and pilot scale samples have a rather low recovery capacity.

Static Results
Figure 2A presents the USAXS profiles obtained before thixotropy measurement.These profiles allow one to understand the length scale of each component, as well as to differentiate the base behavior of each sample.From Figure 2, significant structural disparities can be revealed.The higher intensity observed for the 30% SSS and 30% PPP samples is expected, as it is derived from the greater solid fat content (30% vs. 10% on the pilot scale).Additionally, from the Kratky plot (Figure 2B), it is possible to observe that the CNP bump is located at a similar range in all samples.Smaller deviations are visible for the 30% SSS sample, portraying a bump at higher q-values, indicative of a smaller cross-section.This result is confirmed in Table 2, as the cross-section of all samples seems to be relatively similar, with 30% SSS reporting the smallest value.The corresponding fits are available in Appendix C. In all cases, the CNP thickness and width remain below 150 nm.scale).Additionally, from the Kratky plot (Figure 2B), it is possible to observe that the CNP bump is located at a similar range in all samples.Smaller deviations are visible for the 30% SSS sample, portraying a bump at higher q-values, indicative of a smaller crosssection.This result is confirmed in Table 2, as the cross-section of all samples seems to be relatively similar, with 30% SSS reporting the smallest value.The corresponding fits are available in Appendix C. In all cases, the CNP thickness and width remain below 150 nm.
Figure 2. Static X-ray sca ering results before thixotropy measurement.To the left (panel (A)), the figure presents the I vs. q profiles for 30% SSS in OOO crystallized statically at 10 °C/min until 15 °C and a 10% FHRO in HOSO crystallized to 15 °C on a pilot scale.To the right (panel (B)), a Kratky representation of the same data (q 2 I vs. q), which allows a be er visualization of curve features.Differences in aggregation behavior are more apparent.From Figure 2, we can acknowledge that the palmitic samples report the highest slopes, with a P value of 4.4 for the 30% PPP-Static sample and a P value of 3.9 for the 10% PS-Pilot sample.Stearic samples, on the other hand, seem to have a looser aggregation conformation, reporting similar slopes and mass fractality regardless of the preparation method (see Table 2).
While the available literature for comparison is limited, one study stands out as a valuable reference point for evaluating the fit results of the 30% SSS statically crystallized sample.Peyronel et al. reported a P slope value of 3.0 for a 20% SSS in an OOO system crystallized at a rate of 5 °C/min and subsequently stored for 22 days at 22 °C/min [8,24].Notably, our reported P value of 3.0 closely aligns with their findings, indicating a consistent trend towards mass fractality.Differences in aggregation behavior are more apparent.From Figure 2, we can acknowledge that the palmitic samples report the highest slopes, with a P value of 4.4 for the 30% PPP-Static sample and a P value of 3.9 for the 10% PS-Pilot sample.Stearic samples, on the other hand, seem to have a looser aggregation conformation, reporting similar slopes and mass fractality regardless of the preparation method (see Table 2).
While the available literature for comparison is limited, one study stands out as a valuable reference point for evaluating the fit results of the 30% SSS statically crystallized sample.Peyronel et al. reported a P slope value of 3.0 for a 20% SSS in an OOO system crystallized at a rate of 5 • C/min and subsequently stored for 22 days at 22 • C/min [8,24].Notably, our reported P value of 3.0 closely aligns with their findings, indicating a consistent trend towards mass fractality.

In Situ Thixotropy Results
Given that CNPs and CNP aggregates are non-spherical structures, a preferential orientation can be developed due to shear or strain.The alignment of particles can be observed in the X-ray 2D scattering profiles.In fact, when the particles are randomly oriented (isotropic), the scattering pattern is observed as symmetrical concentric cylinders around the incident beam.In contrast, when the sample is partially oriented (anisotropic), the intensity will be visualized through non-symmetrical patterns.An alternative representation is possible in the corresponding azimuthal projection (available in Appendix D for the three moments evidenced in Figure 1).
Visual inspection of the appendix data suggests minimal initial orientation in the statically crystallized samples (see Figure A4, 30% SSS-Static-Pre-Shear and 30% PPP-Static-Pre-Shear).Following shear application (see Shear), a significant increase in the undulating pattern of the contour plot is observed, indicating the development of orientation.Finally, during the recovery phase, the profile is still characterized by the persistence of orientation within the sample.In contrast, for the pilot scale samples (see Figure A5), the profiles exhibit a weak wavy pattern in the initial contour plot, suggesting a potentially pre-existing orientation, possibly linked to the sample placement within the shear cell.Notably, this undulating behavior persists throughout the shear application and recovery phases.The appendix also presents the normalized images (Figure A6).
The aforementioned results are better visualized and corroborated in Figures 3 and 4. A restricted azimuthal integration allows one to selectively integrate the scattering intensity within a limited angular range.This method helps to isolate and examine scattering features that are present only within a particular orientation or symmetry axis within the sample.Whenever no orientation is present in the sample, all curves will be overlapping.In contrast, deviating curves suggest anisotropy.
intensity will be visualized through non-symmetrical pa erns.An alternative representation is possible in the corresponding azimuthal projection (available in Appendix D for the three moments evidenced in Figure 1).
Visual inspection of the appendix data suggests minimal initial orientation in the statically crystallized samples (see Figure A4, 30% SSS-Static-Pre-Shear and 30% PPP-Static-Pre-Shear).Following shear application (see Shear), a significant increase in the undulating pa ern of the contour plot is observed, indicating the development of orientation.Finally, during the recovery phase, the profile is still characterized by the persistence of orientation within the sample.In contrast, for the pilot scale samples (see Figure A5), the profiles exhibit a weak wavy pa ern in the initial contour plot, suggesting a potentially pre-existing orientation, possibly linked to the sample placement within the shear cell.Notably, this undulating behavior persists throughout the shear application and recovery phases.The appendix also presents the normalized images (Figure A6).
The aforementioned results are be er visualized and corroborated in Figures 3 and  4. A restricted azimuthal integration allows one to selectively integrate the sca ering intensity within a limited angular range.This method helps to isolate and examine sca ering features that are present only within a particular orientation or symmetry axis within the sample.Whenever no orientation is present in the sample, all curves will be overlapping.In contrast, deviating curves suggest anisotropy.The statically crystallized samples portrayed no orientation in the pre-shear stage, as visualized in the overlapping one-dimensional scattering curves.During the shear stage, the profiles between [75 • ; 105 • ] strongly deviate from the rest of the curves, suggesting shear-induced orientational effects.As better visualized in the Kratky representation, most of the deviations occur at lower q-ranges, suggesting that the anisotropy happens at larger length scales.More specifically, deviations start to occur after the Guinier bend, a feature characteristic of CNP cross-section.Finally, during the recovery phase, the deviation is reduced, yet not fully eliminated.In contrast, orientation is already visible in the initial interval for the pilot scale data (Figure 4, more clearly visible in the Kratky plot).We hypothesize that the CNP network was already altered during the placement of the sample in the shear cell, and as a result, orientation is visible in all stages of the process, achieving maximum deviation in the shear stage (see Kratky plots).Concurring with the static observations, all deviations occur at lower q-values, suggesting that the orientation cannot be associated with the CNP crosssection.To be er understand which real-space dimension is effectively oriented, five azimuthal profiles were integrated, namely, [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm], at each thixotropy interval (pre-shear, shear and recovery).This integration involves selectively integrating the sca ering intensity within a limited q-range.By narrowing down the integration to this q-crown, specific length scales can be isolated, and it is possible to focus on the sca ering contributions from particular structural elements (i.e., CNPs, CNP aggregates).Whenever a peak is In contrast, orientation is already visible in the initial interval for the pilot scale data (Figure 4, more clearly visible in the Kratky plot).We hypothesize that the CNP network was already altered during the placement of the sample in the shear cell, and as a result, orientation is visible in all stages of the process, achieving maximum deviation in the shear stage (see Kratky plots).Concurring with the static observations, all deviations occur at lower q-values, suggesting that the orientation cannot be associated with the CNP cross-section.
To better understand which real-space dimension is effectively oriented, five azimuthal profiles were integrated, namely, [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm], at each thixotropy interval (pre-shear, shear and recovery).This integration involves selectively integrating the scattering intensity within a limited q-range.By narrowing down the integration to this q-crown, specific length scales can be isolated, and it is possible to focus on the scattering contributions from particular structural elements (i.e., CNPs, CNP aggregates).Whenever a peak is visible on the resulting curves, orientation is confirmed.In contrast, whenever the scattering profile shows no clear anisotropy, a flat curve is obtained, hence allowing the identification of domain orientation upon shearing.The results are presented in Figures 5 and 6.An arrow is used to identify orientation peaks.visible on the resulting curves, orientation is confirmed.In contrast, whenever the sca ering profile shows no clear anisotropy, a flat curve is obtained, hence allowing the identification of domain orientation upon shearing.The results are presented in Figures 5 and  6.An arrow is used to identify orientation peaks.Based on Figure 5, we can conclude that statically crystallized samples exhibit minimal orientation at rest.Upon shear application, a clear trend emerges: a peak becomes evident at around −90° at length scales greater than 250 nm.This peak progressively increases at increasing dimensions.For the 30% SSS sample, upon relaxation, the intensity of the orientation pa ern diminishes, indicating a partial reduction of the aligned structures.This is not the case for the 30% PPP sample, in which structures above 250 nm remain oriented after shear cessation.
In the pilot scale samples (Figure 6), as expressed before, the samples show a preexisting orientation even at the beginning of the experiment, potentially due to their Based on Figure 5, we can conclude that statically crystallized samples exhibit minimal orientation at rest.Upon shear application, a clear trend emerges: a peak becomes evident at around −90 • at length scales greater than 250 nm.This peak progressively increases at increasing dimensions.For the 30% SSS sample, upon relaxation, the intensity of the orientation pattern diminishes, indicating a partial reduction of the aligned structures.This is not the case for the 30% PPP sample, in which structures above 250 nm remain oriented after shear cessation.
In the pilot scale samples (Figure 6), as expressed before, the samples show a preexisting orientation even at the beginning of the experiment, potentially due to their placement within the shear cell.Interestingly, this length scale of the orientation persists, as peaks in the profiles are only observed above 250 nm.In addition, concurring with the previous observation, the orientation remains in the palmitic sample, whereas the stearic sample seems to return to minimal orientation.
placement within the shear cell.Interestingly, this length scale of the orientation persists, as peaks in the profiles are only observed above 250 nm.In addition, concurring with the previous observation, the orientation remains in the palmitic sample, whereas the stearic sample seems to return to minimal orientation.

Discussion
In all four samples, the results indicate that the shear-induced alignment within the material occurs at length scales that exceed 250 nm.As a result, the structural breakdown between the pre-shear and the shear stage (see Section 3.2.2) can only be associated with the alignment of structures that exceed that threshold.Based on the results of Section 3.2.1, both the width and the thickness of the CNPs remain well below 250 nm.Consequently, rheological breakdown at 10 s −1 can only be associated with the orientation of bigger dimensions, such as CNP length or CNP aggregates.
An additional intriguing observation emerges when comparing the viscoelastic recovery of the pilot scale samples.Despite the CNP cross-section being nearly identical in

Discussion
In all four samples, the results indicate that the shear-induced alignment within the material occurs at length scales that exceed 250 nm.As a result, the structural breakdown between the pre-shear and the shear stage (see Section 3.2.2) can only be associated with the alignment of structures that exceed that threshold.Based on the results of Section 3.2.1, both the width and the thickness of the CNPs remain well below 250 nm.Consequently, rheological breakdown at 10 s −1 can only be associated with the orientation of bigger dimensions, such as CNP length or CNP aggregates.
An additional intriguing observation emerges when comparing the viscoelastic recovery of the pilot scale samples.Despite the CNP cross-section being nearly identical in both samples (see CNP thickness and width in Table 2), the stearic pilot scale sample shows a significantly better recovery at 43.3%, compared to just 4% in the palmitic pilot scale sample.Thus, differences in macroscopic properties cannot be attributed to variations in CNP configuration (width and thickness), but rather to differences in bigger length scales (i.e., CNP length, CNP aggregation behavior, or even higher length scales, such as clusters or flocs).
Given the improbability of orientation solely arising from CNP length (while the length scales of thickness and width do not seem to be disturbed), it is proposed that the observed orientation cannot be solely attributed to individual CNPs, but rather that it originates from the orientation of CNP aggregates.In addition, if structural breakdown occurred as CNPs align lengthwise, we would probably identify alignment in the SAXS area at low shear rates as well.This is not the case in this work, nor in the previous literature [6,9].In fact, it remains important to mention that the same experiment was also performed on the WAXS range (synchrotron radiation) and on the SAXS range on a benchtop XRS unit (Xeuss 3.0, Xenocs, Grenoble, France).No orientation was evidenced at these lower length scales, suggesting that, at a shear rate of 10 s −1 , the rheological breakdown of triglycerides is related to the orientation of CNP aggregates, and not to the alignment of any minor structures (e.g., CNPs, lamellae).These results are crucial as they highlight the significance of CNP aggregates in the rheological breakdown of triglycerides.
An additional point of discussion relates to orientation in the SAXD region reported in the previous literature.In fact, Mazzanti et al. [9] suggested significant orientation in the SAXD region at very high shear forces (1440 s −1 ) [6,9].This leads us to hypothesize that in his work, at 1440 s −1 , shear rates were high enough to disrupt the CNP aggregates, ultimately achieving individual CNP orientation.In our work, shear rates are significantly lower than those used in Mazzanti's work, and therefore, orientation was only perceived at the CNP aggregates level.It is also important to mention that disruptions in orientation were already perceived at very low shear rates, as only placing the sample in the shear cell led to the disruption of CNP aggregates, as evidenced by the pre-existing orientation in the pilot scale samples.
The following further discussion concerns orientation and viscoelastic recovery after shear.The stearic samples tend to recover isotropy more rapidly than the palmitic samples (see Figures 5 and 6).In fact, in the recovery phase, the palmitic samples remain oriented.Interestingly, orientation recovery does not correlate with viscoelastic recovery.For instance, the static 30% SSS sample, despite showing little to no orientation in the recovery phase, reports the lowest value of percentual recovery (at 0.49%).In contrast, despite a much lower SFC content, the 10% FHRO pilot scale sample seems to be able to recover well (at 43.3%).Altogether, we theorize that, whilst rheological breakdown is caused by the orientation of certain domains in the sample (the CNP aggregates being the smallest identified), a realignment of CNP aggregates (and thus, a loss in orientation in the USAXS range) does not necessarily translate to the recovery of the viscoelasticity of the system.In other words, although the randomizing effects of Brownian motion re-induce disorder in the mesoscale, the network formed by CNP aggregates does not go back to the original state.We theorize that disruptions in CNP aggregates during rheological breakdown are accompanied by further alterations in higher-order structures (e.g., clusters, flocs, etc.).As a result, viscoelastic recovery is independent of the ordering in the USAXS, SAXS and WAXS range, and thus, future research is necessary in order to develop new methods to identify which domain is responsible for recovery after shear.
Lastly, while this paper has pinpointed the relevance of CNP aggregates in the structural breakdown of triglycerides and highlighted the importance of higher-order structures in viscoelastic recovery, it is crucial to emphasize that studying CNPs remains vital for understanding the mechanical properties of lipid systems.As the building blocks of triglycerides, a thorough understanding of CNPs' characteristics, formation and assembly is essential.This knowledge will better guide our research efforts toward the nanoscale engineering of fat crystal networks, ultimately enhancing the functionality and performance of lipid-based products.

Conclusions
Although significant progress has been made in the last years into understanding the structure-function relationship of fat crystals, there is little information on how each scale contributes to the buildup of the rheological properties of fats.Up to this day, it is still unknown which structure is responsible for the development or breakdown of rheological properties in triglyceride systems.So far, it has been broadly assumed that CNPs are responsible for the rheological properties of triglycerides; however, no experiments have yet proven this concept.The aim of this paper was to identify the length scale responsible for rheological breakdown.
Our findings suggest that, from all four treatments, the shear-induced alignment within the material occurs at length scales exceeding 250 nm.Given the improbability of orientation arising solely from the CNP length, while width and thickness remain undisturbed, it is proposed that the observed orientation arises from the alignment of CNP aggregates rather than individual CNPs.Unless very high shear rates are applied, leading to individual CNP aggregation disruption and posterior CNP orientation (e.g., 1440 s −1 [6,9]), the rheological breakdown of triglycerides is attributed to the disruption of CNP aggregates.Altogether, our findings underscore that CNP aggregation, rather than the individual CNP cross-section, plays a key role in the viscoelastic breakdown of fat crystal networks.
Lastly, orientation recovery did not correlate with viscoelastic recovery, suggesting that that, while rheological breakdown can be attributed to the alignment of certain domains (of which CNP aggregates are the smallest length scale altered), the restoration of the original network is independent of the orientation of the sample in the mesoscale.Consequently, it is presumed that rheological recovery is attributable to higher-order structures.New techniques are needed to validate this hypothesis.

Figure 1 .
Figure 1.Rheological three-interval thixotropy test (3iTT) results.Filled symbols report com viscosity modulus, while open symbols report viscosity.Le ers indicate the three different ments: pre-shear (A), shear (B) and recovery (C) (see main text).

Figure 1 .
Figure 1.Rheological three-interval thixotropy test (3iTT) results.Filled symbols report complex viscosity modulus, while open symbols report viscosity.Letters indicate the three different moments: pre-shear (A), shear (B) and recovery (C) (see main text).

Figure 2 .
Figure 2. Static X-ray scattering results before thixotropy measurement.To the left (panel (A)), the figure presents the I vs. q profiles for 30% SSS in OOO crystallized statically at 10 • C/min until 15 • C and a 10% FHRO in HOSO crystallized to 15• C on a pilot scale.To the right (panel (B)), a Kratky representation of the same data (q 2 I vs. q), which allows a better visualization of curve features.

Figure 3 .
Figure 3. Azimuthally averaged intensity USAXS profiles for statically crystallized samples.The top panel shows results for 30% SSS, while the bottom panel shows results for 30% PPP.The data are integrated over specific angular ranges, [−15 • ; 15 • ], [30 • ; 60 • ], [75 • ; 105 • ] and [120 • ; 150 • ], represented by the respective 1D curves.These profiles were here used to identify orientation within the sample.Each figure is accompanied by an insert, which presents the Kratky representation of the same data.

Figure 5 .
Figure 5. Azimuthal profile of statically crystallized samples.The panel at the top shows the results for the 30% SSS, while the panel at the bo om shows the results for the 30% PPP sample.The data are integrated over a specific q-range, which corresponds to a specific length scale, namely, [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm].Arrows indicate that orientation is visible in the sample.

Figure 5 .
Figure 5. Azimuthal profile of statically crystallized samples.The panel at the top shows the results for the 30% SSS, while the panel at the bottom shows the results for the 30% PPP sample.The data are integrated over a specific q-range, which corresponds to a specific length scale, namely, [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm].Arrows indicate that orientation is visible in the sample.

Figure 6 .
Figure 6.Azimuthal profile of statically crystallized samples.The panel at the top shows the results for the 30% SSS, while the panel at the bo om shows the results for the 30% PPP sample.The data are integrated over a specific q-range, which corresponds to a specific length scale, namely, [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm].Arrows indicate that orientation is visible in the sample.

Figure 6 .
Figure 6.Azimuthal profile of statically crystallized samples.The panel at the top shows the results for the 30% SSS, while the panel at the bottom shows the results for the 30% PPP sample.The data are integrated over a specific q-range, which corresponds to a specific length scale, namely, [50 nm; 100 nm], [100 nm; 251 nm], [251 nm; 496 nm], [496 nm; 758 nm] and [758 nm; 990 nm].Arrows indicate that orientation is visible in the sample.

Figure A5 .
Figure A5.Azimuthal projections of pilot scale crystallized samples.All profiles here presented were caved to remove masked values (SAXSUtilities2).

Figure A5 .
Figure A5.Azimuthal projections of pilot scale crystallized samples.All profiles here presented were caved to remove masked values (SAXSUtilities2).

Figure A6 .
Figure A6.Normalized projections.All profiles here presented were caved to remove masked values (SAXSUtilities2).

Table 1 .
Complex shear moduli (G*) results at the end of the pre-shear interval (A) and during the recovery interval (C).The percentage of recovery is also presented in the table.The values with different superscript letters in a column are significantly different (P < 0.05).

Table 1 .
Complex shear moduli (G*) results at the end of the pre-shear interval (A) and durin recovery interval (C).The percentage of recovery is also presented in the table.The values different superscript le ers in a column are significantly different (p < 0.05).

Table 2 .
Characterization of CNP and CNP aggregates before shear application.Results here presented were obtained after fi ing static USAXS profiles to Equation (2).P stands for the power law exponent, which describes the aggregation behavior of CNPs.

Table 2 .
Characterization of CNP and CNP aggregates before shear application.Results here presented were obtained after fitting static USAXS profiles to Equation (2).P stands for the power law exponent, which describes the aggregation behavior of CNPs.