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External and internal gelation of pectin solutions: microscopic dynamics versus macroscopic

rheology

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2014 J. Phys.: Condens. Matter 26 464106

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1. Introduction

Pectins are natural anionic polysaccharides extracted from vegetal sources that, besides being extensively used in the food industry as thickeners or stabilizing agents, have recently been exploited for biomedical applications, ranging from drug and gene delivery to wound healing and tissue engineering [1–7]. Although these highly branched polymer chains may contain several diverse monosaccharidic units [8, 9], result-ing in specific chemical structures that strongly depends on the source and method of extraction [5], a common feature in pectins is the occurrence of a linear domain composed of galacturonic acid units (homogalacturonan), which contain carboxylic acids moieties that can be partially esterified with methyl groups according to blockwise or random sequences. The degree of esterification (DE), conventionally used to dis-tinguish low methoxyl pectins from high methoxyl pectins

having a DE > 0.5, plays a key role in designing pectin hydro-gels [8, 9], since carboxylic groups are primarily involved in the gelation of pectin solutions by the addition of multivalent cations, the most commonly used being Ca2+.

Because of this complex and multifarious structure, a detailed description of the molecular mechanisms leading to pectin gelation is lacking. Nevertheless, a basic model, which has reached a general consensus supported by several experi-mental results, identifies the earlier gelation step with the buildup of dimeric structures by cooperative association of parallel-facing chains through ion bridging [10, 11]. The min-imum number of successive non-esterified residues required to obtain divalent ion chelation has been estimated to be in a range of 6–20 [12]. Although the subsequent aggregation of the dimers ending in an arrested gel structure, which may proceed through non-specific electrostatic interactions, is still poorly understood, it is useful to point out that this basic chain

Journal of Physics: Condensed Matter

External and internal gelation of pectin solutions: microscopic dynamics versus macroscopic rheology

E Secchi1, F Munarin1, M D Alaimo1, S Bosisio1, S Buzzaccaro1, G Ciccarella2,3, V Vergaro2, P Petrini1 and R Piazza1

1 Dipartimento di Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, 20133 Milano, Italy2 National Nanotechnology Laboratory (NNL), Istituto Nanoscienze CNR, 73100 Lecce, Italy3 Dipartimento di Ingegneria dell'Innovazione, Università del Salento, 73100, Lecce, Italy

E-mail: eleonora.secchi@polimi.it

Received 6 March 2014, revised 2 April 2014Accepted for publication 9 April 2014Published 27 October 2014

AbstractPectin is a natural biopolymer that forms, in the presence of divalent cations, ionic-bound gels typifying a large class of biological gels stabilized by non-covalent cross-links. We investigate and compare the kinetics of formation and aging of pectin gels obtained either through external gelation via perfusion of free Ca2+ ions, or by internal gelation due to the supply of the same ions from the dissolution of CaCO3 nanoparticles. The microscopic dynamics obtained with photon correlation imaging, a novel optical technique that allows obtaining the microscopic dynamics of the sample while retaining the spatial resolution of imaging techniques, is contrasted with macroscopic rheological measurements at constant strain. Pectin gelation is found to display peculiar two-stage kinetics, highlighted by non-monotonic growth in time of both microscopic correlations and gel mechanical strength. These results are compared to those found for alginate, another biopolymer extensively used in food formulation.

Keywords: pectin gels, photon correlation imaging, rheology

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E Secchi et al

External and internal gelation of pectin solutions: microscopic dynamics versus macroscopic rheology

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association mechanism bears many similarities with what has been found for alginate, another biopolymer gel of particu-lar interest in food formulation [13, 14]. Pectin and alginate share, therefore, a common basic structure built on multivalent ion-bridging [15–17]. At variance with the chemical bonds in simple polymer gels, these ‘physical’ cross-links are prone to break and re-form to relax local internal stresses that build up upon gelation. As a main consequence, the mechanical and rheological properties of the gel depend not only on the den-sity, strength, and lateral extent of the cross-links, but also on their restructuring kinetics.

In this paper, through a detailed investigation performed by Photon Correlation Imaging (PCI), a novel light scattering technique particularly suitable to investigate the microscopic dynamics of spatially inhomogeneous systems, we highlight several features of gelation kinetics and of the restructur-ing processes in pectin gels. Results are compared with the macroscopic viscoelastic properties of the gels obtained via rheological measurement. Specifically, we address structures obtained via two different gelation mechanisms. We first investigate the kinetics of external gelation generated by the perfusion of aqueous solutions of free, immediately avail-able calcium ions [18–20]. Then, the experimental findings are compared with those concerning internal gelation, due to the progressive release of Ca2+ via the dissolution of cal-cium carbonate colloidal particles [7, 20, 21]. A novel feature of these experiments is that the particles' size is in a range of a few tens of nanometers [22]. As we shall see, although these particles tend to aggregate into much larger structures, they nevertheless display an open fractal structure providing a much wider exchange surface with respect to the standard micrometric CaCO3 used in former gelation studies [7], which strongly enhances the ion release speed, leading to a much

more uniform gel structure. Finally, the results of this investi-gation are compared to those found in a former study for the external gelation of alginate solutions.

2. Experimental

2.1. Materials

Low methoxyl pectin (lot CU701), with a degree of esteri-fication DE  =  38% and molecular weight Mw  =  317  kDa (Mn  =  74  kDa), obtained by SEC analysis using pullulan standard [7], was kindly provided by Herbstreith and Fox (Neuemberg, Germany). NaHCO3, NaCl, and CaCl2 were purchased from Sigma-Aldrich (Italy), and used as received. Pectin solutions were prepared by dissolving 1.2% (w/v) pec-tin in water, to which we added 84 mM of NaCl to screen elec-trostatic interactions and 11.5 mM of NaHCO3 to increase pH. The former is a critical parameter to control the rate of internal gelation because it regulates the dissociation of the carboxylic groups and the final molecular weight of the polysaccharide chains. The pH value of 3.55 ± 0.02 we choose is high enough to allow a uniform CaCO3 distribution by slowing down the grain dissolution, but sufficiently acid to prevent degradation of the pectin chains due to COOH deprotonation. All solutions were thoroughly degassed in glass vacuum desiccators for 3 h.

Calcium carbonate (CaCO3) nanoparticles were synthe-sized according to the protocol discussed in [22], using cal-cium chloride dehydrate 99.99% (CaCl2 * 2H2O, Aldrich, USA) and sodium bicarbonate (NaHCO3 Aldrich, USA). The CaCO3 suspension was characterized by optical microscopy, Transmission Electron Microscopy (TEM) and Scanning Electron Microscopy (SEM). The optical micrography in figure 1 shows that these particles tend to aggregate in

Figure 1. Main: optical microscope image of the aggregates of calcium carbonate nanoparticles before sonication. (a) A TEM image of the individual particles. (b) Schematic drawing of the perfusion cell used for external gelation, where the optical configuration used in PCI experiments is also sketched.

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solution, forming loose, fractal-like aggregates with a size in the range of hundreds of micrometers. To reduce the aggre-gate size, and therefore promote faster dissolution, all particle suspensions were extensively sonicated just before sample preparation. The size and shape of the individual particles composing the aggregates was obtained from TEM measure-ments. Samples were prepared by dropping a dilute aque-ous nanoparticle suspension on carbon-coated copper grids (Formvar/Carbon 300 Mesh Cu) and allowing the solvent to evaporate. The TEM images, obtained on a Hitachi HD 2000 instrument operated at an accelerating voltage of 80 kV, show that the particles have approximately a prolate ellipsoid shape, with average major and minor axes of 100 and 40 nm (panel (a) in figure 1). These values are in good agreement with those found from SEM measurements, made with a RAITH150 instrument (RAITH GmbH, Dortmund, Germany) operating at 5 keV beam energy on samples prepared by pouring a drop of particle suspension on a SiO2 wafer, letting the sample dry overnight, and finally sputtering a 5 nm gold layer over the dried film.

2.2. External gelation

Calcium chloride CaCl2 was selected as a cross-linking agent for external gelation studies because, due to its high solubil-ity in aqueous media, it readily provides a controlled amount of free calcium ions. Pectin solution was diluted in water to a final concentration of 1% (w/v) pectin in 9.5 mM of NaHCO3 and 70 mM of NaCl. To follow the gelation kinetics, the pectin solution was confined in the lower optically accessible part of a cuvette (VWR International), by a dialysis membrane (Sigma D-9402, molecular weight cut-off  = 14 000), which was mounted on a custom-made plastic frame that tightly fits into the wedge-shaped connection between the sample com-partment and an upper reservoir (panel (b) in figure 1). This cell geometry allows us to laterally image a rectangular area within the sample with a vertical extent L ≃ 16 mm and a hori-zontal width W ≃ 8 mm, which allows mapping the sample region extending from the cell bottom up to about 2.5  mm below the membrane (in the following, we will call z the verti-cal distance from the membrane). Gelation is started by gently pouring the curing agent (45 mM CaCl2 solution) in the reser-voir atop the membrane, carefully avoiding the presence of air bubbles. Since CaCl2 solution is slightly less dense than the pectin solution, no convective effects due to inverted density profiles are expected. The cuvette was sampled in 3 different areas for rheological tests.

2.3. Internal gelation

For internal gelation, the supply of Ca2+ ions is given by the slow dissolution of CaCO3 nanoparticle aggregates in the acidic environment adjusted by adding NaHCO3. Sonicated CaCO3 particle suspensions were added to a 1.2% (w/v) pec-tin solution in the amount needed to eventually obtain gels with 1% pectin, 12.5 mM CaCO3, 9.5 mM of NaHCO3 and 70 mM of NaCl. All the reagents were gently mixed to prevent

the formation of air bubbles. For PCI measurements, the sample was directly prepared in a cuvette with 10 mm opti-cal path, and immediately placed in the PCI setup for mea-surement. Samples for the rheological measurements were prepared through mixing in a beaker the 1.2% (w/v) pectin solution with CaCO3 suspension to 6.25 mM, 12.5 mM and 25 mM final concentrations, and then poured in Petri dishes. At different times from the preparation, core samples (2 mm in diameter) were extracted from the center of the Petri dish and placed in the rheometer.

2.4. Photon correlation imaging (PCI)

PCI [23, 24] is a recently developed optical correlation tech-nique that, similarly to dynamic light scattering (DLS), pro-vides detailed information on the microscopic Brownian dynamics of a colloidal system, but at the same time retains the spatial resolution of an imaging system. The technique is specifically designed to measure the slow and often intermit-tent time-dynamics of colloidal gels and glasses [25], which is precluded to standard DLS. In addition, it is particularly suitable for investigating spatially-heterogeneous systems, such as the case of a biopolymer solution undergoing a con-trolled gelation process [13]. Additionally, as an imaging tech-nique, it also allows us to single out collective motion within the sample, namely, to detect the presence of large-scale restructuring effects or collective hydrodynamic motion in the sample. A detailed description of the method can be found in [13, 24]. Here, we give only a very qualitative introduction to the basic strategy used in PCI, keeping in mind its application to the kind of systems we are investigating.

In gels, the microscopic Brownian dynamics, although not fully arrested, is limited to local displacements taking place on a very small spatial scale. This has deep consequences on standard DLS measurements, where the normalized correla-tion function of the scattered intensity τ τ= ⟨ + ⟩g I t I t( ) ( ) ( )t

t2 / I t( ) t

2 averaged over the initial time t is usually obtained. Indeed, τg ( )t

2 , besides displaying a ‘contrast’ − ∞g g(0) ( )t t2 2

which is generally very low (the smaller the mean-square dis-placement of the scatterers, the lower the contrast), depends on the specific configuration of the scatterers as seen from a given detection point, because each coherence area (or ‘speckle’) comes from a unique combination of the phases of the individual fields scattered by each particle. Hence

τg ( )t2 does not coincide at all with the correlation function

g2(τ)  =  ⟨I(t)I(t+τ)⟩e / I t( ) e2 that would be obtained by per-

forming an ensemble average over a large number of different statistical configurations of the sample, which is the quantity of real interest. Retrieving sound structural information can be made by a ‘brute force’ method, which consists in displacing or rotating the cell between distinct acquisitions of τg ( )t

2 . Yet, because the dynamics are so slow, the time-dependence scat-tered intensity can be simultaneously measured over a large number of independent speckles using a multi-pixel detector as a CCD or CMOS camera, obtaining the ensemble-averaged correlation function a posteriori via software, instead of using (faster) digital correlator hardware.

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This much more efficient method, called Time Resolved Correlation (TRC, [26]), is not however suited to provide the spatial information required to investigate inhomogene-ous samples. To recover the latter, the PCI strategy consists in forming on the multi-pixel detector an image of the sam-ple, seen from a given scattering angle, by means of a lens. However, a lens would collect the light scattered over a wide range of angles, unless it is suitably ‘stopped down’ by means of a diaphragm. Besides fixing the scattering wave-vector q = (4π n/λ) sin (θ/2), where θ is the scattering angle, λ the inci-dent wavelength and n the sample refractive index, stopping-down plays a much more important role. In fact, because of the presence of the diaphragm, PCI becomes not only an imaging, but also a DLS technique. Whereas using a large (ideally infi-nite) aperture lens each point on the image plane corresponds to a single point on the object plane, stopping-down has the effect of ‘mixing’ the contributions coming from a finite area on the object—technically, the diaphragm consistently widens the point spread function. In practice, then, one gets a ‘speck-led’ image, where the intensity on each speckle fluctuates in time according to the Brownian dynamics of the sample, as in standard DLS or in TRC, but relative to the specific spatial location of the sample mapped on the image plane. This allows us to detect spatially-inhomogeneous dynamics. In addition, because PCI is in fact an imaging technique, it also allows us to single out collective motion within the sample, which is directly mapped into an overall motion of the speckle field. Local physical displacements within the sample can then be obtained by means of an analysis quite similar to that used in Particle Image Velocimetry (PIV) by monitoring the position of the cross-correlation peak between the speckle patterns of two images obtained at different times. This strategy, which has already been profitably exploited to investigate the long-time restructuring dynamics of colloidal gels [27, 28], is effective only provided that the internal dynamics is sufficiently slow that the speckle fields remain correlated enough over the time it takes for the sample to display detectable collective motion.

In our setup the sample, illuminated by a vertical laser sheet (λ = 632.8 nm) with a thickness of 200 µm, is imaged by a lens on a CMOS sensor set at θ = 90° with respect to the illumination plane, with a diaphragm placed in the focal plane of the imaging lens. The analysis of the images collected by the CMOS camera at a proper frame rate first consists in grouping together a suit-able block of adjacent pixels (also called a ‘Region of Interest’), over which the signal average and standard deviation are calcu-lated. Increasing the number of pixels in a single block yields of course better statistics, but reduces spatial resolution. Very often, however, the symmetry of the problem allows us to pick up a single relevant direction along which the physical property of interest varies: in this case, the averaging block can be safely taken as a thin strip along the perpendicular direction. A gen-eral picture of the local dynamics can be obtained by introduc-ing the so-called ‘correlation index’ (or ‘degree of correlation’) cI (τ, t, r) between two images taken at times t and t+τ:

ττ

τ=

+

+−c t

I t I t

I t I tr( , , )

( ) ( )

( ) ( )1,I

r

r r

p p

p p

(1)

where Ip is the scattered intensity measured by the p-th pixel and ⟨···⟩r denotes an average over all the pixels within a block centered around r4. Therefore, in gels displaying a restruc-turing kinetics and, possibly, spatial heterogeneity, the corre-lation index is actually a function of i) the delay time τ, ii) the ageing time t, namely, the time lapse after gelation has occurred, and iii) of the specific location r within the sample. The occurrence of spatial inhomogeneities can be spotted at a glance by plotting a map on a color scale of the values over the whole sample, at a fixed delay τ, of the correlation index averaged over small blocks. Provided that the investigated kinetics is sufficiently slow, the statistical accuracy can be enhanced by time-averaging cI (τ, t, r) over a time window δt that is much shorter than the characteristic evolution time of the investigated kinetics, which allows reduction of statisti-cal noise. When considered as a function of the delay τ, this ‘coarse-grained’ correlation index bears the same information of the ensemble-averaged correlation function: in fact, one simply has: ⟨cI (τ, t, r)⟩δt = g2(τ) −1.

2.5. Rheological tests

Very useful insights about gelation can be found by contrast-ing the micro-structural behavior probed by PCI, with the macroscopical properties obtained with rheological mea-surements [7], [29–31]. In this work, we have performed constant strain measurements by imposing a small-amplitude oscillatory shear at variable frequency f in a standard cone-and-plate geometry. These measurements, which yield both the amplitude and the phase of the stress, provide the storage and the loss moduli G′(f) and G′′(f), respectively related to the elastic energy stored within the system and to viscous dissipation. Provided that the strain amplitude is sufficiently small, measurements are in the linear viscoelastic regime, characterized for a gel by a weak frequency dependence of G′(f) and G′′(f) [29]. To follow the gel evolution kinetics, a simple but very useful parameter is the magnitude of the complex viscosity, defined as:

η η η∣ = ∣ ′ − ′′ ∣ = ′ + ′′f f f G f G f f| *( ) ( ) i ( ) ( ( ) ( )) / ,2 2 1/2 (2)

which for a fully arrested structure and at sufficiently low frequency, where the storage modulus is almost constant and much larger than G′′, follows a power law dependence on the frequency

η∣ ∣ = α−f Af*( ) ,

with α ≃ 1. A similar power-law behavior may be expected to be followed by the gel that progressively stiffens [30]. When the network formation is fully completed, the power-law exponent

4 cI (τ, t, r) is then simply related to the covariance between the intensity measured on the same speckle at two different times, sampled over the given block and, in particular, cI (0, t, r) is the relative variance of the intensity in r at time t. It is, however, useful to point out that the former definition of the correlation index refers to an ideal optical configuration. In practice, cI (0, t, r) is generally smaller than one, because a single pixel on the sensor is larger than a single coherence area. Similarly to what is done in standard DLS, cI (τ, t, r), can in this case be taken as the ratio of the experimental correlation index to its value at τ = 0.

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α value is usually found to reach a limiting value α ≲ 1, while the amplitude A, which depends on cross-link density, quantify the gel strength [31]. Our measurements were performed with an AR-1500ex Rheometer (TA instrument, Italy) using a trun-cated cone-plate geometry with a diameter of 2 cm, a truncation of 32 µm and a working gap of 32 µm. The storage and loss moduli were measured at constant temperature T = 25°C and constant stress σ = 2 Pa, varying f in the range 0.2–10 Hz.

3. Results and discussion

3.1. External gelation

We first consider pectin gelation induced by perfusion of the CaCl2 curing agent. With a negligible delay, due to the time it takes for the ions to cross the separating membrane, the curing agent starts diffusing into the compartment con-taining the pectin solution, triggering the onset of gelation and generating a gelation front that propagates along the cell. It is useful to point out, however, that, at variance with what has been observed for alginate external gelation, the advancement of the gelation front is not marked by an appre-ciable increase of the scattered intensity; this suggests that heterogeneities are much less pronounced in pectin than in alginate gels [13].

Quantitatively, gelation can be detected and accurately fol-lowed by monitoring the dependence on time t of the degree of correlation cI (τ, t, z0) remaining after a fixed delay τ at a given distance z0 from the membrane. The results for several values of τ, relative to a rectangular averaging block of verti-cal thickness Δz = 0.8 mm and horizontal width w = 5.5 mm, centered in z0  =  5.6  mm, are shown in figure 2. Consider

first the values of cI (τ, t, z0) obtained for τ  =  20  s. This value of the delay time is still orders of magnitude longer than the decay time of the correlation function for a fluid pectin solution: hence cI (20, t, z0) ≃ 0 until, at time t = tg, the gelation front enters the considered averaging block. The upper curve in figure 2, where Δt = t−tg plays the role of the actual gel ageing time at position z0, shows that, as soon as the gelation front reaches z0, the correlation index rises rap-idly, attaining a value cI (20, t, z0) ≃ 1 within a time lapse Δt1 = 2 − 3 h. Hence, for an ageing time larger than Δt1, the sample behaves as a fully arrested gel structure over a time scale of at least 20 s. The behavior is, however, different if we consider much larger values of the delay between the two images. Similarly to what is found for τ = 20 s, the degree of correlation shows a rapid increase, which however, after Δt1 reaches a plateau value that is substantially lower than one, decreasing from about 0.65 for τ = 100 s down to about 0.38 for τ = 600 s, remaining then approximately constant till an ageing time Δt2 that increases with τ. After this ‘quiescent’ period, however, cI (τ, t, z0) start rising again, asymptotically leading, over a time scale of tens of hours, to a much higher degree of correlation.

The inset in figure 2 shows that the gelling time tg, when considered over the whole cell, grows linearly with the square of the distance from the membrane, implying a diffusive behavior of the gelation front with a diffusion coefficient D ≃ 0.57 × 10−5 cm2 s−1. With this value of D, which is about half of the value for 25 mM solution of CaCl2 in pure water, Δt1 turns out to be about twice the transit time of the gela-tion front thorough the thickness Δz of the averaging block. The initial rising stage of the correlation index corresponds therefore to a drastic slow down of the microscopic dynamics that take place almost concomitantly with the supply of the curing agent. To inquire about the peculiar two-stage gelation kinetics highlighted by the time-dependence of cI (τ, t, z0) for long delays τ, it is useful to take a look to the full correlation functions g2(τ), which are shown in figure 3 for several values

Figure 2. External gelation by perfusion with calcium chloride of a 1% pectin solution, with 70 mM NaCl added to screen electrostatic interactions. The concentration of the curing agent in the reservoir was chosen so to obtain a final average CaCl2 concentration in the cell equal to 25 mM. Main: correlation index cI (τ, t, z0) at a distance z0 = 5.6 mm from the membrane, plotted as a function of Δt = t − tg, where tg is the instant when the gelation front reaches z0 for diverse values of the delay time τ. Inset: dependence of the gelation time on z, fitted as tg = z2/4D, where the diffusion coefficient D ≃ 0.57 × 10−5 cm2 s−1.

Figure 3. Correlation functions g2(t) − 1, relative to the same sample and averaging box discussed in figure 2, obtained for several values of Δt shown in the legend. The vertical bars correspond to the values of the delay time τ shown in figure 2.

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of Δt. For long ageing time (Δt ≳ 1 day), the initial decay5 of the correlation functions can be rather accurately fitted by a single exponential, with a decay time τl ≃ 50 min. For shorter ageing, however, g2(τ) shows an additional, much faster initial decay: in fact, all correlation functions can be roughly fitted as the sum of two exponentials

τ − = + −ττ

ττg a a( ) 1 e (1 )e ,2

- -s l

where τl is fixed to the values found at large Δt. In addition, for Δt ≲ 10 − 12 h, the decay time τs and amplitude a of the first exponential are roughly constant (τs ≃ 2 min, a ≃ 0.5), whereas, by further increasing Δt, τs weakly increases and a rapidly decreases until the first decay stage becomes negligi-ble. Therefore, the two-stage increase of the correlation index in figure 2 witnesses in fact a progressive change in shape of g2(τ), due to the concurrence of two distinct de-correlation mechanisms in the microscopic dynamics, a faster one operat-ing only at short Δt, followed by a much slower one persisting up to a very long gel ageing time.

Extending the analysis from a single averaging block to the whole sample reveals that, with external gelation by perfusion of the curing agent, the gel structure and microscopic dynam-ics can be very inhomogeneous, even after a very long time. The correlation map displayed in panel (a) of figure 4 shows indeed the occurrence of three roughly defined regions in the sample, which are better highlighted by the horizontally-averaged correlation index cI (τ, t, z) displayed in panel (b). Whereas the top part of the gel (region T, z ≲ 7 mm) is basi-cally fully correlated even for the longest measured delay time τ = 600 s, by further increasing the distance from the membrane the correlation index rapidly decreases (region M) to rather low values close to the cell bottom (region B, z ≳ 10 mm), indicating that consistent microscopic dynamics persists even

after 40 h from sample preparation. At this stage, the cell was extracted from the PCI setup, and samples scooped with a tiny spatula from the three regions approximately sketched by dot-ted squares in panel (a) and they were subjected to constant-stress rheological measurement in a frequency range 0.2 Hz ⩽ f ⩽  10 Hz. Panel (c) shows that, in all the three regions, the magnitude of the complex viscosity shows, at least at suf-ficiently low frequency, a power law behaviour |η*| = A f −α with the same exponent α ≃ 0.9, but with an amplitude A that decreases by almost two orders of magnitude from T to B, indicating that slower microscopic dynamics correspond to a macroscopically much stiffer gel at the top than at the bottom.

3.2. Internal gelation

The peculiar kinetics observed in gelation by external per-fusion is mirrored by several restructuring events observed in experiments where pectin gelation takes place uniformly within the sample perforce of the dissolution of internally dis-persed CaCO3 nanoparticles. These puzzling events are clearly highlighted by the series of correlation maps shown in the top part of figure 5. Panels A–F show that, initially, the correla-tion index ⟨cI⟩ averaged over the whole map monotonically increases, witnessing the progressive structural arrest brought in by the supply of gelation agent coming from the slow dis-solution of the CaCO3 nanoparticle aggregates. The maps also show, however, the microscopic dynamics gets less heteroge-neous with ageing. This is better appreciated by plotting the relative standard deviation σ c/c II as in the body of figure 5. After about 4 h, when the value of ⟨cI⟩ is already larger than 0.9 and its standard deviation has fallen to about 20%, the gela-tion process seems to be approaching completion, yet, panel C shows that a major decorrelation event takes later place, lead-ing to a sudden increase of both ⟨cI⟩ and σ c/c II that lasts for about 2 h, after which the gelling solution reverts to an almost fully-correlated state. Yet, the following overall evolution of

Figure 4. (a) Correlation index map for the whole sample discussed in figure 2, 40 h after the CaCl2 solution has been poured into the upper cell reservoir. The field of view was divided into averaging blocks with size of 320 × 320 µm2 and the correlation index cI (τ = 600 s, t = 40 h, r) evaluated for each block and plotted according to the displayed color scale. (b) Profile along z of the correlation index ̂ τ =c ( 600I  s, t = 40 h, z) obtained by horizontally averaging the correlation map. (c) Dependence on the shear frequency of the magnitude |η*( f )| of the complex viscosity for samples extracted from regions T, M and B, compared to a power law |η*( f )| = A f −0.9 (dashed line).

5 Fitting is limited to delays short enough to ensure that the gel displays negligible ageing within the same period (τ ≲ 20 min).

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the system towards a more homogeneous state, quantified by the decrease σ c/c II , is again interrupted after about 16 h by a second shorter decorrelation event, which is highlighted in panel E. It is finally useful to note that, as also evidenced by panel F, the standard deviation of the correlation index remains rather high even at very long ageing time, suggesting that the gel is much more heterogeneous than those obtained by exter-nal gelation at fixed z. Arguably, this structural heterogeneity originates from the intrinsically heterogenous supply of cal-cium ions from strongly localized sources, regardless of the fact that the dissolving particles have been rather uniformly dispersed by the initial mixing. The presence of decorrela-tion events, which were found to be reproducible over several

samples undergoing internal gelation, corroborates the hint gathered from figure 2 that the kinetics of pectin dynamic arrest is highly non-trivial.

That internal gelation does not proceed steadily in time is further highlighted by the rheological measurements pre-sented in figure 6. Panel (a) shows that, even after a very short gelling time, the magnitude of the complex viscosity already shows a power-law dependence |η*( f )| = Af −α on frequency with an exponent that is only slightly smaller than the value α = 1 usually found for fully arrested gels [31]. With ageing, the amplitude A increases, showing the gel progressively stiff-ens. However, gel stiffening does not proceed steadily in time: as shown in panel(b), after a rapid increase lasting for only

Figure 5. Panels A–F: correlation index maps after a delay τ = 1000 s obtained at different aging times t for a 1% pectin solution undergoing internal gelation via the addition of nanoparticles, amounting to a CaCO3 concentration of 12.5 mM. The full field of view in the picture (8 mm × 11 mm) has been split into square blocks with side 320 µm. The average values of the correlation index are shown below the images. Body: relative standard deviation of the correlation index maps as a function of the aging time t, where the black dots correspond to the correlation maps A–F.

Figure 6. (a) Magnitude of the complex viscosity |η*( f )|, for a 1% pectin solution undergoing internal gelation via the addition of nanoparticles, amounting to a CaCO3 concentration of 12.5 mM, taken at different aging times. Solid lines are fits with a power law |η*( f )| = Af −α, with α ≃ 0.9. (b) Value of the amplitude A in the fits of |η*( f )| as a function of the aging time.

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10–15 min, |η*( f )| does not show any appreciable increase up to about 5 h, after which it resumes a steady growth.

Panel (b) also highlights that, even at long ageing time, the magnitude of the complex viscosity A is still as low as a few Pa, which is surely far smaller than the average complex viscosity observed for the inhomogeneous gel shown in figure 4. Hence, gels obtained by internal gelation look notably weaker than those forming by external perfusion. Actually, the magnitude of |η*( f )| is in the range of the values obtained for the looser region of externally-gelled pectin, close to the cell bottom. However, similar values of the macroscopic mechanical properties do not necessarily imply that these two structures are alike in terms of microscopic organization and dynamics. Although sharing a similar two-step kinetics, external and internal gelation may not indeed proceed according to the same microscopic mechanism, due to the very different kinetics of release of the Ca2+ ions. Whereas in internal gelation the slow dissolution of CaCO3 par-ticles, largely governed by the pH of the pectin solution, is the rate-limiting factor for pectin dimerization, in external gelation this first gelation step readily takes place because the Ca2+ ions are already homogenously dispersed in the pectin solution, and is limited only by the free ionic diffusion, barely affected by pectin acidification. As a result, similar macroscopic proper-ties may actually conceal a different structural organization in terms of balance of the amount of pectin dimers that form in the first kinetic step, versus the weak interchain bonds, which progressively strengthen the gel at a later stage. This legitimate suspicion is fully supported by the very different nature of the microscopic dynamics of the two structures unraveled by PCI. Indeed, a comparison of the correlation index maps in figure 4(a) and in panel F of figure 5 readily highlights that, while the bottom part of the gel obtained by external perfusion is almost completely decorrelated, over a comparable timescale the inter-nally gelled sample shows a fully arrested dynamics. More gen-erally, the observation we made is a caveat against claiming, as unfortunately often done, that similar rheological properties involves alike structural organization, unless this claim is cor-roborated by clear microscopic evidence.

4. Conclusions

By combining PCI and rheology, we have investigated the kinetics of formation and aging of pectin gels in the presence of a neutral electrolyte. We have addressed two different gelation mechanisms: external gelation, generated by the perfusion of aqueous solution of calcium ions—a method previously used to study alginate gels [13]—and internal gelation, obtained by the progressive release of the same ions via dissolution of cal-cium carbonate nanoparticles dispersed in bulk. Although the chain association mechanism is assumed to be similar in pectin and alginate, our experimental findings suggest that significant differences between the two systems exist both in the gelation kinetics and in the structure of the gels that form.

First, in the presence of added NaCl the advancement of the gelation front in pectin is diffusive, in striking contrast with the peculiar linear dependence on time reported in [13]. Although a detailed explanation for the non-diffusive behavior

of gelation in alginate is lacking, a plausible mechanism is related to the occurrence of an osmotic unbalance at the gel front, where the local ionic strength shows a steep gradient. In colloidal suspensions, salinity gradients are known to gen-erate Donnan effects, which may strongly influence particle diffusion or settling [32]. Whether similar effects occur during the formation of ionic polymer gels is still an open question, but the recovery of fully diffusive behavior in pectin by the addition of electrolytes supports an electrostatic origin of the anomalous behavior found for alginate.

Second, in alginate the timescales of microscopic dynam-ics and aging are widely different, and the correlation functions g2(τ)−1 eventually decay to zero, regardless of the aging time, showing that the microscopic dynamics does not come to a com-plete halt, so that alginate gels slowly ‘creep’ over a long time. Conversely, pectin gels, although showing much slower micro-scopic dynamics which actually intermix with the ageing kinet-ics, eventually get fully arrested (namely, they are ‘true’ gels).

Finally, whereas the correlation functions of the alginate gels studied in [13] are well described by single exponential decay at any aging time, pectin dynamic arrest seems to dis-play two-stage kinetics for both internal and external gelation. It is useful to point out that a multi-step gelation pathway has been recently reported by Larobina and Cipelletti [14] for alg-inate gels obtained by internal gelation. In these experiments, three different relaxation mechanisms of the time-correlation functions can be spotted. A first fast relaxation, attributed to the thermally-activated overdamped vibrations of the gels strand at fixed topology, takes place over tens of ms, a time-scale too fast to be probed with our setup, is followed by an intermediate decay occurring between 10–100 s, a timescale comparable with the faster decay we measured (τs ≃ 2 min). The final, long-time decay displays a peculiar ‘compressed exponential’ form g2(τ) ∼ exp[−(τ/τ0)α], with α >1, which has often been ascribed to the relaxation of internal stress accumulated during the formation of a network structure [33, 34]. For pectin gels, the long-time decay of the correlation functions, although occurring over comparable timescales, is conversely found to be fitted by a simple exponential decay even at long times, similarly to what was previously found for external gelling of alginate without added salt [13]. With respect to the latter system, however, the absence of sudden correlation ‘bursts’ in cI suggests that pectin gels are much less stressed, probably due to the presence of a neutral electro-lyte that reduces the rigidity of the polymer chains, hindering the formation of localized frozen stresses. As a matter of fact, preliminary results we have obtained show that, in the absence of added NaCl, pectin gels display intermittent and heteroge-neous dynamics similar to those reported in [13].

Further studies are required to investigate a possible con-nection between the two-stage gelation kinetics we observed and a two-step mechanism of calcium gelation that has been proposed, where the formation of strongly linked dimer pair-ing is followed by the formation of weak inter-chain associa-tions [10, 16]. Nevertheless, the evidence we have collected indicates that care should be taken in comparing different experiments, because biopolymer gelation is very sensitive to the method of gelation and sample preparation.

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Acknowledgments

This work was supported by grants from MIUR, PRIN 2010–11 project (prot. 2010FPTBSH 009) to P Petrini. M D Alaimo was supported by MIUR FIRB, ANISOFT/RBFR125HOM project.

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