water layers

Accepted Manuscript Full Length Article Modelling the non-linear interfacial shear rheology behaviour of chickpea protein-adsorbed complex oil/water layers Manuel Felix, Alberto Romero, Cecilio Carrera-Sanchez, Antonio Guerrero PII: DOI: Reference:

S0169-4332(18)33148-9 https://doi.org/10.1016/j.apsusc.2018.11.074 APSUSC 40920

To appear in:

Applied Surface Science

Received Date: Revised Date: Accepted Date:

23 August 2018 7 November 2018 9 November 2018

Please cite this article as: M. Felix, A. Romero, C. Carrera-Sanchez, A. Guerrero, Modelling the non-linear interfacial shear rheology behaviour of chickpea protein-adsorbed complex oil/water layers, Applied Surface Science (2018), doi: https://doi.org/10.1016/j.apsusc.2018.11.074

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Modelling the non-linear interfacial shear rheology behaviour of chickpea protein-adsorbed complex oil/water layers Manuel Felix1, Alberto Romero2, Cecilio Carrera-Sanchez3, Antonio Guerrero1,* 1

Departamento de Ingeniería Química, Escuela Politécnica Superior, Universidad de Sevilla, 41011 Sevilla,

Spain. 2

Departamento de Ingeniería Química, Facultad de Física, Universidad de Sevilla, 41012 Sevilla, Spain.

3

Departamento de Ingeniería Química, Facultad de Química, Universidad de Sevilla, 41012 Sevilla, Spain

*Antonio GUERRERO Escuela Politécnica Superior, Universidad de Sevilla, 41011 Sevilla, Spain. E-mail: [email protected] Phone: +34 954557179; fax: +34 954556447.

Abstract The objective of this work is the evaluation of chickpea protein adsorption at oil/water (O/W) interface as a function of protein concentration and pH value (2.5, 5.0 and 7.5). To assess molecular interpretation, interfacial tension is determined as a function of concentration with a Wilhelmy plate, whereas interfacial small amplitude oscillatory shear (i-SAOS) properties are determined using a double wall-ring (DWR) geometry controlled by a DHR3 rheometer (TA Intruments) and a pendant drop tensiometer (IT Concept) is used to determine linear viscoelastic dilatational measurements. This work provides a model which could predict both the linear and non-linear viscoelastic behavior of complex fluid-fluid interfacial layers. To this end, relaxation tests using the DWR device are carried out at the interface under the linear and non-linear regimes. Steady state viscosity values are also obtained to check the ability of the model to predict the interfacial flow behaviour. Results show that the Wagner-I model can 1

reproduce fairly well the steady state flow behaviour of chickpea protein-adsorbed interfaces. This model is based on the use of a memory function calculated from the generalized Maxwell (obtained from i-SAOS measurements) and a damping function obtained by the Laun model from linear and non-linear relaxation tests.

Keywords: Damping function; Interfacial Rheology; Legume proteins; Non-Linear viscoelasticity; Pendant Drop; Wagner Model

2

1. Introduction The adsorption of protein layers at fluid-fluid interfaces is a widely studied phenomenon, however its comprehensive understanding requires to overcome some complexities related to the mechanisms which govern the protein adsorption, the denaturation process that takes place once protein molecules reach the interface, the nature of protein interactions, the formation of protein aggregates and the interactions with other biopolymers [1,2]. The complex behaviour of protein aggregates, polymers, or colloidal particles at the fluid-fluid interface is usually related to a complex microstructure, which is generally dominated by surface rheological properties [3,4]. It is for this complexity of protein-based interfacial layers that most of the studies use model proteins, either being carried out by means of interfacial small amplitude oscillatory shear (i-SAOS) or by dilatational measurements [5–7]. Unfortunately, commercial products based on emulsions or foams require the use of far more complex systems typically containing a mixture of proteins. Therefore, a further effort has to be carried out in order to characterize surface properties, particularly interfacial rheology, of complex fluid-fluid layers at which these proteins are adsorbed. Among these proteins, those extracted from plants are fairly attractive for food applications as they can replace those widely used proteins from animal sources. In this sense, knowledge of the main factors which affect the techno-functional properties of proteins at complex fluid-fluid interfaces would foster the development of new food products with novel functionalities based on commercial proteins [8]. Among the different options available in global markets, legume proteins (i.e. chickpea protein) has attracted attention since these proteins are regarded to be fairly cost efficient and present high nutritional and techno-functional properties [9,10]. Chickpea proteins have been called to be used in many food products, substituting other proteins as functional constituents. Chickpea seeds are rich in protein (20–25%) and starch. In this context, the development of a procedure which increases the protein content can be interesting for its use in food products 3

[11,12]. Protein concentrates from chick peas have a globulin fraction with the albumins constituting approximately one-fourth of the former [13]. In this globulin fraction, legumin (11S):vicilin (7S) ratio is 6:1 [14]. These protein fractions make chickpea protein concentrates suitable for the stabilization of interfaces, being already demonstrate for other legume such as soy bean [15]. Functional properties of proteins have been related to the response of these proteins to surface shear and dilatational deformations at complex fluid-fluid interfaces is particularly relevant. Some authors correlated the stability and bulk rheology of emulsions to the interfacial rheology of complex fluid-fluid interfaces [5,16–20]. However, this correlation should be carefully considering since cross-linking between protein films may lead to droplet aggregation, decreasing the kinetic stability [21]. In fact, Karbaschi et al. [22] only correlated surface dilatational visco-elasticity and the bulk viscoelasticity. However, there are other authors such as Lucassen-Reynders et al. [23] who indicated that dilatational rheology can be correlated to short-term stability, whereas i-SAOS measurements may provide information about the middle or long-term stability. Nonetheless, obtaining significant interfacial rheological functions is demanding: firstly, because of the deformation of an interface generally requires the application of very small stresses. Secondly, and more fundamentally, because of this challenge is associated to the effect that the shear viscosity of the bulk exerts on the response of the interface to a deformation or flow. In fact, the influence of the adjoining sub-phases often hinders the analysis of the fluid mechanics at fluid-fluid interfaces [24–26]. To overcome the first requirement, it is necessary to use a highly sensitive equipment. However, to discard the second limitation it is necessary to verify that interfacial shear rheological measurements are not affected by the adjoining sub-phases. When a planar interface is deformed by shear, the contribution of the subphase to the measured torque can be

4

assessed through the Boussinesq number ( interfacial and bulk viscosities (

where

and

) which is proportional to the ratio between the

):

is a characteristic length that will be dependent on the dimensions of the

measurement geometry. This parameter involves three length scales: , wchich is related to the ratio of the contact area and the contact perimeter between the geometry and the interface; LS and LB that are the interfacial and bulk momentum decay length scales. According to Fitzgibbon et al. [27], these later characteristic lengths correspond to the distance required for the interfacial and bulk momentum to be attenuated, respectively. In this study, it is assumed that the responses of the measured torque to shear deformations are dominated by the interface, which gives rise to large

values (

>10) and, hence, the contribution of the

adjoining sub-phases can be neglected. Most of the research studies found on interfacial shear rheology are devoted to the linear viscoelasticity regime, using i-SAOS measurements [20,24,28–30], or creep measurements [31,32]. However, applications where interfacial shear rheology has been found to be relevant, typically involve occurrence of non-linear interfacial shear deformations, far beyond the linear viscoelastic limit. Thus, the manufacture of emulsions and foams typically requires the use of high energy inputs, which give rise to fairly non-linear interfacial deformations. Basically, the research studies found on the characterization of non-linear viscoelastic properties of complex fluid-fluid interfaces has been carried out by means of large amplitude oscillatory shear measurements [33–35]. An interesting review on the use of this technique for fluid-fluid interfaces has been recently published by Sagis & Fischer [3]. In contrast, some studies on the steady state shear flow measurements has been carried out for the interfacial shear rheological characterization [6,32]. However, to our knowledge, other techniques such

5

as stress relaxation tests or creep tests have not been applied to complex interfaces in the nonlinear regime. In addition, modelling the viscoelastic behaviour of the planar oil/water (O/W) interface (including the linear regime and particularly the non-linear viscoelasticity regime) is of paramount importance to predict its behaviour when a shear field is applied to the complex fluid-fluid interface. This modelling would bring substantial benefits for the understanding of protein-adsorbed interfacial behaviour, as well as for the assessment of emulsion or foam stability patterns and eventually for emulsion or foam-based product development [36]. Unfortunately, this modelling issue has received much less attention at the interface than in the bulk. To this end, modelling of the planar interface has been used in this study following an analogue scheme to some of those used in the bulk by means of well-known constitutive equations, in order to achieve a suitable description for both the surface linear and non-linear viscoelasticity behaviour. This study is conducted within the framework of a research project with the overall objective of analysing the ability of legume proteins (i.e. from chickpea) to form biointerfaces which would provide long-term stability to food emulsions. A comprehensive characterization of linear viscoelastic properties, as well as transient and steady state flow properties of the chickpea protein-based fluid-fluid interface is essential to gain a better understanding of its behaviour under different conditions. The specific aim in this work is the analysis of the interfacial behaviour of chickpea protein at three pH values (2.5, 5.0 and 8.0). The interfacial assessment is carried out by: i) surface dilatational measurements (using a pendant drop tensiometer) and ii) interfacial shear rheology (using a double-wall-ring geometry controlled by a rheometer). 2. 2.1.

Material and methods Protein powder 6

Herba Ingredients (Seville, Spain) supplied a chickpea (CP) flour used in the framework of this research. This protein flour was obtained from direct milling of chickpeas. However, a protein concentrate was obtained due to its low protein content (c.a. 19 wt.%) according to previous studies [11]. This procedure consisted of two stages: (i) Alkalinisation of protein dispersion at pH 8, to improve protein solubility and centrifugation to remove the non-soluble fraction (depleted in protein); (ii) Neutralization an acidification of the aqueous phase (rich in protein) up to the isoelectric point (IEP). At the IEP, protein aggregation is favoured by the lack of net surface charges, which leads to the precipitation of most of the proteins present. In this case, the aqueous phase (depleted in protein) was discarded and the pellet (rich in protein) was freeze-dried. The protein content of the CP system was around 64 wt. %. Thus, according to the Pearson classification this protein system cannot be considered as a protein concentrate. Moreover, the CP protein system contained up to 16.4 wt. % of lipids. Regarding the ashes, the ash content of the CP systems was 3.8 wt. %. These ashes are inorganic soluble salts, since the non-soluble salts were removed during the protein-extraction procedure. In any case, 1 wt.% of NaCl was added to all samples in order to cushion the effect of these inorganic salts on interfacial measurements. The composition of the CP protein system was completed with 0.1 wt.% moisture (related to the previous stage in the freeze-dryer). All measurements were carried out using this CP protein concentrate, avoiding any further processing. Moreover, all interfacial measurements were carried out using Capicua high-oleic sunflower oil supplied by Coreysa (Seville, Spain). Finally, appropriate buffers from Sigma-Aldrich were used to compare results obtained under different conditions: at low pH, when protein surfaces are positively charged; near the isoelectric point (IEP), at which the net charge is virtually zero; and at pH higher than the IEP where a dominant negative charge is observed. 2.2.

Interfacial characterization

2.2.1. Determination of interfacial tension at equilibrium 7

Interfacial tension was determined after 24h protein adsorption using a Wilhelmy plate fitted to a Sigma tensiometer (KSV, Helsinki, Finland). These measurements were performed as a function of bulk protein concentration (0.1, 0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0 and 5.0 wt.%) and at three different pH values (2.5, 5.0 and 7.5). Oil phase was added after placing the Wilhelmy plate in the interfase, continuous interfacial tension values were recorded until reaching constant values over 5 min. 2.2.2. Pendant droplet measurements Interfacial characterization of protein adsorbed at O/W interface was carried out by means of pendant droplet (TRACKER, IT Concept, France), determining adsorption kinetics. Water-droplet profiles were processed according to the Laplace equation as was described by Castellani, Al-Assaf et al. [37]. Moreover, the viscoelastic moduli of protein adsorption layers were determined at 5 % strain amplitude at 0.1 Hz before reaching the pseudo-equilibrium state, as well as after reaching the pseudo-equilibrium state (10,800 s protein adsorption) as a function of frequency (from 0.0075 to 0.1 Hz). 2.2.3. Interfacial shear rheological properties Interfacial shear rheology analysis was carried out using a double-wall-ring geometry (DWR). Details about the geometric features of the DWR were reported by Vandebril et al. [25]. The protein solution was contained in a double wall cup and the ring was then positioned at the air/water (A/W) interface. Subsequently, sunflower oil was carefully added to the interface. The ring was controlled by a DHR-3 rheometer (TA Instruments, USA) [25]. Mechanical spectra were obtained by means of frequency tests, which were carried out within the linear viscoelastic range (assessed through stress sweep tests that were performed before frequency sweep tests). The frequency tests were performed during the protein adsorption (from 0.314 to 6.14 rad/s) and after reaching the equilibrium (from 0.06 to 6.14 rad/s). In addition, a time sweep test was carried out over the protein adsorption, over 10,800 s at 0.1

8

Hz. The stress relaxation measurements were carried out after the protein adsorption, applying several torque values at O/W interface. The deformation obtained was measured for 900 s. Finally, flow curves were carried out from 0.5·10-4 to 50 s-1, monitoring the viscosity of the O/W interface. Boussinesq number (

) was used to analyse the flow field as a function of the interfacial

viscoelastic properties, evaluating the contributions of the subphases [25]. 2.3. Statistical analysis At least three replicates of each measurement were carried out. Measurement uncertainty was determined by means of standard deviation. 3. Results and discussion 3.1 Characterization of the O/W interface 3.1.1. Determination of interfacial tension at equilibrium First of all, the protein system was adsorbed at O/W interface over 24h to reach an apparent equilibrium state and subsequently the interfacial tension was measured with a Wilhelmy plate. Then, interfacial pressure ( ) values are calculated from interfacial tensions of protein layers at the apparent equilibrium ( ) at several CP concentrations (0.1, 0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0 and 5.0 wt.%) and pH values (2.5, 5.0 and 7.5) as follows:

Parameter

is the O/W interfacial tension in absence of any surface active agent.

Fig. 1 shows the values obtained for the interfacial pressure at the O/W interface, after reaching the apparent equilibrium. It can be noticed that, although some effects can be masked by minor components of the oil phase and protein system, the effect of pH should be mainly attributed to changes in the protein surfaces. Thus, regardless of the pH used, an increase in interfacial pressure between sunflower oil and water was observed with increasing protein content, showing a tendency to reach a plateau value that corresponded to the 9

saturation of the interface. The interfacial tension value strongly depends on protein conformation, which in turn depends on the pH value. In this sense, the pH value affect to the net charge of protein surfaces as it departs from the IEP (being positive at pH below the IEP or negative above this point). Previous results indicated that, for this protein system, pH 2.5 is below the IEP, pH 5.0 is close to the IEP and pH 7.5 is above the IEP [11]. At this point, it should be noted that this may affect the interactions among protein macromolecules, particularly as they approach to the saturation of the interface. These results confirm that the interactions among adsorbed protein molecules are dependent on pH. Moreover, the pH value causes two opposite effects, which may be related to the closeness to the isoelectric point (which is around 4.0). The systems whose pH values are far from the IEP (2.5 and 7.5) reaches higher interfacial pressure plateau values than the one obtained at pH 5.0. Thus, the saturation concentration reached is 2.0, 0.5 and 3.0 wt.% for the CP protein system at pH 2.5, 5.0 and 7.5, respectively. This means that the pH value not only modulates the plateau interfacial pressure value, but it also shifts the concentration at which the interface was saturated. This may be related to the fact that near the IEP the protein surface is poorly charged. On the other hand, low-charged protein molecules are not capable of reducing the interfacial tension as much as the same protein at pH 2.5 or 7.5, where the surface charge is much higher. 3.1.2. Adsorption kinetics Measurements using the TRACKER drop tensiometer are carried out in order to determine the interfacial pressure ( ) over protein adsorption time. These measurements allow us to obtain the adsorption kinetics of CP protein systems at the O/W interface and, as a result, a kinetic model can be applied. Fig. 2A shows the transient interfacial tension response for the CP protein system at the O/W interface, at the saturation concentration previously determined in the Wilhelmy plate experiment.

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In all cases, the adsorption of protein at the O/W interface is characterized by a rapid increase in interfacial pressure, which is followed by a slower evolution and a tendency to reach a constant value (

sat

). However, this pseudo-constant value clearly depends on pH. Thus,

while the interfacial pressure of the systems at pH 2.5 and 5.0 was around 16 mN/m, the plateau interfacial pressure for the system at pH 7.5 was ca. 20 mN/m. A comparison of these results with the previous interfacial pressure measurements (using the Wilhelmy plate) suggests two different assumptions. The systems at pH 5.0 and 7.5 are near the equilibrium state. However, after 10,800 s, the system at pH 2.5 had not reached the equilibrium state yet (although a plateau zone could be observed). The adsorption kinetics can be discussed on the basis of a simplified model which postulates the occurrence of different stages for the migration of the protein from the bulk to the O/W interface [38]. Thus, a rapid step takes place in the first stage, which is characterized by a fast increase in interfacial pressure. This first stage is related to the protein diffusion from the bulk to the interface [6]. During this first step, the diffusion is the rate-controlling step, and a modified form of the Ward and Tordai equation [39,40] can be used to correlate the change in the surface pressure ( ) as a function of time (t):

where

is the protein concentration in the bulk phase (mol/L),

is the ideal gas constant

(J/K·mol), T is the absolute temperature, and D is the diffusion coefficient. Thus, the diffusion rate ( slope of the plot of

) of protein towards the interface can be easily deduced from the

vs. t1/2, as reported by Rodríguez Patino, Rodríguez Niño, & Carrera

Sánchez [41].

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It can be noticed that, in many cases, the first step of the protein diffusion is too short to be properly measured, and the kinetics does not correspond to those of rate-controlling diffusion and the diffusion constant obtained is apparent (

) [7].

This initial stage is followed by a decrease in the rate at which protein molecules penetrate through the interfacial layer. The adsorption kinetics becomes slower due to the existence of an energy barrier after the diffusion stage, and the process starts to be controlled by protein adsorption (the transition from the subsurface layer to the interface), where the steric interactions must be taken into account [42]. To compare the different rates, a first-order phenomenological equation can be used to fit the evolution of surface pressure with time:

where

,

and

are the interfacial pressure at the final adsorption time ( ), at any time

( ), and at the initial time (0), respectively, and kA is the first-order constant that can be associated to the above described process [7,43]. Fitting to Eq. 4 and 5 can be observed in Fig. 2B and 2C, respectively. The values of kD and kA parameters are shown in Table 1: The data obtained for the diffusion rate (kD) should be taken into account with caution since this stage was relatively fast at the concentrations studied. Consequently, only a limited number of data points can be used to fit Eq. (2). In fact,

is used (at pH 2.5 and 7.5) since,

most probably, protein diffusion towards the interface was so rapid that this parameter was also affected by the subsequent stage (protein penetration). Moreover, both values are much higher for this system than the one found at pH 5.0. Thus, protein diffusion was remarkably slower at pH 5.0, at which larger aggregates are likely formed. The parameter kA, obtained from Eq. (5) showed its highest value at pH 2.5. This is probably the reason why the plateau is reached earlier at this pH value, and might be related to some protein denaturation, taking place at low pH, even before protein adsorption. On the other hand,

at pH 7.5 was higher

12

than the one found at pH 5.0. In any case, systems at pH value 2.5 and 5.0 reached similar interfacial pressure value after 1800s (Fig. 2A). 3.1.3. Interfacial rheology measurements Linear viscoelastic dilatational measurements Figure Fig. 3A shows protein adsorption kinetics may also be analysed to determine the evolution of the response obtained from interfacial dilatational rheology measurements at three different pH values (2.5, 5.0 and 7.5). Both apparent viscoelastic moduli obtained at 0.1 Hz (

and

) undergo opposite effects, indicating an increase in the gel-like character of

the interface. Thus, the elastic component typically undergoes a clear increase over time whereas the viscous component undertakes an initial decrease, both of them tending to reach respective equilibrium values. This response is similar to that previously obtained for the adsorption of different proteins at the O/W interface [18,19] and it may be related to the formation of a gel-like protein film at the O/W interface immediately after its adsorption [7]. Regarding the effect of pH, it exerts a strong influence on both apparent components ( ). Thus, the highest

and

values are obtained for the lowest pH value (2.5). Similar results

were observed previously and they were explained in terms of some protein unfolding taking place at low pH even prior to protein adsorption at the O/W interface [18]. This strong pH effect has been previously related to the initial structure of the protein in the aqueous subphase [44]. In this sense, at low pH value, the protein structure was initially more expanded on the aqueous subphase [45]. On the other hand, the (rheo)kinetics of the system at pH 7.5 is different, since the

profile undertakes a slight decrease after reaching the plateau.

A tendency towards a second plateau may be expected at longer time. This response has been previously related to some protein rearrangement [46,47]. Moreover, Fig. 3A also evidences the slowest (rheo)kinetics obtained for the system whose pH is closer to the IEP (system at pH 5.0), while the fastest (rheo)kinetics corresponds to the lowest pH value (2.5).

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Fig. 3B shows the response obtained by means of interfacial dilatational frequency sweep tests for CP protein-adsorbed layers as a function of pH (2.5, 5.0 and 7.5), after reaching the pseudo-equilibrium state. The profile of both viscoelastic components (

and

)

may suggest the contribution of strong protein interactions at the O/W interface. This assumption can be considered on the basis of the low-frequency dependence of both functions as well as the difference in magnitude between

and

(around one order of

magnitude). In any case, these moduli are not only determined by the exchange of interfacial protein molecules between interface and adjoining bulk phases, but also in-plane viscoelastic stresses have to be considered in complex fluid-fluid interfaces [48]. Linear viscoelastic interfacial shear measurements The linear viscoelasticity (LVE) behaviour of a 2D interface may be described by using an extrapolation from the behaviour of a material defined in a 3D space. Accordingly, the linear viscoelastic behaviour of an interface may be obtained when the total interfacial shear stress or strain applied, for a given history of deformation, is so small that the structure of the interface remains unperturbed. A straightforward consequence of this is that the LVE behaviour for any complex fluid-fluid interface may be described using an equation adapted from the approach given by the Lodge equation [49]:

where

is the interfacial stress tensor,

elapsed time and

the interfacial Finger strain tensor,

is the

the interfacial memory function, which is the time derivative of

the interfacial linear relaxation modulus

:

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Interfacial shear rheology can directly provide relevant information on the specific linear viscoelastic moduli of the interfacial layer, and it allows to follow the evolution over protein adsorption and to obtain the mechanical spectra at the pseudo-equilibrium. Fig. 4A shows the evolution of both the interfacial shear elastic modulus (

) and loss tangent (

) over

protein adsorption at the O/W interface obtained from small amplitude oscillatory shear (iSAOS) measurements. Despite the fact that the values obtained from i-SAOS measurements are different compared to those obtained from the pendant drop, the evolution followed by and

is rather similar. Thus, the adsorption of protein molecules at O/W interface involves

a rapid increase of the interfacial shear elastic modulus (

) with a tendency to reach a

plateau value. This result is in accordance with the adsorption of the protein at O/W interface, which induces the formation of a protein-based film. Consequently,

values decrease

(specially for systems at pH 5.0 and 7.5), which denotes the increase in magnitude of the elastic modulus over protein adsorption. Eventually, it may be noted that the highest values of the elastic modulus (

or

)

are obtained at pH 2.5, regardless of the technique used (pendant drop or i-SAOS). This different behaviour can be attributed to the contribution of bending rigidity to the dilatational modulus, which is dominant as mentioned above, and is much lower at pH 7.5. Once the pseudo-equilibrium was reached, i-SAOS measurements are carried out at several frequency values in order to obtain the linear viscoelastic mechanical spectra of the O/W interface. Thus, Fig. 4B shows the mechanical spectra obtained for the adsorbed protein at the O/W interface at three different pH values (2.5, 5.0 and 7.5). The response found puts forward the elastic-dominant gel-like behaviour of the interfacial layer, with the elastic modulus (

) being greater than the viscous modulus (

), both functions show weakly

frequency- dependent gel behaviour. In addition, the linear viscoelastic behaviour for the gellike interface is described in this figure by the generalized Maxwell model (GM). This model

15

considers a superposition of a series of n independent relaxation processes, having each element a relaxation time,

, and a relaxation strength,

. According to this model the

shear stress, τs (t), may be written as a function of the surface strain deformation, must be pointed out that

and

. It

represent the components τs12(t) and

the interfacial stress tensor ( ) and the interfacial Finger strain tensor (

of

), respectively:

It must be pointed out that for solid-like viscoelastic interfaces one of the relaxation times must be infinite and its contribution should be represented by Maxwell elements and ,

or

e present case, three

Thus, the linear functions of the interface (i.e. ) can be obtained from this model as follows [50,51]:

According to these expressions, Eq. (9) and (10) can be used to calculate the discrete relaxation spectrum by selecting a set of relaxation times < 1) [51], calculating the values of

(provided that

> 1 and

by simultaneously using the method of

least squares to both equations. The experimental values of

and

are

successfully fitted to the generalized Maxwell model (Eq. (9) and (10)). Moreover, the values obtained for

and

can be used to calculate

(results shown later).

Fig. 5 shows the evolution of the interfacial shear mechanical spectra obtained during protein adsorption at the O/W interface until the pseudo-equilibrium state was reached, as a function

16

of pH (2.5, 5.0 and 7.5). These results suggests that these globular legume proteins are able to provide high values of interfacial shear viscoelastic properties, which suggests that the adsorbed proteins are able to form a fairly cohesive interfacial layer [52]. A marked evolution can be clearly distinguished as protein is continuously adsorbing at the O/W interface particularly at pH 5.0. Thus, the first frequency sweep test, after 10 min of protein adsorption, is dominated by the viscous component over the experimental frequency range. Subsequently, the mechanical spectrum shows a crossover point between

and

which shifts to higher frequencies along protein adsorption, eventually leading to the formation of a gel-like behaviour at the O/W interface. This process taking place after protein adsorption at the interface would involve protein unfolding and aggregation, leading to the development of a 2D elastic gel network. The gelation process at the interface has been described previously by several authors using other techniques different than interfacial shear rheology such as the use of gelators or high intensity ultrasounds [53,54]. It is worth mentioning that the interfacial shear rheology technique used in this study allows to monitoring the evolution of the viscoelastic properties over the development of the proteinadsorbed interfacial layer. These results indicate that the rheokinetics of the above-mentioned evolution is rather different depending on the pH value. At pH 7.5, the evolution is similar to the one found at pH 5.0, however the rheokinetics is faster, showing the crossover at higher frequencies and disappearing from the experimental frequency window at shorter times. This effect must be related to the presence of negative charges at the protein surfaces that would lead to electrostatic repulsive interactions between protein segments [29,55]. In contrast, at low pH, a gel-like protein-adsorbed interfacial layer is already formed after 10 min (Fig. 5A). This apparently faster evolution found at pH 2.5, may be related to the high and kA, especially to kA since it is related to the protein unfolding and rearrangement, which cause the gelation of the interface [56]. This effect may be probably related to some protein

17

denaturation occurring at this low pH value. The presence of electrostatic repulsive interactions among positively charged protein surfaces has to be also taken into account, leading to the development of higher viscoelastic moduli. According to Narsimhan [52], the interfacial shear rheology is influenced by the ability of the adsorbed proteins to exhibit cohesive interactions with neighbouring molecules, which in turn depends on pH. Previous results obtained for other protein systems indicate that if the substrate is close to the IEP, repulsions between protein molecules adsorbed at the interface are minimized, promoting the formation of more cohesive adsorbed layers [57,58] and, as a result, leading to a slower rheokinetics [59]. It should be emphasized that the evolution found from interfacial dynamic shear measurements (where a crossover point was observed) can be hardly measured by oscillatory dilatational tests. This may be a consequence of the predominance of bending rigidity on the dilatational response as it was previously indicated. In any case, note that after reaching the pseudo-equilibrium state all interfacial O/W protein-adsorbed layers show an apparent gellike response, regardless of the pH value. Dilatational vs. interfacial shear rheology Table 2 summarizes the parameters obtained from both, dilatational rheology and interfacial shear rheology obtained at 0.1 Hz. (

,

and

). In this sense, values

obtained from dilatational measurements evidence the predominant gel-like behaviour of the interface since these values of

are lower than 0.15 in all cases. This parameter also

reflects the strong pH dependence exerted by the CP protein system. A comparison with previous studies reveals that similar or even much lower present study. Thus,

values are obtained in the

values are around 0.1 for rice protein-stabilized O/W

interfaces at pH 2.0 and 8.0 [60], whereas potato protein-stabilized O/W interfaces led to values around 0.6 and 0.1 at pH 2.0 and 8.0, respectively [19]. O/W interfaces stabilized by

18

crayfish protein isolate showed respectively [61]. These low values for

values around 0.2 and 0.13 at pH 2.0 and 8.0, may indicate either the occurrence of

strong interactions at the interface [62] or the formation of a densely packed interface with denatured protein molecules [28]. The interfacial shear parameter (

) is always

higher than the dilatational one, which is a consequence of the smaller values obtained for the shear elastic modulus. As discussed above, the elastic modulus obtained from dilatational measurements is dominated by bending rigidity; while the moduli obtained from the interfacial shear rheology is related to protein-protein interactions. In fact, it is worth analysing the difference between the elastic parameters obtained from dilatational and interfacial shear measurements. As may be seen in Table 2, the highest difference between and

is obtained at pH 5.0, followed by pH 2.5 and 7.5.

Non-linear viscoelastic interfacial shear measurements When the strain applied to a material or to an interface exceeds a limiting value, a deviation from LVE response takes place. This being the case, Eq. (7) no longer applies and the material or the interface exhibits nonlinear viscoelasticity. To describe this behaviour a constitutive equation for nonlinear viscoelasticity must be used. A class of constitutive equations that has been widely used in bulk rheology is given by the Kaye-BKZ equation [49,63]:

where and

is the interfacial Cauchy tensor, Is1 and Is2 are the first and second invariants of is the interfacial elastic potential function. The selection of a

variety of expressions for the interfacial potential function

will allow to

define different constitutive equations for the description of different types of non-linear viscoelasticity behaviour. A particularly interesting simplification consists in selecting a 19

potential function that can be separated in two terms, one depending on the interfacial strain and the other being a function of time:

where invariants

is the scalar interfacial potential, which would be only dependent on the and

. Introducing the specific function given by Eq. (13) into Eq. (12), the

well-known time-deformation factorable or separable expression of the Kay-BKZ constitutive equation may be written in terms of

and

:

This equation can be rewritten in terms of two non-dimensional scalar functions for the deformation of the interface

and

as

follows:

A further simplification is obtained by assuming that the contribution of the surface Cauchy tensor can be neglected. This may be achieved by assuming that

. In this way,

the Wagner-I equation, which also involves time–strain separability, is obtained [49,64]:

where

is the interfacial expression for the so-called damping

function.

20

Considering only the simple shear component of the interfacial stress tensor, the equation results:

where

is the interfacial simple shear strain component and

is the damping

function for this component. This constitutive equation can be applied to reproduce the flow behaviour of the O/W interface studied, provided that suitable expressions for the interfacial memory and damping functions could be found. Such expressions should fit experimental results with reasonable accuracy and, on the other hand, they should be simple enough to permit prediction of the interfacial flow behaviour by solving Eq. (17). It should also be borne in mind that the interfacial memory function must reflect the LVE behaviour, whereas the damping function aims for the description of the non-linear behaviour of the interface at shear strains larger than the critical value. A classical procedure extensively used to obtain information about non-linear viscoelasticity at the bulk has consisted in the application of non-linear relaxation tests. This kind of test may also be applied to the interfacial layer to obtain the non-linear shear viscoelasticity response under shear. Interfacial relaxation tests involve the sudden imposition of a shear strain at the interfacial layer which is maintained over time, recording the stress response over the relaxation of the O/W interface, from which the relaxation modulus can be obtained

.

It is important to distinguish between the application of either a small or large strain. Likewise, for bulk relaxation tests, when a small strain is applied to the interfacial layer, the linear relaxation modulus response is obtained, being independent of the applied strain. However, above a critical strain the response corresponds to the interfacial relaxation modulus corresponding to the non-linear viscoelastic regime. The experimental values of the relaxation moduli,

, are provided in Fig. 6 at three different pH values: 2.5, 5.0 and 7.5 (A, B 21

and C, respectively). Their respective values for the linear relaxation modulus predicted by the GM model, previously obtained from i-SAOS measurements, are also shown in Fig. 6. In this sense, when the strain applied is small, the relaxation modulus tends to overlap onto the linear viscoelastic modulus

. Moreover, the magnitude of the overlapped relaxation

modulus is the same as the linear relaxation modulus obtained from the GM model (Eq. (11)), where the only deviation was found at pH 5.0. On the other hand, when the interfacial shear strain is increased, the non-linear relaxation modulus decreases dramatically, being nearly parallel regardless of the strain applied. Consequently, the interfacial film shows a relaxation behaviour that may be regarded as timestrain factorable at the three pH values studied. This being the case, the non-linear viscoelastic interfacial shear relaxation modulus

can be separated into a time-dependent function,

the interfacial linear relaxation modulus, function,

, and the strain-dependent interfacial damping

, as follows:

This time-strain factorability has been widely used for the bulk rheology of entangled polymers [65–67], or even emulsions [68–70] and other complex fluids [64]. However, the damping function has not been previously calculated for the O/W interface. Rolón-Garrido and Wagner [64] have reported an extensive review on the damping function in shear and elongational bulk rheology. Some extensively used models, derived from the K-BKZ equation, have been chosen to interpolate the experimental results [71–73]. Among the most used of them are the exponential models that can be expressed as follows:

This equation includes two well-known damping function models: and

22

The Laun model, where

and

>0

Moreover, a generalized sigmoidal expression, the Soskey-Winter model, has been widely used as a representation of the damping function:

It is worth mentioning that the experimental values of the damping function for the O/W interface have been calculated in the same way as those of the bulk, i.e. from the linear to non-linear interfacial relaxation modulus ratio:

Thus, experimental data and fitting from models are shown in Fig. 7 for the three pH values studied: 2.5, 5.0 and 7.5 (A, B and C, respectively). This figure reveals a remarkable strain softening behaviour for all studied systems. Consequently, the non-linear behaviour seems to appear at much smaller deformations compared to those predicted by the Doi-Edwards tube model theory for entangled linear polymers [74] or the force-balanced network model by Marrucci et al. [75]. Interestingly, the non-linear viscoelastic behaviour of the O/W interface is similar to the one reported previously for plant protein-stabilized emulsions, since the parameters of the damping function for the Soskey-Winter model are similar in values [70]. Regardless of the pH value at the water subphase, the damping function for the interfacial layer fits fairly well to either the Soskey-Winter model, described by Eq. (20), or the Laun model (Eq. 20), both of them describing a clear strain softening behaviour. This strain dependence is higher at pH 5.0, according to the value of parameter “a” from the Soskey-Winter model, which is similar for the interfacial layers at pH 2.5 and 7.5. Strain softening has been explained for proteinstabilized emulsions in terms of shear-induced deflocculation (physical) phenomena. By analogy, strain softening of protein adsorbed interfacial layers may be regarded as the result

23

of shear-induced disruption of physical interactions among protein chains. The extent of this effect depends on pH since the interactions are different. Fig. 8 displays the experimental interfacial steady state viscosity obtained at the three pH values studied: 2.5, 5.0 and 7.5 (A, B and C, respectively). A power-law decay for the interfacial viscosity as a function of shear rate can be observed for the three pH values. As previously outlined, this interfacial steady state viscosity may be predicted by means of a suitable constitutive equation involving time-strain separability. According to Rolón-Garrido and Wagner [64], the application of time-strain factorability has been widely used for a wide variety of polymeric systems, including protein-stabilized emulsions. Thus, some studies on protein-based concentrated O/W emulsions have applied time-strain separability by means of a non-linear viscoelastic model such as the Wagner-I constitutive equation [68,70,76–78]. The apparent interfacial viscosity at constant shear rate,

, can be obtained from the

Wagner-I constitutive equation (Eq. 17) either for stress growth tests, as a function of time, , or for steady state flow, where the total strain is for

.

The steady state interfacial viscosity is a function of the imposed shear rate but is no longer a function of time and can be calculated as follows:

On the other hand, according to the definition of the memory function by the GM model (Eq. 7) and the damping function for the Laun model (Eq. 19), the final expression for the Wagner-I equation at constant

is given by Eq. (23):

This equation can be rearranged in the form: 24

Which can be integrated, obtaining the following solution:

An obvious limitation for this model is that it is not able to predict a high shear rate limiting viscosity. Thus,

when

.

On the other hand, when the damping function is represented by the Soskey-Winter analytical expression, the Wagner-I equation has to be numerically solved for each case. Steady state interfacial viscosity values calculated from Eq. (25) for the Wagner and Laun models are included in Fig. 8, as well as data estimated numerically using the Wagner-I model in combination with the memory function for the GM model and the Sokey-Winter damping function. As may be deduced, the Wagner-I constitutive equation with Laun damping function provides a fairly well prediction of the experimental interfacial flow behaviour. Some deviations from experimental data can be only appreciable for the protein-adsorbed interfacial layer at pH 5.0 (Fig. 8B). This deviation is an error propagation from i-SAOS fitting carry out at pH 5.0, using the GM model (Fig. 6B). Moreover, the values of the interfacial complex viscosity for each pH studied are also displayed in Fig. 8 as a function of frequency. This figure indicates that the Cox-Merz rule, which involves an equivalence between complex and steady state viscosity for a variety of polymers, cannot be applied in its original form for these O/W interfaces. This occurs even though the slope for both interfacial complex and steady state viscosities are quite similar, as may be seen in Table 3, which also shows the reduction rate (RR) obtained by shifting from linear viscoelasticity (

) to steady state flow conditions (

). These negative slopes,

25

being not far from unity (i.e. 0.920.01) regardless of pH, indicate that the O/W interface shows a very shear-thinning behaviour. This very shear-thinning behaviour, with similar slopes, has been also reported for highly flocculated emulsions and has been associated to a shear-induced deflocculation process [18,70]. In the present case, the strong dependence on shear may be related to a progressive disruption of physical interactions among protein segments that remain adsorbed at the O/W interfacial layer. The similarity in values for the power-law slopes of

and (

allows using a modified expression of the Cox–Merz rule [79] that consists in the application of a shift factor (B) for the shear rate:

The values of the shift factor are also included in Table III. Parameters RR and B, particularly the latter, show a decrease with increasing pH, which suggests that electrostatic interactions among positively charged protein chains are more sensitive to shear forces than negative electrostatic interactions. It may also be noted that the RR values are close to those values reported for plant protein-stabilized emulsions [70], being slightly higher for the O/W interface studied. In addition, as previously mentioned, the model described in Eq. (24) cannot predict the occurrence of a high shear rate limiting viscosity. However, it is worth highlighting that these apparent deviations between the model and the experimental data observed in Fig. 8 at high shear are rather due to the contribution of the bulk viscosities than to the limitation of the model. This can be inferred from the values of for both phases (

and

obtained in this region. When the viscosity

) are considered, this number can be expressed as follows:

The contribution of the surrounding phases are dominant when Bo  1 [25]. In any case, their contribution should not be neglected below Bo = 10. 26

4. Concluding remarks Results from i-SAOS measurements are much more efficient than data from dilatational measurements for the assessment of the influence that pH exerts on the LVE properties of the O/W interface. The highest interfacial viscoelastic response against shear deformation is obtained for the protein system at pH 2.5. This effect may be explained in terms of repulsive interactions among protein-surface charges and some protein unfolding, taking place at low pH, prior to the adsorption at the interface, which may also explain its faster rheokinetics under such conditions. The response of the O/W interface to a small amplitude oscillatory shear deformation after protein adsorption reveals the evolution towards a well-developed gel behaviour, reflecting the occurrence of apparent protein-protein interactions. In addition, the shear flow properties of this protein-adsorbed O/W interface correspond to a very shear thinning behaviour, suggesting that those interactions are essentially physical in nature. In other words, the interface can exhibit a high sensitivity to shear forces, thereby making the characterization of the non-linear viscoelastic response necessary to improve understanding of the behaviour of the interface during the emulsification process. A factorable constitutive equation for non-linear viscoelasticity of the O/W interface can be used to reproduce experimental data obtained from steady state interfacial flow measurements fairly well. The constitutive equation is based on the Wagner-I model, using an expression of the GM model for the linear viscoelastic memory function and the Laun damping function for the non-linear strain dependence. It must be emphasized that this equation can properly describe the O/W interfacial behaviour ranging from its linear viscoelastic response to a very shear-thinning behaviour found for dependence of interfacial flow properties on the shear rate. The information obtained from the interfacial characterization of O/W layers carried out in this study can be regarded as highly useful to produce food emulsions under optimal

27

conditions. The low interfacial tension values observed for CP-adsorbed interfaces (particularly at pH 7.5) would favour a hypothetical emulsification process, whereas the higher elastic behaviour found at low pH would results in an enhancement of emulsion stability. In this sense, i-SAOS may be regarded as a powerful tool that might be used to make predictions on the stability of protein-based emulsions, even before carrying out emulsification. 5. Acknowledgments The authors acknowledge the Functional Characterization Service (CITIUS-Universidad de Sevilla) for providing full access to DHR-3 Rheometer. Authors also acknowledge to Herba Ingredients for supplying the chickpea flour used in this research. The authors also acknowledge University of Seville for a grant supported by VPPI-US. 6. References [1]

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36

Figure Captions Fig. 1: Values for the interfacial pressure

at the O/W interface at different pH values (2.5, 5.0 and

7.5) after reaching the apparent equilibrium (i.e. after 24 h) as a function of protein concentration for the aqueous phase

measured using a Wilhelmy plate.

Fig. 2: Protein adsorption kinetics at the O/W interface at different pH values (2.5, 5.0 and 7.5), recorded for the concentration of the aqueous phase at which the O/W interface becomes saturated: (A) Values for the interfacial pressure the interfacial pressure

as a function of adsorption time

as a function of the square root of time

Dimensionless interfacial pressure

as function of time

Fig. 3: Evolution of the linear dilatational moduli (

and

; (B) Initial values of

for the diffusion stage; (C) after the diffusion stage.

) at a strain amplitude of 5 %

and different pH values (2.5, 5.0 and 7.5), obtained for the concentration of the aqueous phase at which the O/W interface becomes saturated: (A) As a function of adsorption time (at a constant frequency of 0.1 Hz); (B) As a function of frequency after reaching the pseudo-equilibrium (i.e. after 180 min). Fig. 4: Evolution of the interfacial shear elastic modulus

and loss tangent

at a

strain amplitude and of 0.05% and three different pH values (2.5, 5.0 and 7.5), obtained for the concentration of the aqueous phase at which the O/W interface becomes saturated: (A) As a function of adsorption time (at a constant frequency of 0.1 Hz); (B) As a function of frequency after reaching the pseudo-equilibrium (i.e. after 180 min). Fig. 5: Evolution of the linear interfacial shear mechanical spectra obtained at different time intervals during protein adsorption at the O/W interface until the pseudo-equilibrium state, at a strain amplitude and of 0.05% and different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the protein concentration at the bulk aqueous phase was the one at which the O/W interface becomes saturated. Fig. 6: Experimental values of the relaxation modulus, relaxation modulus

and calculated values of the linear

from the generalized Maxwell (GM) model, obtained for the concentration

37

of the aqueous phase at which the O/W interface becomes saturated, at three different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the measurements were carried out after reaching the pseudoequilibrium state (i.e. after 180 min). Fig. 7: Experimental and calculated damping function values (

) from the Wagner, Laun and

Soskey-Winter models, obtained for the concentration of the aqueous phase at which the O/W interface becomes saturated, at three different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the measurements were carried out after reaching the pseudo-equilibrium state (i.e. after 180 min). Fig. 8: Experimental and predicted interfacial steady state viscosity from the Wagner-I model, obtained for the concentration of the aqueous phase at which the O/W interface becomes saturated, at three different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the measurements were carried out after reaching the pseudo-equilibrium state (i.e. after 180 min).

38

Highlights - The formation of protein films can be followed by interfacial shear measurements. - The properties of the film formed strongly depends on the pH value. - Surface charges and protein interactions determine rheological properties. - The Wagner-I model can properly describe the behaviour of O/W interfaces. - The model can reproduce interfacial linear, non-linear viscoelastic and flow results.

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Table 1

pH 2.5 5.0 7.5

kD · 103 (mN/m·s-1/2) 51200* ± 520a 2.07 ± 0.06b 36800* ± 739c

kA · 104 (s-1) -3.52 ± 0.02A -2.61 ± 0.04B -3.04 ± 0.01C

Table 1: values of kD and kA for protein adsorption as a function of pH value. Superscript indicates apparent diffusion rate constant (

). Different letters within a column indicate significant differences (p < 0.05).

41

Table 2

Dilatational pH 2.5 5.0 7.5

Shear (mPa·m)

0.07 ± 0.01α 0.14 ± 0.02β 0.02 ± 0.01γ

27.1 ± 0.3a 21.6 ± 0.4b 13.2 ± 0.6c

(mPa·m) 0.17 ± 0.03Г 0.19 ± 0.01П 0.23 ± 0.02Ф

17.1 ± 0.2A 8.0 ± 0.5B 8.6 ± 0.3B

Table 2: parameters obtained from both, dilatational rheology and interfacial shear rheology obtained at 0.1 Hz. Different letters within a column indicate significant differences (p < 0.05).

42

Table 3

pH

1-n

2.5

0.94 ± 0.01

5.0 7.5

0.91 ± 0.02 0.92 ± 0.01

1 - n* a a a

B

0.91 ± 0.02 0.93 ± 0.02 0.93 ± 0.01

A

A A

RR (%)

31.4 ± 0.3 22.3 ± 0.2 12.9 ± 0.2

α β

γ

95.9 ± 0.2 94.3 ± 0.4 90.6 ± 0.3

Γ

Π Φ

Table 3: parameters obtained from fitting interfacial steady state viscosity curves. Different letters within a column indicate significant differences (p < 0.05)

43