Analysis of gelatin chain aggregation in dilute aqueous solutions through viscosity data

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FOOD

HYDROCOLLOIDS Food Hydrocolloids 20 (2006) 1039–1049 www.elsevier.com/locate/foodhyd

Analysis of gelatin chain aggregation in dilute aqueous solutions through viscosity data Marı´ a L. Olivares, Marta B. Peirotti, Julio A. Deiber Instituto de Desarrollo Tecnolo´gico para la Industria Quı´mica, INTEC (UNL-CONICET), Gu¨emes 3450-(3000), Santa Fe-Argentina Received 14 July 2005; accepted 17 October 2005

Abstract Viscosity data of gelatin solutions with concentrations between 10
5 and 10
3 g/cm3 are studied in a horizontal capillary viscometer for a wide range of shear rates, covering the dilute and very dilute zones, where either intermolecular aggregation and intramolecular folding are possible, respectively, and the sol–gel transition is not observed. It is found that the dilute solutions behave as Newtonian fluids for the range of shear rates studied. Intrinsic viscosity values revealed that the maturation temperature has a relevant influence on the type of chain aggregations forming thermo-reversible clusters. The use of potassium thiocyanate and urea partially inhibited cluster formations. On the contrary, the aggregation process was not modified with the addition of surfactant sodium dodecylsulphate, indicating that hydrophobic interactions were not the cause of this phenomenon. The evolution of cluster formations in the dilute zone was analyzed through Smoluchowski aggregation theory and the aggregate-size distribution function was evaluated allowing one to conclude that it tends to be Gaussian and high polydisperse as the maturation time increases. Calculations show that disordered aggregates with high amount of occluded solvent are formed at low temperatures, while for higher temperatures, more compact structures are attained. Through the evaluation of the colloidal stability ratio, it is shown that the aggregation process is very slow in the dilute zone with an energetic barrier of around 25 times the Brownian thermal energy, and that the possibility of significant aggregation in the very dilute zone must be excluded. r 2006 Elsevier Ltd. All rights reserved. Keywords: Dilute gelatin solutions; Chain aggregation; Gravitational viscometry; Smoluchowski aggregation theory

1. Introduction Gelatin is a polydisperse biopolymer obtained from different collagen sources and production processes (see for example, Ledward, 1986; Ward & Courts, 1977). Therefore, the characterization of gelatin requires the consideration of different physicochemical properties like, for instance, amino acid configuration, molecular weight distribution (MWD), basic molecular scales and average chain conformations in the sol and gel states. These considerations provide one a better interpretation of other measurements widely used in applications, like gel bloom and standard solution viscosity values, among other basic Corresponding author. Tel.: +54 342 4559174/77; fax: +54 342 4550944. E-mail address: treofl[email protected] (J.A. Deiber).

0268-005X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodhyd.2005.10.019

tests carried out typically in the food, pharmaceutical and photographic industries. Although main sources of collagen for gelatin production are mammalians in general (Ward & Courts, 1977) diseases such as bovine spongiform encephalopaty have provoked the increment in using alternative sources (Ferna´ndez-Dı´ az, Montero, & Go´mez-Guille´n, 2003; Gilsenan & Ross-Murphy, 2000, 2001; Go´mez-Guille´n et al., 2002; Haug, Draget, & Smidsrød, 2004). One may find in the literature well-documented rheological and physicochemical studies concerning gelatin chain behavior in solution, for different concentration C, temperature T, ionic strength I, pH and chemical formulations of the background electrolyte. In fact, gelatin characterization has been carried out in different temperature and concentration zones or ranges, each one presenting quite specific phenomena. In this sense, it is appropriate

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M.L. Olivares et al. / Food Hydrocolloids 20 (2006) 1039–1049

to visualize that one of the zones most frequently studied was that involving the gelation process, where for a concentration above a critical value C g (around 10
2 g/ cm3) a transition from sol to gel was observed at a given maturation time tm , when the maturation temperature T m is set below a gel temperature T g , above which gel is not achieved. Throughout this work, it is understood that the gel temperature is a function of C (see, for instance, Bohidar & Jena, 1993; te Nijenhuis, 1997); thus a function T g ðCÞ exists for C4Cg with the critical gel temperature T ng ðC g Þ. Also to define roughly different zones in this work, T g and T ng are used as a guide, without introducing additional considerations involving, for instance, the coil–helix transition temperature T ch or the gel melt temperature T melt (see, for instance, Joly Duhamel, Hellio, Ajdari, & Djabourov (2002), Joly Duhamel, Hellio, & Djabourov (2002), for an analysis and discussion of these parameters when different gelatin sources are used). At present, detailed revisions and specific works considering mainly the gel zone (C4C g and ToT g ) are available (Clark & Ross-Murphy, 1987; Djabourov, Maquet, Theveneau, Leblond & Papon, 1985; Djabourov & Papon, 1983; Ledward, 1986; Ross-Murphy, 1997; te Nijenhuis, 1997; Tosh, Marangoni, Hallett, & Britt, 2003). Other zones are described briefly here to visualize precisely the concentration and temperature ranges considered in the present work. For instance, the entanglement domain, for T4T g and C4C g (Herning, Djabourov, Leblond, & Takerkart, 1991; Pezron, Djabourov, & Leblond, 1991). One of the relevant conclusions in this zone is that these solutions show collective movement and two diffusion dynamic modes are detected as specific phenomena. Another relevant zone studied by these authors is defined for CoC g and T4T ng where chain clusters are formed (see also Bohidar, 1998; Bohidar & Jena, 1994). A relevant study concerning this zone was also presented by Tromp, ten Grotenhuis, and Olieman (2002) for CE2  10
3 g/cm3, where it was suggested that two hydrophobic chain areas attracting each other are locally linking two stretched zones of chains with energy of the order of kB T, where kB is the Boltzmann constant. A fourth zone involves C c oCoC g and ToT ng . Thus, at these temperatures, in principle, coil to helix transition is possible having into account that T g oT ch (Harrington & von Hippel, 1961; Harrington & Karr, 1970; Harrington & Rao, 1970). Here C c is around 10
4 g/cm3 and define the limit, under which significant intramolecular conformations are expected in the very dilute zone (Benguigui, Busnel, & Durand, 1991; Busnel, Morris, & Ross Murphy, 1989; Horsky´ & Sˇvantner, 1993). Thus, a very dilute zone may be defined for CoC c and ToT ng . Within this wide phenomenological framework, described briefly above, kinetics of gelatin chain renaturation were studied mainly in the zones comprised for C4C c and ToT g , having into account that the intramolecular

refolding is, in principle, first order in concentration. Most authors concluded in general that the kinetic order depends on concentration ranges, and that a kinetic second order of chain association for C4C c and ToT g (around two zones) is more probably at a relatively short and intermediate period of time (see, for instance, Benguigui et al., 1991; Busnel et al., 1989; Normand, Muller, Ravey & Parker, 2000; Ross-Murphy, 1992; te Nijenhuis, 1997). In regard to a kinetic expression covering a wider range of maturation time relevant results are reported by Djabourov and Papon (1983), Djabourov et al. (1985), Tosh et al. (2003), and Ross-Murphy (1997). Important for our work here is that nucleation as a pair interaction mechanisms may be prone to be studied through Smoluchowski aggregation theory at early stages of the process, under dilute conditions. Thus, any deviation of experimental data from this theoretical framework may introduce additional information concerning the underlying mechanisms of chain aggregations. In this work, we are precisely concerned with the aggregation of gelatin chains in the dilute (C c oCoC g ) zone, at temperatures below the gel point (ToT ng ), which are subject at different maturation temperatures T m during maturation times tm . The very dilute zone (CoC c ) is also considered. For these purposes, we quantify the conformational evolution of gelatin chains through measurements of the solution intrinsic viscosity. A well-suited horizontal capillary viscometer is used. Experimental data from this device allow one to obtain the intrinsic viscosity within a wide range of shear rate. Exploiting this experimental possibility, we studied the intrinsic viscosity as function of maturation temperature, through different thermal histories. In order to visualize predominant mechanisms of chain aggregation in this zone, it is also investigated the inhibition of this process in dilute solutions by using two types of reactants: KSCN and urea. Finally, in order to study the evolution of chain aggregation with maturation time in these zones, specific viscosity measurements were carried out to visualize if chain aggregation in dilute solutions may be considered predominantly bimolecular at relatively short times. Hence, the basic theoretical framework of Smoluchowski aggregation theory is applied to get relevant conclusions concerning the size and number of chain in the clusters as function of time. In regard to the relevance of this subject, it is important to observe that gelatin applications are not limited only to gelling properties. In fact, gelatins are also used as colloid stabilizer, foaming and surface absorbed agent and emulsifier (Ward & Courts, 1977). This branch of gelatin applications is associated with the evolution of chains in rather dilute solutions, becoming relevant the aggregation stability. Apart from these applications, the characterization of gelatins in dilute solution is of interest to understand polyampholyte chain behaviors (see, for example, Dobrynin, Colby, & Rubinstein, 2004; Kudaibergenov, 1999), a subject of research at present.

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2. Materials and methods 2.1. Sample preparation and experiences A commercial gelatin provided by PB Leiner Gelatin (Santa Fe-Argentina) from bovine skin (isoelectric point around 4.8), with a Bloom value of 227 g, a 6.66% w/w standard viscosity at 60 1C of 39 mps was used. The number average molecular weight M n ¼ 133 kDa provided was validated by using PAGE-SDS and computational densitometry. Gelatin solutions with protein concentrations ranging from 10
5 to 10
3 g/cm3 were prepared for specific and intrinsic viscosity determinations. The pH was fixed at 9.8 with NaOH and an ionic strength of I ¼ 110 mM was formulated with NaCl. The ionic strength was high enough to make negligible the effect of contraions on the electrically charged chain expansion, as more dilute solutions were prepared to evaluate the intrinsic viscosity (Tanford, 1961). This value of I also allowed us to neglect the primary electroviscous effects in viscosity calculations (see Section 3.3). Furthermore, the pH selected is far enough from the isoelectric point to assign to each chain a negative net charge providing a stable solution (Herning et al., 1991). The samples were prepared as follows. First the gelatin powder is subject to a hydration step with deionized water at 50 1C for around 10 min. The dissolution of the hydrated powder in a volume of water with NaCl near that required for the final concentrations desired is carried out. Magnetic stirring is supplied for around 40 min. Then the pH is adjusted with NaOH, and the final volume is achieved with the validation of the pH required. Also, 0.02% of sodium azide was added to prevent bacterial degradations during the maturation period. Finally, solutions are filtered and subject to the maturing process at the temperatures fixed for each experience described below. Thus, at the end of the maturation process, the intrinsic viscosity is measured (see Section 2.2) at 25 1C for all the experiences, which are described as follows: Experience 1 (E1): Gelatin solutions at four concentrations required to measure the intrinsic viscosity were matured for 20 h at the following different maturation temperatures: 5, 15, 20, 25, 30 and 35 1C. Experience 2 (E2): Gelatin solutions at four concentrations required to measure the intrinsic viscosity were matured for 20 h at 5 1C. Then the solutions were heated at 50 1C during 1 h prior to the viscometric test. Experience 3 (E3): Gelatin solutions from E2 were rematured again for 20 h at 5 1C. Experience 4 (E4): Gelatin solutions at four concentrations required to measure the intrinsic viscosity were matured for 20 h at 5 1C; in this case the ionic strength of 110 mM was achieved with KSCN only. Experience 5 (E5): Gelatin solutions at four concentrations required to measure the intrinsic viscosity with urea at 5, 20, 50 and 500 mM, were matured for 20 h at 5 1C. Experience 6 (E6): A gelatin solution with concentration 10
3 g/cm3 was matured at 5 1C during 24 h, and the specific viscosity was evaluated at 25 1C for the following

1041

maturation times: 0, 2, 5, 8, 11, 20 and 24 h. This test was also carried out for maturation temperatures of 15, 20 and 25 1C. In this sense, the specific viscosity was measured at a quite low gelatin concentration to get values close enough to the corresponding intrinsic viscosity of the gelatin solutions by keeping also the constraint C4C c to avoid intramolecular helix generation (see also below). Experience 7 (E7): Sodium dodecylsulphate (SDS) was added to a gelatin solution with a protein concentration 10
3 g/cm3, (final SDS concentrations was 6  10
4 M) which was then matured at 15 1C during 24 h. Then the specific viscosity was evaluated at 25 1C for the following maturation times: 0, 2, 5, 8, 11, 20 and 24 h. The surfactant concentration used was well bellow the critical micellar concentration (8  10
3 M) (see also Herning et al., 1991). This experience was carried out in order to test if hydrophobic interactions were also taking place in the chain aggregation phenomenon in the dilute zone. It is relevant to point out here that the average rate of cooling for the most critical situation (maturation at 5 1C for 24 h in E6) was around 3.7 1C/min giving around 12 min for the period of transient decaying temperature, which is around 1% of the total maturation time. Having into account that the gelatin maturation process is slow (see, for instance, Winter and Mours (1997) for a discussion concerning the so-called maturation number) this period of transient temperature is very small compared to the total maturation time of around 24 h to affect appreciably the expected isothermal process. 2.2. Viscometric device and measurement methodology For all experiences we used a horizontal gravitational capillary viscometer and the rheometric theory reported recently by Berli and Deiber (2004). In this apparatus the sample flows through the capillary due to its own weight, and as the sample height in the reservoir falls down a pressure change is generated at the capillary entrance yielding thus a continuous spectrum of shear rate g_ w at the capillary wall. Since the value of the intrinsic viscosity is required, the apparatus was built by placing the capillary horizontally with a counter-pressure reservoir for the sample collection at the outlet, to get thus low values of g_ w . For instance, for a fluid with a viscosity of the order of that of the solvent (water and electrolyte) the range of shear rate achieved was 50o_gw o2500 s
1 . This range is also wide enough to probe the mechanical response of microstructure under different shear rates as discussed below. For the proper evaluation of the viscosity as a function of shear rate the apparatus is placed in a thermostatic bath where a constant temperature is controlled with a precision 70.01 1C. Although a detailed description of the experimental and theoretical aspects are reported elsewhere (Berli & Deiber, 2004) it is relevant to indicate here that the difference in reservoir heads HðtÞ as a function of time t is used to obtain the shear rate at the capillary wall. The apparatus may be used with any fluid model, as it has been shown previously in the literature. In this work, a reservoir

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where r is he fluid density, g is the gravity constant, H o ¼ Hð0Þ and Z ¼ tw =_gw is the Newtonian viscosity in this particular case. Therefore, the best fitting equation of data H versus t defines the type of fluid describing the solution in shear flow. To determine the precision of the experimental technique, 20 independent measurements of water viscosity were carried out and the data were analyzed statistically. We found that the water viscosity value at 25 1C was obtained with a standard deviation of 4.5  10
6 P. The experimental set up was cleaned with a sulfochromic solution to eliminate protein residual, washed with distilled water and 0.01% w/w nonionic detergent to remove undesired fat and contaminants. Then two washing steps with deionized water followed before the evaluations of H versus t was carried out, at each experimental run. Each test was repeated three times. For the processing of E experimental data, the fitting relative error e is evaluated as follows:  E  exp 1X H ðti Þ
Hðti Þ  e¼ (2) , E i¼1  H exp ðti Þ where ti are the time values at which measurements of the sample height H exp ðti Þ are carried out, while Hðti Þ is the theoretical sample height obtained at ti for any fluid model considered. For instance, Hðti Þ from Eq. (1) is required to verify if the gelatin solution is Newtonian. In this regard one should observe that dilute solutions of macromolecules might present significant shear thinning (see, for instance, Fox, Fox, & Flory, 1951; Privalov, Serdyuk, & Tiktopulo, 1971; Tanford, 1961). Then, the intrinsic viscosity [Z] at a given shear rate is calculated from both Huggins and Kraemer equations (see, for example, Bohdanecky´ & Kova´r˘ , 1982). In this process, we define the specific viscosity Zsp ¼ ðZ
Zs Þ=Zs , where Zs is the solvent viscosity, and also evaluate the Huggins parameter k1 , representing a measure of chains interaction (Bohdanecky´ & Kova´r˘ , 1982; Flickinger, Dairanieh, & Zukoski, 1999) and its counterpart constant k2 from Kraemer equation for discussion of experimental results below. Further, k1 and k2 satisfy the constrain k1 þ k2  1=2.

shear rate range comprised between 50 and 2800 s
1. Thus all the experimental data obtained as H versus t were fitted with Eq. (1) in this range. Fig. 1 illustrates a typical example of experimental data fitted with Eq. (1) giving e ¼ 0:019; the corresponding linear square regression coefficient was r2 X0:999. Also in this figure the value of shear rate achieved at each time is indicated through a dashed line. This response is satisfied for all the experiences carried out in the dilute zone for different maturation times, temperatures and added chemicals. Therefore, one expects that the microstructure associated with dilute solutions be composed of both single chains and aggregates of rather symmetric conformations (no pseudoplastic effects were found even for this shear rate range). In this sense, it is well known that for no spherical structures (for instance, rod-like structures) one should expect to find pseudoplastic effects. Although the apparatus used here did not allow us to get values of shear rate lower than 50 s
1, the shear rates measured are significantly lower than those obtained from vertical capillary viscometers frequently used in practice, which provide viscosity values within the approximate range of 1000–3000 s
1. Experimental data of intrinsic viscosity [Z] reported throughout this work are found to be independent from shear rate in the specified range achieved experimentally. 3.2. Intrinsic viscosity After having a Newtonian response of dilute gelatin solutions in the experimental shear rate range for C c oCoC g and ToT ng , one procedure to evaluate the microstructure size and to infer possible chain conformations is to quantify the intrinsic viscosity in this low

2800

0.0

2400

-0.5

2000

-1.0

1600

-1.5 -2.0

1200

ln (H/Ho)

radius Ro ¼ 1 cm, a capillary radius Rc ¼ 0:03724 cm and a capillary length L ¼ 10:048 cm were used. In particular for Newtonian fluids one obtains,
H ¼ H o expð
trgR4c 4ZLR2o Þ, (1)


W

1042

-2.5

800

3. Results and discussion

-3.0

As indicated in the Introduction section, following we analyze our experimental results for two concentration zones, C c oCoC g and CoC c , while ToT ng . 3.1. Apparent viscosity For the dilute zone, C c oCoC g and ToT g , we found that gelatin solutions behaved as Newtonian fluids in the n

400 -3.5 0 0

100

200

300

400 t (s)

500

600

700

Fig. 1. Newtonian behavior of a gelatin solution with concentration 10
3 g/cm3. The thermal history belongs to E1 at 25 1C. Symbols (K) refer to experimental values and the solid line is evaluated with Eq. (1). The dash line shows the variation of shear rate during the quasi-steady flow.

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Table 1 Intrinsic viscosity [Z] and coefficients k1 and k2 of dilute gelatin solutions for pH ¼ 9.8 and I ¼ 110 mM, obtained through the fitting of experimental data with Huggins and Kraemer equations Tm (1C)

E1

E2 E3 E4 E5

5 15 25 30 35 5 5 5 5 5 5 5

Urea (mM)

5 20 50 500

[Z] (cm3 g
1) (Huggins)

[Z](cm3 g
1) (Kraemer)

k1

k2

116.2 92.6 62.6 59.5 56.8 56.5 110.3 77.7 94.3 84.6 85.7 85.8

115.5 92.3 62.4 59.2 56.7 56.4 110.0 77.3 94.1 84.5 85.5 85.5

0.22 0.23 0.14 0.031 0.14 0.13 0.28 0.11 0.33 0.33 0.29 0.22

0.23 0.23 0.31 0.44 0.32 0.32 0.20 0.31 0.17 0.15 0.19 0.23

concentration range. In Table 1 a summary of the intrinsic viscosity values obtained are reported. One observes that the maturation temperature has a significant effect on these results. Thus the average lower value obtained ½Z ffi 56:5 cm3 =g belongs to E2 where all the possible chain aggregations during a maturation of 20 h at 5 1C were disaggregated by heating the solution at 50 1C during 1 h prior to carrying out the tests. This state could be achieved only for a temperature heating substantially greater than T ng . It is relevant to indicate that the intrinsic viscosity values obtained are of the order of magnitude expected (see, for instance, Boedtker & Doty, 1954; Bohidar & Jena, 1994; Haug et al., 2004; Joly Duhamel et al., 2002). Since k1 is related to solvent–particle and to particle–particle interactions in general, one finds that the values of k1 reported in Table 1 indicate that these interactions decrease substantially as the maturation temperature approaches T ng by generating smaller units in size. This result also shows that the coil–helix transition is diminished or eventually terminated at around 30 1C. Since k1 increases again above 30 1C, one should expect a higher and different interaction between chains above T ng (for instance, hydrodynamic interaction effects are recovered), where the basic hydrodynamic units are under more intense Brownian movement proportional to kB T m , and probably do not contain triple helixes any more. This result is consistent with the value T ng ffi 26 o C for the same gelatin sample, estimated from Braidot and Deiber (1999). Although it is not possible at present to provide an additional theoretical explanation (see Bohdanecky´ & Kova´r˘ , 1982), this result was verified through experimental reproducibility. It is clear that the increase of the intrinsic viscosity for lower values of maturing temperature (see Table 1) should be associated to the triple helix aggregation of chains, despite CoC g ; thus the hydrodynamic volume occupied by these aggregates is higher than that corresponding to E2. This result is clearly reflected in the increase of k1 for matured gelatin solution at lower T m . Further, through E3 one concludes that the aggregation process is thermally reversible because the

value of the intrinsic viscosity found in E1 at 5 1C was practically reproduced. For the purpose of verifying this aggregation phenomenon, hydrogen bonds inhibitors were used in E4 and E5. Thus, KSCN and urea were found to inhibit the aggregation process because the intrinsic viscosity values obtained were lower than those values of the equivalent experimental situation without inhibitors, but still greater than the value obtained in experience E2 (see Table 1). Thus in E4 the inhibition process was partially achieved, and a concentration of 110 mM KSCN allowed gelatin chains to evolve to a small aggregation only. From E5, it is observed that the intrinsic viscosity decreases as urea concentration is increased. For urea concentrations greater than 20 mM a constant value of intrinsic viscosity of around 85 cm3/g is obtained (Table 1). These results suggest that the effect of inhibition process is saturated at urea concentrations greater than 20 mM; thus the intrinsic viscosity value obtained at this stage is still greater than that found in E2. In this regard, Boedtker and Doty (1954) obtained intrinsic viscosity values of gelatin solutions at 40.2 1C and found similar results in presence of urea 9 M (quite above the saturation value). These authors also reported that chains presented an expansion giving a greater value of intrinsic viscosity. Therefore, one may infer that the same expansion phenomenon may be present in E5 when urea concentration surpasses 20 mM. Thus, one expects that urea does not allow the stabilization of the triple helix formations in the aggregation process for CoC g . The molecular basis for urea ability to denature a given protein (or to inhibit the secondary structure) remains under research (Bennion & Daggett, 2003). In Fig. 2 the specific viscosity is plotted as a function of the maturation time (see also E6 for experimental details). Experimental results show that Zsp increases linearly with tm giving a linear square regression coefficient greater than 0.98. Through E7, it was possible to observe that specific viscosity values as function of maturation time were the same as those reported in Fig. 2 (identical thermal

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0.15 0.14 0.13 0.12

sp

0.11 0.10 0.09 0.08 0.07 0.06 0.05

0

5

10

15 tm (h)

20

25

30

Fig. 2. Specific viscosity Zsp as a function of maturation time tm for E6 at 5 1C (+), 15 1C (’), 20 1C (.) and 25 1C (K).

conditions in the absence of surfactant). These results suggest that hydrophobic interactions are not responsible for chain aggregation in the ‘‘cool dilute solution’’ (see also Herning et al. (1991), where it was reported that hydrophobic interactions are possibly causing chain aggregation when the different zone CoC g and T4T ng is considered; i.e., for the ‘‘hot dilute solution’’). Thus, we may conclude that in the dilute zone (below the gelling zone), clusters are formed through chain aggregation involving triple helix physical bonds. 3.3. Exploring the application of Smoluchowski theory to the aggregation of gelatin chains in the dilute zone It is appropriate to indicate here that at the initiation of maturation, values of Zsp/C are close to [Z] as obtained from E2 (Table 1), in the four experiences described in E6 (Fig. 2). Thus, the difference between them is not greater than around 0.41%. This result shows that for a gelatin concentration 10
3 g/cm3 used in E6, the macromolecules are not associated at the beginning of the maturation process. This concentration is low enough to get viscosity values near the intrinsic viscosity, but still high enough to avoid the very dilute zone (CoC c ). Following our previous discussion in the Introduction section, for a gelatin concentration range 10
3–10
4 g/cm3, the nucleus formation may be considered predominantly bimolecular. This association mechanism can be adopted as valid for the maturation process imposed in E1–E6. In addition, as the nucleus formation is the controlling kinetic step (Busnel et al., 1989; Harrington & von Hippel, 1961), one infers that the aggregation phenomenon of gelatin

chains may be interpreted, as a first approximation, through the classical Smoluchowski theory, to explore the validity of several basic mechanisms associated with the aggregation process in dilute solution. The application of this theory to gelatin chains is based on the Flory–Fox model designated ‘‘equivalent sphere’’ or ‘‘pseudospherical particle’’ for flexible chains with occluded solvent (Flory, 1969; Tanford, 1961). For this purpose two aspects are relevant: (a) gelatin polypeptide chains are on the average at least higher than around 200 for the sample studied here and (b) a high salt concentration (I ¼ 110 mM) to screen electrical charges is used. Following previous studies, it is considered that gelatin chains in the dilute solution are random coils initially, and then suffer a partial conversion by parts to the poly-L-prolyne helix conformation when the temperature is sufficiently low. This theoretical framework is described in terms of fractions of aggregates having each one k molecules with an equivalent radius ak (pseudo-spherical radius). The growing process is controlled by the rate of collision of pair of aggregates (see for instance Russel, Saville, & Schowalter, 1989) where ni and nj are the number densities of aggregates having i and j molecules, respectively, and W ij is the corresponding colloid stability ratio. In this process the initial condition is n1 ð0Þ ¼ n0 , and nk ð0Þ ¼ 0 for kX1. Here n0 is the initial number density of chains. An analytical solution of this problem is available by assuming (a) a collision is carried out between pair of aggregates of near equal size, and (b) the stability ratio is independent on the size of aggregates yielding W ij ¼ W . Therefore, with hypothesis (a) and (b), one gets,
n0 ðtm tp Þk
1 nk ¼ , (3)
ð1 þ tm tp Þkþ1 where the characteristic time is tp ¼ 3Zs W =4n0 kB T. Then, the total number of aggregates per unit volume ntot ¼ P 1 i¼1 ni is used to define the average number of molecules per aggregate N ¼ n0 =ntot at maturation time tm ; thus, one finds N ¼ 1 þ tm =tp . In this expression the characteristic time may be also expressed tp ¼ 1=ka n0 , where ka ¼ 4kB T=3Zs W ¼ kd =W is the rate constant of aggregation and kd is the rate constant of the diffusion limited aggregation (Hunter, 1992). It is well known that for rapid aggregation W ¼ 1 and ka ¼ kd . On the other hand, when an energetic barrier is present in the interaction of the kinematical units, the frequency of collision between them yields ka akd with W41. In addition, N may be related to the viscosity of dilute solutions of gelatin chains through Zsp ¼ bfa , where fa is the effective volumetric fraction of the discrete phase in the aggregate state and b is the particle shape factor, which for a pseudo-spherical particle is around 2.5. One also needs a relation between fa and the initial chain volumetric fraction f of single chains, expressed f ¼ ð4=3Þpa3 CððN A Þ=ðM n ÞÞ, where N A is the Avogadro number and a is the initial average radius of the pseudo-sphere formed by

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 N¼

 Zsp f =ð3
f Þ tm ¼1þ . bf tp

(4)

In this sense, an iterative procedure was carried out by giving different values of f in Eq. (4) to obtain values of N as function of maturation time tm . Then, tp was evaluated through Eq. (4) with the best linear square regression coefficient obtained in the iterative process; this result is shown in Fig. 3. Since n0 ¼ CN A =M n ¼ 4:53 1015 chains=cm3 , we are able to report in Table 2 values of f, tp , ka and W; the linear square regression coefficients for each temperature are also provided. Following the evolution of ka or tp , one observes in Table 2 that the rate of aggregation increases as the temperature decreases. In this sense, W increases with T m , consistently. These results validate quantitatively that lower temperatures promote gelatin chain aggregation in the dilute zone. From the high values of W reported in Table 2, one also concludes that the slow aggregation rate regime applies for all maturation temperatures. In addition, for 5, 15 and 20 1C the fractal dimensions are rather low. These values probably indicate that the nucleation phenomenon promoted at low temperatures yields disordered aggregates occluding a high amount of solvent. This situation changes for 25 1C where the fractal dimension is f ¼ 2:43. Thus, at higher temperatures (T m closer to T ng ) one expects to find simultaneous

3.5

3.0

2.5 N=no/ntot

coils in the sample, having into account that this biopolymer is also polydisperse. In this sense, within the framework of the theory used here, it is assumed that chains aggregate in the dilute regime by forming fractal structures at maturation temperatures below T ng . Thus these aggregates constitute clusters occluding solvent. Therefore, N is related to the fractal dimension f p3 through N ¼ ðR=aÞf (Russel et al., 1989), where R is the average radius of the aggregate population at a given maturation time. It is appropriate to indicate that f depends on the rate of aggregation. For instance, for high rates f ¼ 1:75 while for low rates f ¼ 222:2. For further use below, one also observes that secondary kinetic processes may produce a rearrangement of the internal structure of aggregates by removing occluded solvent, what gives a more compact structure. The consequence of this mechanism is a value of f closer to 3 (Russel et al., 1989). For this purpose, one uses the number average molecular weight M n . Consequently, a may be estimated from the experimental value obtained for ½Z ¼ ðb4pa3 N A =3M n Þ (Tanford, 1961) through E2. It was found a ffi 106 A˚. Therefore, within this framework, the effective volumetric fraction of aggregate fa ¼ f N ð3
f Þ=f is defined on the average to obtain N ¼ ðZsp =b fÞf =ð3
f Þ . The value of the initial chain volumetric fraction may be estimated from f ¼ Zsp =b at tm ¼0, when aggregates are absent in the solution. Thus, it was found f ¼ 0:023 for C ¼ 10
3 g=cm3 . In order to evaluate parameter tp at each maturation temperature, the value of f is required in the following expression:

1045

2.0

1.5

1.0

0

5

10

15

20

25

tm (h) Fig. 3. Average number of gelatin molecules per aggregate N as a function of maturation time tm for E6 at 5 1C (+), 15 1C (’), 20 1C (.) and 25 1C (K).

nucleation and growing of junction zones (see Harrington & Karr, 1970; Harrington & Rao, 1970) thus generating more compact fractal structure. It is also possible to observe that for 25 1C the linear square regression coefficient r2 is around 0.84, which is a rather lower value than those for the lower temperatures. This result is probably due to the fact that the aggregation model is based on the bimolecular triple helix nucleus formation as basic mechanism of doublet generation, and at this temperature, the growing process is becoming also relevant. These conclusions are consistent with those obtained by Harrington and Karr (1970) through optical rotational measurement of dilute gelatin solutions in the sense that at higher temperature the growing process is substantially enhanced. It is also relevant to evaluate the aggregate size distribution Sk ¼ knk =n0 . Since the number k of molecules per aggregate with radius ak satisfies k ¼ Afk with Ak ¼ ak =a (Russel et al., 1989), it is then clear that Sk may be expressed through the dimensionless time tm =tp ; thus, from Eq. (3), one obtains, kn0 ðtm =tp Þk
1 . (5)
n0 ð1 þ tm tp Þkþ1 P Eq. (5) satisfies 1 k¼1 S k ¼ 1. Fig. 4 shows the variation of S k as function of k for different maturation times obtained for E6 at 5 1C. It is observed that S k tends to be highly polydisperse with a Gaussian-like shape as the maturation time increases from 20 to 24 h. Here, one can estimate the average number ok4 at each maturation Sk ¼

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Table 2 Fractal dimension f, characteristic time tp , kinetic aggregation constant ka stability factor W and linear square regression coefficient r2 obtained through Smoluchowski aggregation theory applied to experimental data from E6 Tm (1C)

F

tp (h)

ka (cm3 seg
1)

W

r2

5 15 20 25

1.79 1.79 1.82 2.43

10.8 18.7 26.5 60.2

5.7  10
21 3.3  10
21 2.3  10
21 1.0  10
21

5.8  108 1.4  109 2.3  109 6.0  109

0.99 0.99 0.98 0.84

280

0.7

260

0.6

240 0.5 220

Sk

R (Å)

0.4

200 180

0.3

160 0.2 140 0.1

120 100

0.0 1

4

7

10

13

16

k

0

5

10

15 Tm (°C)

20

25

30

Fig. 4. Aggregate size distribution Sk as a function of the number of gelatin molecules per aggregate k for E6 at 5 1C. The maturation times are: 2 h ð
 
Þ, 10 h ð


Þ, 20 h ð     Þ and 24 h (—).

Fig. 5. Average radius of aggregate population R as a function of maturation temperature T m from E6. The maturation times are: 2 h (J), 5 h (m), 8 h (,), 11 h (K), 20 h (&) and 24 h (’).

time corresponding approximately to the peak of Sk . The average radius of aggregates in the solution at a given P maturation time and temperature is R ¼ 1 k¼1 S k ak . Fig. 5 shows the evaluation of R as a function of maturation temperature, while the maturation time is kept constant. Thus the sample average radius decreases linearly with increments of the maturation temperature within the range of the experiments carried out in this work, which is clearly a consequence of the formation of more compact aggregates at high T m . After the evaluation of the stability factor reported in Table 2, it is relevant to carry out an estimation of the energy barrier associated with the aggregation of gelatin chains in the dilute regime involving long-range forces. For this purpose, W is expressed through the total interaction energy between pair of particles U T ðhÞ (Russel et al., 1989), including also the hydrodynamic correction factor GðhÞ reported by Hunter (1992), where h is the surface–surface distance between particles. For a rough estimation of U T ðhÞ, one observes that gelatin chains are negatively charged at pH ¼ 9.8. Thus, these chains are predominantly

hydrophilic, and hydration generates a repulsive force between pair of particles (Berli, Deiber, & An˜o´n, 1999a, b). In this theoretical context, and with the approximation that chains are spherical kinematical units, U T ðhÞ may be expressed as the sum of the repulsive electrostatic potential U R (for ka410, where k is the inverse Debye length), the attractive van der Waals potential U A and the repulsive structural potential U S . For this purpose the particle potential estimated is around 10 mV by considering that a gelatin chain for the sample average molecular weight has a wild net charge number of around 75 (see also, Piaggio, Peirotti, & Deiber, 2005) and the initial average particle radius is approximately 106 A˚, as established above. The required Hamaker constant is around 10kB T for water– protein systems (Coen, Blanch, & Prausnitz, 1995). Also it is considered that U S decreases exponentially with a characteristic length of around 1 nm (Berli et al., 1999b), and the associated free energy DG measuring the degree of hydrophilicity/hydrophobicity between two gelatin chains in water must be determined to meet the value of W obtained in Table 2. Our calculations show that the pair

ARTICLE IN PRESS M.L. Olivares et al. / Food Hydrocolloids 20 (2006) 1039–1049 Table 3 Free energy DG for the non-DLVO particle interaction for different temperatures of E6 DGðmJ m
2 Þ

5 15 20 25

10.5 11.2 11.6 11.9

0.014 0.012 0.010

sp

Tm (1C)

1047

0.008 0.006

interaction potential energies normalized with the Brownian thermal energy kB T as a function of distance h=a presents a barrier of around 25kB T, which is controlling the aggregation process. Table 3 also presents values of DG that satisfy the values of W obtained from E6 and reported in Table 2. Thus, DG has the order of magnitude expected (see, for instance, Israelachvili, 1992). These values show that as maturation temperature decreases, DG is lower, and hence the aggregation process is significantly favored. In this context, one also observes that, in the aggregation phenomenon, the poly-L-proline helix transition is present by forming intermolecular triple helix nucleus. This conformational change during the coil–helix transition possibly induces a reorganization of water molecules around particles favoring the decrease of the structural repulsion force (see, for instance, Fennema, 1997), which is the main potential barrier impeding the aggregation process. Before ending this section, it is appropriate to indicate here that the primary electroviscous effect was found to be negligible for the gelatin chains studied here, when I ¼ 110 mM and pH ¼ 9.8. For this purpose the approximate Booth theory was used (see also, Yamanaka, Ise, Miyoshi, & Yamaguchi, 1995).

0.004 0.002

20

40

60

80

100 tm (h)

120

140

160

180

Fig. 6. Specific viscosity Zsp as a function of maturation time tm of a gelatin solution with a concentration 10
5 g/cm3 and a maturation temperature of 25 1C. Full lines are placed for illustration purposes only.

were obtained (tp of the order of 4  10
4 h, corresponding to Wo1) which were inadmissible having into account the small increments of specific viscosity during such a long maturation period before stabilization, indicating a very slow process. Thus, this process is not aggregative. From these results one may also infer that intramolecular triple helix formation is the basic phenomenon, where gelatin chains evolve to a more compact structure as was suggested previously (Busnel et al., 1989; Harrington & Karr, 1970; Harrington & Rao, 1970). 4. Conclusions

3.4. The very dilute zone In order to analyze the evolution of gelatin chains when the concentration is much less than C c (the very dilute regime), a gelatin solution of 10
5 g/cm3 was matured at 25 1C during 168 h (7 days). This value of T m is near T ng , and hence, appropriate to promote the formation of rigid rod-like macromolecules (Harrington & Rao, 1970). The specific viscosity values showed relatively small increments during the maturation time (Fig. 6). Appreciable differences with the solvent viscosity were obtained only after 24 h, and the solution viscosity became constant after 72 h of maturation. This last result indicates that the chain evolution in this very dilute range is quite different from that associated with chain aggregation in the zone C c oCoC g and ToT ng . Thus, after around 72 h a definite microstructure is achieved, which may only be explained through the intramolecular folding process of individual chains. Furthermore, when experimental data in the zone CoC c and ToT ng were interpreted through the Smoluchowski aggregation theory, very low values of tp and W

The results obtained show that for C c oCoC g the maturation temperature affects the intrinsic viscosity value due to the thermo reversible aggregation of gelatin chains forming clusters when the maturation temperature is below a critical value. Experimental results with SDS indicated that hydrophobic interactions are not responsible of chain aggregations in the cool dilute solution. Urea and KSCN inhibited the aggregation process giving intrinsic viscosity values lower than those obtained with the same solution without inhibitor agents. For urea concentrations greater than 20 mM, a constant value of intrinsic viscosity greater than that of the un-matured solution is obtained. In the dilute zone, the cluster formation process may be interpreted through Smoluchowski aggregation theory, consistently with experimental data. It is found that this process produces polydisperse clusters as maturation time increases. At lower temperatures the aggregates are more disordered and occlude significant amounts of solvent. On the other hand, at higher temperatures the clusters are more compact. Through the evaluation of the stability

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ratio, it is shown that the aggregation process is very slow in the dilute zone due to an energetic barrier of around 25kB T, and also that the possibility of significant aggregation in the very dilute zone must be excluded. Finally, it is clear that relevant conclusions may be achieved concerning the evolving dilute and very dilute gelatin solutions when a macroscopic probe, like the evaluation of intrinsic viscosity, is used. Although results obtained here contribute to understand better the aggregation of chains in the dilute zone, further research is still required by using, in addition, experimental probing involving smaller scales.

Acknowledgments Authors wish to thank the financial aid received from Universidad Nacional del Litoral, Santa Fe, Argentina (CAI+D 2002), SEPCYT-FONCYT (PICT 09-09752) and CONICET (PIP 02554).

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