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Inhomogeneous fine-stranded β-lactoglobulin gels
Food Hydrocolloids Vol.6 no.5 pp.455-470. 1992
Inhomogeneous fine-stranded 13-lactoglobulin gels Mats Sta ding, Maud Langton and Ann e-Marie Herm ansson SI K- The Swe dish Institute fo r Food Research, PO Box 5401, S-40229 Goteborg, Swe den Abst ract. Inh om ogene ities occur in the network of fine-stranded 13-lactog lobu lin gels. The y have been character ized by electro n microsco py a nd their intlu ence o n the rheologic al pro pe rties at sma ll defor mation s measured. The inhomoge neities occ urred as de nse a nd loose region s in the netwo rk a nd their forma tio n depend ed o n the heat ing rate durin g ge l form at ion (O.0 I7- 12°Clmin) at pH 7.5 or on pH if close to where the network structure shifts from fine-stra nded to particula te (pH 5.86.5) . An inho moge neo us microstructur e was formed a t pH 7.5 with a slow heati ng rate , where as the network was homogene ous after fast heat ing. Th ese homogeneous gels had higher G' than the inhomoge neo us ge ls . In add ition the character , as expressed by the freq uency de pendence , changed from strong homogeneous gels to weaker, mor e frequency-d ep en dent inh om ogen eous gels. Th e formati on of the inhomogeneities was mon itored at the slowest heat ing rat e by measuring G' during gelation . G ' showed a maximu m around 70°C , indicating a sep aration int o polymer-rich and polym er-p oor regions in the network . Electron microscopy showed a tra nsient, homogeneous network befor e the separation . Both types of inhomogeneous gels had broken frequency curves, i.e . G '/ had two slopes. which were cause d by different relaxation times in the den se and loose region s. Re laxation measur ements of the inhom oge neou s gels showed relaxation time spec tra with two peak s. A model was used to con firm that a broken fre quency curve may be caused by two peaks in the relaxat ion time spectru m.
Introduction Gels consist of a solid net work interspersed by a fluid , which is water in the case of biop olymer gels. The network is thr ee-dim ension al with strands forming a porous and almost solid materi al , eve n though the solid conte nt may be only fractions of a percent. The scale of the network as expresse d by pore size or persisten ce length varies between different gels. The stra nds may be built up by anything from mole cules to colloida l parti cles. The network is usually regarded as homogeneous when viewed on a scale sufficientl y larger than a typical size of the network . Some net works do , however , show inhomogeneities of some kind. Parts of the network may , for exampl e, be den ser , i.e. have smaller pores than the rest of the network , see Figure 1. Porisometry and scattering measurements on synthetic gels have given pore rad ii in the range 10-7500 nm in a styre ne-divinylbenzene gel and 0.25-250 nm in polyacrylamide gels (1,2). A broad distribution of pore sizes does not necessarily lead to inhomogeneities. It could also result in a network structure with a wide but uniform pore-size distribution throughout the sampl e . Inh om ogeneities have been defin ed by Burch ard as 'a sudden change of a property when passing from one point in space to another' (3). Thi s not only includes microstructural inhomogen eit ies but also other properties such as refractive index , optic al density and scattering properti es, wh ich are prob ably, but not necessaril y, caused by microstru ctural inhomogeneities. In this art icle, we will conside r onl y microstru ctural inho moge neities, i.e. 455
M.Stading, M.Langton and A.-M.Hermansson
Fig. l. Schematic example of an inhomogeneous network.
different regions of the network having different structures. Inhomogeneity may be due to different pore sizes, but there could also be different types of strands or different types of cross-links. There are different explanations for the formation of inhomogeneous networks. Inhomogeneities are either inherent in the formation mechanism or occur after the gel is formed. Kuhn pointed out as early as 35 years ago that gels prepared in the presence of a swelling medium almost necessarily have to be inhomogeneous (4). Bastide and Leibler have theoretically demonstrated this by assuming a site percolation model for network formation (5). Inhomogeneities were formed when the gel swelled because the percolation clusters forming the network did not swell as much as the rest of the gel. The same phenomenon occurs in a stretched gel. The theory was tested by neutron scattering experiments which showed that the expansion of the gel was heterogeneous (68). The scattering of the stretched gels also showed abnormal butterfly patterns for strain E > 0.28, which were directly attributed to the inhomogeneous network structure. A theoretical network of rigid rods has also been shown to contain large density fluctuations in the equilibrium swollen state (9). Inhomogeneities can also occur when the gel-forming material is not stable in the final gel. A cold-setting polymer may, for instance, be stable in solution at high temperatures, whereas it tends to precipitate at lower temperatures. If gelation occurs before precipitation the elastic network will prevent precipitation, but if the force to separate is strong enough, the network may separate into polymer-rich and polymer-poor regions. This phenomenon has been called micro phase separation (10) or microsyneresis (1,11). Galina et at. defined micro syneresis as a local phase separation not followed by a relaxation of the whole system (1). Another condition resulting in an inhomogeneous network has been reported for the gelation of agarose and was then referred to as spinodal decomposition (12-16). The spinodal decomposition occurred before gelation and was observed by a peak in the apparent viscosity. A distinct peak in the storage modulus, G', was observed for K-carrageenan in the presence of potassium ions (17,18). K-Carrageenan forms a gel on cooling and at the peak a fine network was found in which the cross-links appeared to be
456
Inhomogeneous 13-lactoglobulin gels
formed by double helices. When the temperature was lowered further the network became coarser, because the helices aggregated into stiff superstrands which formed the final network. Myosin gels also show a peak in the storage modulus during gelation (19). The maximum in G' became less pronounced when the heating rate was increased from 0.1 to 2SC/min. Hermansson has found phase separation in both blood plasma gels and whey protein gels (20-23). Both systems are mixtures of proteins and form gels on heating. The degree of phase separation increased with heating temperature above the gelation temperature, i.e. the gels which were heated to 95°C were more phase-separated than the gels that were heated to 75°C. The phase separation led to an inhomogeneous network structure and impaired water holding was measured. Addition of sodium chloride also led to increased phase separation (23). I3-Lactoglobulin has been used as a model system in this study because it forms inhomogeneous network structures depending on heating rate and pH. It is heatsetting and forms different gel structures depending on pH: a particulate network at intermediate pH (4-6) and a fine-stranded network below and above this interval (24-26). Langton and Hermansson have reported inhomogeneities at the shift between these two types (26). Electron micrographs showed that 13lactoglobulin forms an inhomogeneous microstructure in a narrow interval at the upper shift around pH 6. The network was homogeneous at pH 6.5 but began to show inhomogeneity when pH was decreased to 6.3. At pH 6.05 there were large density fluctuations in the network and at pH 6.0 the network shifted to a particulate state. At the lower shift around pH 4, the network was mixed rather than inhomogeneous and the pH interval was broader. The network consisted of a mixture of particulate and fine-stranded microstructures. Mulvihill et al. observed the same behaviour in 13-lactoglobulin gels at pH 8.0 on addition of NaCI (27). The network was homogeneous and fine-stranded for 0.05 mol/drn", inhomogeneous for 0.20 mol/drrr' and particulate for 1.0 mol/drrr'. The large deformation properties were maximal at 0.20 rnol/drrr'. This paper will show the microstructure of inhomogeneous fine-stranded gels of 13-lactoglobulin as revealed by electron microscopy. The rheological effects of the inhomogeneities will be demonstrated and explained.
Material and methods
Material The 13-lactoglobulin powder was obtained from the Sigma Chemical Co. (St Louis, MO) (L-0130, lot no. 98F8030 and 106F8120). For details of the 13lactoglobulin powder, see references 24 and 25.
Sample preparation and heat treatment The 13-lactoglobulin was dissolved in degassed, distilled, water and pH was adjusted with :::;1 mol/dm' HCI or :::;1 mol/drrr' KOH. The samples were then 457
M.Stading, M.Langton and A.·M.Hermansson
heated at a controlled heating rate of between 0.017°C/min (1°C/h) and 5°C/min from 30 to 90°e. Some samples were also put directly in a water bath at 90°C, which corresponds to an average heating rate of ~ 12°C/min. The samples were kept at 90°C for 1 h and then cooled at the fastest cooling rate to 20°C, at which they were kept for 30 min. The slowest heating rate gave the same rheological results as when heating the sample first to 70°C at 1°C/min, keeping it at 70°C for 10 h, and then raising the temperature to 900 e at 1°C/min. The latter heating was therefore treated as equivalent to the 0.017°C/min heating rate and was sometimes used to avoid microbial growth. The ~-lactoglobulin concentrations referred to in this paper are given in weight percent (w/w). Experimental techniques Microscopy. After the heat treatment small cubes of the gel, 1 x 1 x 1 mm, were cut out and prepared for transmission electron microscopy (TEM) using the following procedure: the sample was immersed in 2% v/v glutaraldehyde with 0.1 % w/v ruthenium red for 60 min at 8°C, washed 2 x 10 min at 8°C followed by 2% w/v OS04 for 120 min at 8°C. The samples were then rinsed for 3 x 10 min in 0.025 mol/dm' KCl solution before being dehydrated in a graded ethanol series, 50, 70, 95 and 99.5% v/v. To prevent osmotic effects, 0.025 moll drrr' KCl was added to the fixative and washing solutions. The samples were transferred to propylene oxide after dehydration and were then embedded in Polybed (Polyscience Inc.). Thin sections (~60 nm) were cut on a diamondknife and were double-stained with uranyl acetate and lead citrate. The sections were examined in a transmission electron microscope (Jeol 100 eX-II, Jeol Ltd, Tokyo, Japan), at an acceleration voltage of 80 kV. Dynamic measurements. A ~-lactoglobulin solution of 2.5 ml was heated in the measuring cup of a Bohlin VOR Rheometer. A thin layer of paraffin oil was applied on top of the sample to avoid evaporation, and a couette type cup and bob measuring system (DIN 53019) with an inner cylinder diameter of 14 mm was used. The bob was suspended in an interchangeable torsion bar with momentums at maximum deflection of between 3 x 10- 5 and 2 x 10- 3 Nm. The frequency was 1 Hz when temperture was the independent variable and during the frequency sweep 0.001-5 Hz. As ~-lactoglobulin is strain-sensitive during gelation, the strain was kept as low as 4-10 x 10- 4 so as not to disturb the process (24). This was well within the linear region. The sample was oscillated only when recording G *. The cup holder of the rheometer was modified to reduce axial deformations caused by thermal elongation of the cup holder (24). Relaxation. The relaxation was performed at 20°C after the heat treatment. A step strain of 8 x 10- 4 was applied to the sample during a strain rise time of 0.8 S. The relaxation modulus G was then monitored as a function of time, and the relaxation time spectrum H(T) was calculated by the Bohlin VOR software using Alfrey's approximation (28). The H(T) inversion by Alfrey's approxi-
458
Inhomogeneous 13-lactoglobulin gels
mation is slightly dependent on how the relaxation curve is filtered. All curves were therefore identically filtered. Results and discussion
Inhomogeneous networks were formed both at pH 7.5 as an effect of the heating rate during gelation and at the microstructural shift from fine-stranded to particulate networks at ~pH 6. The microstructure of the gels in this transition region has been characterized earlier by electron microscopy (26). Microstructure
The kinetic effects on microstructure were studied at four different heating rates at pH 7.5: 12, 1, 0.1 and O.017°C/min, and at three concentrations: 12, 13 and 14.6%. The microstructures formed at the two extreme heating rates, the fastest and the slowest, are demonstrated in Figure 2a,c and b.d respectively. Figure 2a shows a homogeneous network of evenly thick strands formed at the fastest heating rate at 13% concentration, whereas Figure 2b shows an inhomogeneous network, with small and large pores, formed at the slowest heating rate at the same concentration. At 14.6% and the fastest heating rate, the network was also homogeneous but very dense, and the strands ~ere difficult to observe separately. At slow heating rates, both regions with large pores and regions with small pores were formed, resulting in an inhomogeneous network, cf. Figure 2c and d. See also Figure 3, which is a schematic drawing of the microstructure formed at the different heating rates. The inhomogeneities formed at slow heating rates were not as coarse as those formed at the structural shift around pH 6, which indicates that the electrostatic forces influence the structure more than the kinetics of gelation (26). Figure 4 shows the microstructure of 13-lactoglobulin gels formed at the lowest concentration, 12%. The network formed at the fastest heating rate was also homogeneous at this concentration (Figure 4a) and was composed of long and distinct strands with relatively long distances between the cross-links. The microstructure resembled a snapshot of a concentrated polymer solution. Decreasing the concentration from 14.6 to 12% did not influence the homogeneity of the homogeneous networks, but the distance between crosslinks became longer. Figure 3a schematically presents the homogeneous network structure shown in the two micrographs Figures 2a and 4a. When the heating rate was decreased to 1°C/min or slower, the strands appeared to be formed by a different mode of aggregation' than at the fastest heating rate, cf. Figure 4a,b and c. This is also schematically shown in Figure 3b. The gels formed at 1 and 0.1DC/min had somewhat shorter and thicker strands, which were not as distinct as the strands formed at the fastest heating rate. The micrographs showed a network constructed of numerous small meshes of thick strands. In addition, an incipient inhomogeneity with some large pores appeared. The cross-links appeared weaker from a microscopical point of view, and even broken in some regions, which accounts for the incipient inhomogeneities. 459
M.Stading. M.Langton and A.·M.Hermansson
2a
2b
2c
2d
Fig. 2. Micrographs of [3-lactoglobulin gels formed at pH 7.5 at different heating rates and concentrations: (a) homogeneous microstructure. 12°Clmin, 13%; (b) inhomogeneous microstructure. 10 h at 70°C, 13%; (c) homogeneous microstructure. 12°C/min. 14.6%; (d) inhomogeneous microstructure, O.017°Clmin. 14.6%. The diameter of a [3-1actoglobulin molecule is. as a comparison, ~3.6 nm.
A further decrease in the heating rate led to the formation of an inhomogeneous network. The micrographs showed both dense regions of small meshes clustering together and loose regions with long, stretched strands, some of which were broken. These correspond to the polymer-rich and polymer-poor regions shown in Figures 2b,d and 3c. The effect of heating rate indicates that the inhomogeneities are formed during gelation and are not a result of gel shrinkage after gelation.
Formation of inhomogeneities The gelation of 13-lactoglobulin at pH 7.5 was monitored by the build up of 460
Inhomogeneous 13-lactoglobulin gels
Fig. 3. Sch emati c represent at ion of th e 13-lactoglobulin microstructure formed at different he alin g rates: (a) 12°C/min , (b) 1-0. 1°C/min and (c) O.017°C/min.
ela sticit y as a function of increasing temperature as expressed by G'(T)' Figure 5 shows the gelation at the slowest heating rate (O.017°C/min) at which the inhomogeneities wer e most dominant. The peak in G ' around 70°C was only observed with the slowest heating rate. No peak was observed for the inhomogeneous gels formed at the shift around pH 6, not even with slow heating, which indicates a different formation of the inhomogeneities at the shift. The inhomogeneities formed at pH 7.5 and O.l oC/min were not dominant enough to influence the rheological behaviour during gelation . The peak demonstrates a different aggregation behaviour with slow heating th an with fast heating at pH 7.5 . Th e different aggregation beh aviour with slow heating also affects the gelation temperture of 13-lactoglobulin , which has been found to increase with an increase in the heating rate (24) . De Wit has studied the effect of heating rate on whe y protein den aturation and separated the reaction into unfolding and aggregation (29). The aggregation was most do'minant during slow 461
M.Stad ing, M.Lan gtoll and A.-M. Her mansson
4a
4b
4c
Onm Fig. 4. Micrographs of 12% [3-lactoglobulin gels formed at pH 7.5 at (a) 12°C/min, (b) 1°C/min and (c) 0.1°C/min. The arrows point to examples of the meshes.
heating and was conclude d to be the rate-d eterm ining step for den aturation of whey prot eins. . Th e frequ en cy was continuously scanne d from 0.002-2 Hz during heating in or de r to obta in inform ation abo ut the cha rac ter of the gel from the slope log G' versus log f[ see Frequency dependence belo w (30)]. The slope of log G' versus log f decreased continuously from the start of the gelation at T = 61°e , wher e
462
Inhomogeneous f3.lactoglobulin gels
0.2 ,......., 0.15 0
0.... ....:::.:::
L...---J
C:J
0.1 0.05 0 50
60
70
80
90
T rOC] Fig. 5. Gelation of 14.6% f3-lactoglobulin at pH 7.5 at a heating rate ofO.017°C/min (1°C/h). G'rf) is shown for three frequencies: 0.002, 0.05 and 1 Hz.
6
Onm Fig. 6. Micrograph of a 12% f3-lactoglobulin gel heated directly to 70°C, held there for 1 h, and then cooled directly to 20°C without further heating.
G starts to increase, up to 90°, without inflections at the transient structure. This means that these rheological characteristics did not reveal any change in the microstructure at the peak. The transient structure appeared at temperatures higher than the denaturation temperature, Td , which is 63°C at pH 7.5 (31). The phase angle, 8, dropped to 8 = 10° at the start of gelation at 6PC. It then decreased to 8 = 5° at the second increase in G' at T> 80°C. Figure 6 shows a gel which was heated directly to 70°C, held there for 1 h, and then cooled to 20°C i.e. not heated up to 90°C. This heating was comparable to a heating rate of 0.1°C/min. The network was homogeneous with distinct strands in contrast to the thick strands formed when heating the sample at 0.1°Clmin to I
463
M.Stading, M.Langton and A.·M.Hermansson
90°e. The period of time when the gel is kept at -70°C seems to be important for the conformation of the strands , and the aggregation mechanisms need to be further studied. An explanation of the transient structure is that, at first , a homogeneous structure (see Figure 6) starts to form and G' increases, but at the maximum in G' the microstructure divides into a polymer-rich and a polymer-poor fraction, causing a decrease in G' after the maximum. The structure formation then continues and G' increases again as a result of the increasing strength of the network . When the gel is cooled to 20°C, the microstructure remains essentially the same , and the resulting inhomogeneous network structure is shown in Figure 2b. As mentioned in the introduction, this phenomenon has been referred to earlier as microphase separation (10) or microsyneresis (1 ,11). Frequency dependence The frequency dependence of the shear modulus for a gel is characteristic of the type of gel (30). G* of a gel with strong, covalent cross-links far away from the gel point is independent of frequency, whereas G* is slightly dependent on the frequency for a physical gel. The dependence can usually be described by G' oc G" cc f" , which gives a straight line with slope n, in a log-log plot. A strong gel has, consequently, a lower value of n than a physical gel has. For an entanglement gel, G' and G" strongly depend on the frequency and even show a cross-over at some frequency. The frequency dependence of the fine-stranded gels was studied (i) at pH 7.5 for different heating rates and (ii) at the shift between particulate and findstranded network structure at -pH 5.8. The frequency dependence was recorded after cooling the gels to 20°e. (i) At pH 7.5 the gels formed at 5°C/min were homogeneous, had the highest G' and were less frequency-dependent than the inhomogeneous gels formed at slower heating rates (see Figure 7). This means that the homogeneous gels had more of the character of strong gels. It could be speculated that these properties relate to the microstructure , i.e. depend on differences in the cross-links or perhaps in the dynamics of the cross-links, but unfortunately , micrographs cannot show this. The micrographs do, however, indicate a different character of the strands at fast heating rates, which may cause more elasticity in the strands resulting in less frequency-dependent gels, as shown in Figure 4. When the frequency dependence of the inhomogeneous gels (see 0.1 and O.017°C/min in Figure 7) is examined more closely , it becomes even more complex . The curves of G' ( f) consist of two slopes: one steep slope at low frequency and a shallower one at high frequency (see Table I). One explanation of this could be that the regions having different den sities dominate the response at different frequencies (see Model below for further explanation). (ii) The network structure shifts from particulate to fine-stranded at -pH 6: below 6 the structure is particulate , and above it is fine-stranded. Langton and Hermansson have earlier shown that the network structure just above the shift is inhomogeneous (26) . The electron micrographs of the inhomogeneous struc464
Iohomogeneous 13-lactoglobulin gels
10 ,..----, 0
0~
'----'
0 1 0.001
0.01
0.1
10
f [Hz] Fig. 7. The frequency dependence G'(f) of 14% 13-lactoglobulin gels at pH 7.5. The heating rates of the different curves are presented in DC/min. The lines are fitted to the experimental data.
Table I. The slope n in G' pH
ex:
f"
from the frequency curves of 13-lactoglobulin gels
Heating rate °C/min
7.5 7.5 7.5 7.5
5
5.58 5.81 5.97 6.33 6.50
5 5 5 5 5
0.8 0.1 0.017
n, first slope
second slope
0.2 0.2
0.03 0.06 0.07 0.1
0.1 0.1 0.1
n2
0.01 0.06 0.04 0.06 0.2
Data taken from Figures 7 and 8.
tures in reference 26 were taken of 13-lactoglobulin in another batch, which had the structural shift at pH 6 instead of at pH 5.8, and a heating rate of lOoC/min. Figure 8 shows that just above the shift (pH 5.81, 5.97, 6.33) these gels had a frequency dependence G' (f) consisting of two slopes. The behaviour of G' (f) is similar to that of the 13-lactoglobulin gels formed with a slow heating rate at pH 7.5 (Figure 7), even though the gels formed at the shift were heated at a fast rate. The gel at pH 5.58, which had a particulate structure, had a higher G' which was almost independent of frequency. At pH >6.33 the two slopes became less obvious, and at pH 6.5 there was only one slope. The slope is steeper (n is higher) at pH 6.5 for the concentration used (12%) because it is closer to the critical gel concentration than at lower pH (24). G decreased when passing the shift from a particulate to a fine-stranded gel structure, but was maximal at ~pH 6.0 before decreasing again at higher pH. I
465
M.Stading, M.Langton and A.-M.Hermansson
100
GI [kPa] 5.58 5.97
10
5.81 6.33
6.50
1
0.1 0.001
0.01
0.1
10
f [Hz] Fig. 8. The storage modulus as a function of frequency G' (f) around the upper shift between a particulate and a fine-stranded network structure for 12% 13-lactoglobulin gels heated at 5°C/min. The lines are fitted to the experimental data . • pH 5.58, 0 pH 5.81, 0 pH 5.97. 0 pH 6.33,. pH 6.50.
The maximum in G' at -pH 6.0 may depend on the rather coarse network occurring just above the shift (26). When the pH was further increased, the structure became more and more homogeneous, which explains the flattening out of the slope at low frequencies. Changes in the electrostatic forces. caused by, for instance, pH or salts, seem to have a stronger influence on the network structure than different heating rates. A change in pH may even change the network structure from finestranded to particulate, which is not possible by changes in the heating rate. Relaxation
Another way of expressing the concept of different regions being responsible for the different slopes of the frequency curve is to assume that the dense and the less dense regions have different relaxation times. The relaxation of an inhomogeneous gel at pH 7.5 and a homogeneous gel formed at pH 7.5 (see Figure 7, 0.017 and SO/min respectively) are shown in Figure 9. G(t) of the gel formed at 0.01 TCimin seems to consist of two components. The relaxation time spectra in Figure 9 show two peaks for the inhomogeneous gel, which also 466
Innomogeneous 13-lactoglobulingels
10
10
_ _-;-~ ....
1 \
0.1
:::r::
\ 0.1
++----f-+-----f---I----+-------.,f----t-
0.01
0.1
10
100
o.a1
1000 10000
time [5] Fig. 9. The filtered relaxation modulus G as a function of time for 14% 13-lactoglobulin at pH 7.5 heated at O.017"C/min (thick lines) and 12% 13-lactoglobulin at 5°C/min (thin lines). H is the relaxation time spectrum calculated using Alfrey's approximation.'
implies two dominant relaxation times. The spectra have to be treated with caution because they were calculated from limited time intervals. Relaxation times outside the intervals may very well occur, especially at longer times. It would therefore be desirable to continue the relaxation experiments to longer times but sample degradation and instrumental drift prevents this. The relaxation behaviour of the inhomogeneous gels is different from the homogeneous gels despite these experimental difficulties. Model. The frequency response of a material with two dominant relaxation times has also been modeled to find out if this really can cause a frequency curve with two slopes. Figure 10 shows the very simplified relaxation time spectrum used as a model. The two different relaxation times are represented by two peaks in the relaxation time spectrum, which was used to calculate a frequency curve, G' (f)' The calculated frequency curve was compared with the experimental results. The relation between G' and the relaxation time spectrum H(T) is (28)
(1) where w = 2'ITf, f is the frequency and T is the relaxation time. G' (w) was calculated by inserting the relaxa tion time spectrum H (T) shown in Figure 10 into eqn (1). G' was then determined by the constants H], H 2 , T" T2, T3, T4 in Figure 10 and non-linear regression was used to fit the constants to the measured values. The model gave a qualitative fit to the measurements (see 467
M.Stading, M.Langton and A.-M.Hermansson
H
Fig. 10. The relaxation time spectrum used to model the behaviour of the inhomogeneous finestranded gels.
10
0.1 0.001
~
0.01
0.1
__ --.-- b a
10
f [Hz] Fig. II. The frequency curve G'(f) of 14% 13-lactoglobulin at pH 7.5 heated at O.loC/min is indicated by The lines show the calculated frequency curves resulting from eqn (I) and the relaxation time spectrum described in Figure 10. Curves a and b are calculated using different sets of constants, as shown in the text.
+.
O.I°C/min in Figure 7) for HI = 150 kPa, H 2 = 160 kPa, TI = 13.3 s, T2 = 13.7 S, T3 = 140 S, T4 = 150 s as shown by curve a in Figure 11. These are all plausible values, which give a fair fit, but a perfect fit could not be obtained for any other reasonable values of the constants because the model spectrum is too simple. The real relaxation time spectrum is much broader, probably also broader than the 'measured' spectra in Figure 9. The two peaks in the relaxation time spectrum of the model (Figure 10) can be compared with the 'measured' relaxation time spectrum in Figure 9, and it can be concluded that the measured spectrum occurs at shorter relaxation times. When the constants are set to HI = 5 kPa, H 2 = 8 kPa, TI = 0.003 S, T2 = 0.02 S, T3 = 0.1 S, T4 = 10 s, the model 468
Inhomogeneous 13-lactoglobulin gels
spectrum becomes more similar to the measured spectrum. The calculated frequency curve then gets the right shape but is too exaggerated (see curve b in Figure 11). Other values of the constants may also give a different shape to the frequency curve. Weiss and Silberberg used a similar model to explain another frequency behaviour (32). They studied inhomogeneous polyacrylamide gels and found a plateau at low frequency and a rise at high frequency, i.e. the opposite to the results presented here. They found a qualitative agreement for their modelled relaxation time spectrum, which assumed a triangular peak at low frequency and a rectangular distribution at high frequency. Both the models are very simple and contain enough constants to fit both types of behaviour, but the models still show that a broken frequency curve may be caused by a relaxation time distribution with two peaks, i.e. different relaxation times in the dense and less dense regions may give a broken frequency curve. Conclusions
(i) 13-Lactoglobulin gels formed at pH 7.5 have an inhomogeneous microstructure when heated slowly but not when heated quickly. Inhomogeneities form during gelation as a result of microphase separati'on. (ii) 13-Lactoglobulin gels formed close to the shift from a fine-stranded to a particulate network structure at -vpl-l 6 also have an inhomogeneous network, even when heated quickly. (iii) The dense and loose regions of the inhomogeneous network have different relaxation times, which causes a broken frequency curve G' (f)' i.e. G'(f) forms two slopes. (iv) Heating rate influences the character of the gels formed at pH 7.5. The quickly heated gels have a high storage modulus which is not very frequency-dependent, whereas the slowly heated gels have a lower storage modulus which is more frequency-dependent. Acknowledgements
The authors thank Siv Kidman and Ina Storm for their skilled technical assistance. Financial support from The Swedish Council for Forestry and Agricultural Research and from the Nordic Industrial Fund is gratefully acknowledged. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
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12. San Biagio ,P .L. . Mad oni a,F ., Newman ,J . a nd Palma,M. U. (1986) Bi opolym ers, 25, 2255. 13. San Biagio ,P.L. , Bulonc.D .. Emanu ele ,A .. Modonia ,F ., Di Stefano ,L. , Giacomazza ,D .. Trapanese .M ., Palm a-Vittorelli ,M.B . an d Palrn a.MiU . ( 1990) Makrom ol. Chern. Macromol. Symp ., 40, 33. 14. Leone .M .. Sciortino ,F. , Migliore.M .. Forn ili,S.L. and Palma-Vittorelli,M .B . ( 1987) Biopolym ers , 26, 743-761. IS. Bulon e ,D. and San Biagio,P.L. (1991) G em . Phys. Lett.. 179,339. 16. Emanuele.A .. Di Stcfan o.L.; Giacomazza ,D .. Trapanese ,M .. Palma-Vittor elli,M.B. and Pahn a .M,U . (1991) Biopolymers, 31. 859. 17. Herm an sson ,A .-M . (1989) Carbohyd. Polym .. 10, 163. 18. He rmansson ,A .-M .• Erik sson.E. and Jordan sson .E . (1991) Carbohy d. Polym . , 16. 297. 19. Egel and sdal ,B .. Fr eth eim,K . and Harbitz,O . (1986) J. Sci. Food Agric.. 37 . 944. 20. Herm ansson ,A .-M . and Lucisano ,M . ( 1982) J . Food Sci. , 47, 1955 . 21. Herrnansson.Ai-M . (1983) Qual. Plant Fds Hum. NII/r., 32, 369. 22. Herman sson ,A .-M. (1983) In McLoughlin ,J .V . and McKenn a,B.M. (eds), Proceedings of Sixth International Congr ess oj Food Science Technology . Boole Press. Dublin. p. 107. 23. Hermansson ,A .-M . (1986) In Mitchell ,J .R . and Ledward,D .A . (eds) , Functional Prop erties oj Food Macrom olecules. Elsevier. Lond on . p. 273. 24. Stad ing .M . and Herm ansson ,A.-M . (1990) Food Hydro co//.. 4, 121. 25. Stading,M. and Herm ansson.A.-M. (1991) Food Hydro co/l. , 5, 339. 26. Langton,M. and Herm ansson ,A.-M. (1992) Food Hydro co/l., 5. 523. 27. Mulvihill ,D .M .. Rector,D. and KinsellaJ .E . (1990) Food Hydrocoll .. 4. 267 28. Whorlow ,R.W. (1980) Rheological Techniqu es. Ellis Horwood , Chichester. 29. De Wit.J .N . (1990) J. Dairy Sci., 73, 3602. 30. Clark ,A .H . and Ros s-Murphy,S.B . (1987) Advances in Polym er Science. Springer Verla g, Berlin . 31. He gg,P .-O . ( 1980) ACIa A gric. Scand. . 30, 401. 32. Weiss,N. and Silberberg .A . (1977) Br. Polym . J. , 144.
470
Inhomogeneous fine-stranded 13-lactoglobulin gels Mats Sta ding, Maud Langton and Ann e-Marie Herm ansson SI K- The Swe dish Institute fo r Food Research, PO Box 5401, S-40229 Goteborg, Swe den Abst ract. Inh om ogene ities occur in the network of fine-stranded 13-lactog lobu lin gels. The y have been character ized by electro n microsco py a nd their intlu ence o n the rheologic al pro pe rties at sma ll defor mation s measured. The inhomoge neities occ urred as de nse a nd loose region s in the netwo rk a nd their forma tio n depend ed o n the heat ing rate durin g ge l form at ion (O.0 I7- 12°Clmin) at pH 7.5 or on pH if close to where the network structure shifts from fine-stra nded to particula te (pH 5.86.5) . An inho moge neo us microstructur e was formed a t pH 7.5 with a slow heati ng rate , where as the network was homogene ous after fast heat ing. Th ese homogeneous gels had higher G' than the inhomoge neo us ge ls . In add ition the character , as expressed by the freq uency de pendence , changed from strong homogeneous gels to weaker, mor e frequency-d ep en dent inh om ogen eous gels. Th e formati on of the inhomogeneities was mon itored at the slowest heat ing rat e by measuring G' during gelation . G ' showed a maximu m around 70°C , indicating a sep aration int o polymer-rich and polym er-p oor regions in the network . Electron microscopy showed a tra nsient, homogeneous network befor e the separation . Both types of inhomogeneous gels had broken frequency curves, i.e . G '/ had two slopes. which were cause d by different relaxation times in the den se and loose region s. Re laxation measur ements of the inhom oge neou s gels showed relaxation time spec tra with two peak s. A model was used to con firm that a broken fre quency curve may be caused by two peaks in the relaxat ion time spectru m.
Introduction Gels consist of a solid net work interspersed by a fluid , which is water in the case of biop olymer gels. The network is thr ee-dim ension al with strands forming a porous and almost solid materi al , eve n though the solid conte nt may be only fractions of a percent. The scale of the network as expresse d by pore size or persisten ce length varies between different gels. The stra nds may be built up by anything from mole cules to colloida l parti cles. The network is usually regarded as homogeneous when viewed on a scale sufficientl y larger than a typical size of the network . Some net works do , however , show inhomogeneities of some kind. Parts of the network may , for exampl e, be den ser , i.e. have smaller pores than the rest of the network , see Figure 1. Porisometry and scattering measurements on synthetic gels have given pore rad ii in the range 10-7500 nm in a styre ne-divinylbenzene gel and 0.25-250 nm in polyacrylamide gels (1,2). A broad distribution of pore sizes does not necessarily lead to inhomogeneities. It could also result in a network structure with a wide but uniform pore-size distribution throughout the sampl e . Inh om ogeneities have been defin ed by Burch ard as 'a sudden change of a property when passing from one point in space to another' (3). Thi s not only includes microstructural inhomogen eit ies but also other properties such as refractive index , optic al density and scattering properti es, wh ich are prob ably, but not necessaril y, caused by microstru ctural inhomogeneities. In this art icle, we will conside r onl y microstru ctural inho moge neities, i.e. 455
M.Stading, M.Langton and A.-M.Hermansson
Fig. l. Schematic example of an inhomogeneous network.
different regions of the network having different structures. Inhomogeneity may be due to different pore sizes, but there could also be different types of strands or different types of cross-links. There are different explanations for the formation of inhomogeneous networks. Inhomogeneities are either inherent in the formation mechanism or occur after the gel is formed. Kuhn pointed out as early as 35 years ago that gels prepared in the presence of a swelling medium almost necessarily have to be inhomogeneous (4). Bastide and Leibler have theoretically demonstrated this by assuming a site percolation model for network formation (5). Inhomogeneities were formed when the gel swelled because the percolation clusters forming the network did not swell as much as the rest of the gel. The same phenomenon occurs in a stretched gel. The theory was tested by neutron scattering experiments which showed that the expansion of the gel was heterogeneous (68). The scattering of the stretched gels also showed abnormal butterfly patterns for strain E > 0.28, which were directly attributed to the inhomogeneous network structure. A theoretical network of rigid rods has also been shown to contain large density fluctuations in the equilibrium swollen state (9). Inhomogeneities can also occur when the gel-forming material is not stable in the final gel. A cold-setting polymer may, for instance, be stable in solution at high temperatures, whereas it tends to precipitate at lower temperatures. If gelation occurs before precipitation the elastic network will prevent precipitation, but if the force to separate is strong enough, the network may separate into polymer-rich and polymer-poor regions. This phenomenon has been called micro phase separation (10) or microsyneresis (1,11). Galina et at. defined micro syneresis as a local phase separation not followed by a relaxation of the whole system (1). Another condition resulting in an inhomogeneous network has been reported for the gelation of agarose and was then referred to as spinodal decomposition (12-16). The spinodal decomposition occurred before gelation and was observed by a peak in the apparent viscosity. A distinct peak in the storage modulus, G', was observed for K-carrageenan in the presence of potassium ions (17,18). K-Carrageenan forms a gel on cooling and at the peak a fine network was found in which the cross-links appeared to be
456
Inhomogeneous 13-lactoglobulin gels
formed by double helices. When the temperature was lowered further the network became coarser, because the helices aggregated into stiff superstrands which formed the final network. Myosin gels also show a peak in the storage modulus during gelation (19). The maximum in G' became less pronounced when the heating rate was increased from 0.1 to 2SC/min. Hermansson has found phase separation in both blood plasma gels and whey protein gels (20-23). Both systems are mixtures of proteins and form gels on heating. The degree of phase separation increased with heating temperature above the gelation temperature, i.e. the gels which were heated to 95°C were more phase-separated than the gels that were heated to 75°C. The phase separation led to an inhomogeneous network structure and impaired water holding was measured. Addition of sodium chloride also led to increased phase separation (23). I3-Lactoglobulin has been used as a model system in this study because it forms inhomogeneous network structures depending on heating rate and pH. It is heatsetting and forms different gel structures depending on pH: a particulate network at intermediate pH (4-6) and a fine-stranded network below and above this interval (24-26). Langton and Hermansson have reported inhomogeneities at the shift between these two types (26). Electron micrographs showed that 13lactoglobulin forms an inhomogeneous microstructure in a narrow interval at the upper shift around pH 6. The network was homogeneous at pH 6.5 but began to show inhomogeneity when pH was decreased to 6.3. At pH 6.05 there were large density fluctuations in the network and at pH 6.0 the network shifted to a particulate state. At the lower shift around pH 4, the network was mixed rather than inhomogeneous and the pH interval was broader. The network consisted of a mixture of particulate and fine-stranded microstructures. Mulvihill et al. observed the same behaviour in 13-lactoglobulin gels at pH 8.0 on addition of NaCI (27). The network was homogeneous and fine-stranded for 0.05 mol/drn", inhomogeneous for 0.20 mol/drrr' and particulate for 1.0 mol/drrr'. The large deformation properties were maximal at 0.20 rnol/drrr'. This paper will show the microstructure of inhomogeneous fine-stranded gels of 13-lactoglobulin as revealed by electron microscopy. The rheological effects of the inhomogeneities will be demonstrated and explained.
Material and methods
Material The 13-lactoglobulin powder was obtained from the Sigma Chemical Co. (St Louis, MO) (L-0130, lot no. 98F8030 and 106F8120). For details of the 13lactoglobulin powder, see references 24 and 25.
Sample preparation and heat treatment The 13-lactoglobulin was dissolved in degassed, distilled, water and pH was adjusted with :::;1 mol/dm' HCI or :::;1 mol/drrr' KOH. The samples were then 457
M.Stading, M.Langton and A.·M.Hermansson
heated at a controlled heating rate of between 0.017°C/min (1°C/h) and 5°C/min from 30 to 90°e. Some samples were also put directly in a water bath at 90°C, which corresponds to an average heating rate of ~ 12°C/min. The samples were kept at 90°C for 1 h and then cooled at the fastest cooling rate to 20°C, at which they were kept for 30 min. The slowest heating rate gave the same rheological results as when heating the sample first to 70°C at 1°C/min, keeping it at 70°C for 10 h, and then raising the temperature to 900 e at 1°C/min. The latter heating was therefore treated as equivalent to the 0.017°C/min heating rate and was sometimes used to avoid microbial growth. The ~-lactoglobulin concentrations referred to in this paper are given in weight percent (w/w). Experimental techniques Microscopy. After the heat treatment small cubes of the gel, 1 x 1 x 1 mm, were cut out and prepared for transmission electron microscopy (TEM) using the following procedure: the sample was immersed in 2% v/v glutaraldehyde with 0.1 % w/v ruthenium red for 60 min at 8°C, washed 2 x 10 min at 8°C followed by 2% w/v OS04 for 120 min at 8°C. The samples were then rinsed for 3 x 10 min in 0.025 mol/dm' KCl solution before being dehydrated in a graded ethanol series, 50, 70, 95 and 99.5% v/v. To prevent osmotic effects, 0.025 moll drrr' KCl was added to the fixative and washing solutions. The samples were transferred to propylene oxide after dehydration and were then embedded in Polybed (Polyscience Inc.). Thin sections (~60 nm) were cut on a diamondknife and were double-stained with uranyl acetate and lead citrate. The sections were examined in a transmission electron microscope (Jeol 100 eX-II, Jeol Ltd, Tokyo, Japan), at an acceleration voltage of 80 kV. Dynamic measurements. A ~-lactoglobulin solution of 2.5 ml was heated in the measuring cup of a Bohlin VOR Rheometer. A thin layer of paraffin oil was applied on top of the sample to avoid evaporation, and a couette type cup and bob measuring system (DIN 53019) with an inner cylinder diameter of 14 mm was used. The bob was suspended in an interchangeable torsion bar with momentums at maximum deflection of between 3 x 10- 5 and 2 x 10- 3 Nm. The frequency was 1 Hz when temperture was the independent variable and during the frequency sweep 0.001-5 Hz. As ~-lactoglobulin is strain-sensitive during gelation, the strain was kept as low as 4-10 x 10- 4 so as not to disturb the process (24). This was well within the linear region. The sample was oscillated only when recording G *. The cup holder of the rheometer was modified to reduce axial deformations caused by thermal elongation of the cup holder (24). Relaxation. The relaxation was performed at 20°C after the heat treatment. A step strain of 8 x 10- 4 was applied to the sample during a strain rise time of 0.8 S. The relaxation modulus G was then monitored as a function of time, and the relaxation time spectrum H(T) was calculated by the Bohlin VOR software using Alfrey's approximation (28). The H(T) inversion by Alfrey's approxi-
458
Inhomogeneous 13-lactoglobulin gels
mation is slightly dependent on how the relaxation curve is filtered. All curves were therefore identically filtered. Results and discussion
Inhomogeneous networks were formed both at pH 7.5 as an effect of the heating rate during gelation and at the microstructural shift from fine-stranded to particulate networks at ~pH 6. The microstructure of the gels in this transition region has been characterized earlier by electron microscopy (26). Microstructure
The kinetic effects on microstructure were studied at four different heating rates at pH 7.5: 12, 1, 0.1 and O.017°C/min, and at three concentrations: 12, 13 and 14.6%. The microstructures formed at the two extreme heating rates, the fastest and the slowest, are demonstrated in Figure 2a,c and b.d respectively. Figure 2a shows a homogeneous network of evenly thick strands formed at the fastest heating rate at 13% concentration, whereas Figure 2b shows an inhomogeneous network, with small and large pores, formed at the slowest heating rate at the same concentration. At 14.6% and the fastest heating rate, the network was also homogeneous but very dense, and the strands ~ere difficult to observe separately. At slow heating rates, both regions with large pores and regions with small pores were formed, resulting in an inhomogeneous network, cf. Figure 2c and d. See also Figure 3, which is a schematic drawing of the microstructure formed at the different heating rates. The inhomogeneities formed at slow heating rates were not as coarse as those formed at the structural shift around pH 6, which indicates that the electrostatic forces influence the structure more than the kinetics of gelation (26). Figure 4 shows the microstructure of 13-lactoglobulin gels formed at the lowest concentration, 12%. The network formed at the fastest heating rate was also homogeneous at this concentration (Figure 4a) and was composed of long and distinct strands with relatively long distances between the cross-links. The microstructure resembled a snapshot of a concentrated polymer solution. Decreasing the concentration from 14.6 to 12% did not influence the homogeneity of the homogeneous networks, but the distance between crosslinks became longer. Figure 3a schematically presents the homogeneous network structure shown in the two micrographs Figures 2a and 4a. When the heating rate was decreased to 1°C/min or slower, the strands appeared to be formed by a different mode of aggregation' than at the fastest heating rate, cf. Figure 4a,b and c. This is also schematically shown in Figure 3b. The gels formed at 1 and 0.1DC/min had somewhat shorter and thicker strands, which were not as distinct as the strands formed at the fastest heating rate. The micrographs showed a network constructed of numerous small meshes of thick strands. In addition, an incipient inhomogeneity with some large pores appeared. The cross-links appeared weaker from a microscopical point of view, and even broken in some regions, which accounts for the incipient inhomogeneities. 459
M.Stading. M.Langton and A.·M.Hermansson
2a
2b
2c
2d
Fig. 2. Micrographs of [3-lactoglobulin gels formed at pH 7.5 at different heating rates and concentrations: (a) homogeneous microstructure. 12°Clmin, 13%; (b) inhomogeneous microstructure. 10 h at 70°C, 13%; (c) homogeneous microstructure. 12°C/min. 14.6%; (d) inhomogeneous microstructure, O.017°Clmin. 14.6%. The diameter of a [3-1actoglobulin molecule is. as a comparison, ~3.6 nm.
A further decrease in the heating rate led to the formation of an inhomogeneous network. The micrographs showed both dense regions of small meshes clustering together and loose regions with long, stretched strands, some of which were broken. These correspond to the polymer-rich and polymer-poor regions shown in Figures 2b,d and 3c. The effect of heating rate indicates that the inhomogeneities are formed during gelation and are not a result of gel shrinkage after gelation.
Formation of inhomogeneities The gelation of 13-lactoglobulin at pH 7.5 was monitored by the build up of 460
Inhomogeneous 13-lactoglobulin gels
Fig. 3. Sch emati c represent at ion of th e 13-lactoglobulin microstructure formed at different he alin g rates: (a) 12°C/min , (b) 1-0. 1°C/min and (c) O.017°C/min.
ela sticit y as a function of increasing temperature as expressed by G'(T)' Figure 5 shows the gelation at the slowest heating rate (O.017°C/min) at which the inhomogeneities wer e most dominant. The peak in G ' around 70°C was only observed with the slowest heating rate. No peak was observed for the inhomogeneous gels formed at the shift around pH 6, not even with slow heating, which indicates a different formation of the inhomogeneities at the shift. The inhomogeneities formed at pH 7.5 and O.l oC/min were not dominant enough to influence the rheological behaviour during gelation . The peak demonstrates a different aggregation behaviour with slow heating th an with fast heating at pH 7.5 . Th e different aggregation beh aviour with slow heating also affects the gelation temperture of 13-lactoglobulin , which has been found to increase with an increase in the heating rate (24) . De Wit has studied the effect of heating rate on whe y protein den aturation and separated the reaction into unfolding and aggregation (29). The aggregation was most do'minant during slow 461
M.Stad ing, M.Lan gtoll and A.-M. Her mansson
4a
4b
4c
Onm Fig. 4. Micrographs of 12% [3-lactoglobulin gels formed at pH 7.5 at (a) 12°C/min, (b) 1°C/min and (c) 0.1°C/min. The arrows point to examples of the meshes.
heating and was conclude d to be the rate-d eterm ining step for den aturation of whey prot eins. . Th e frequ en cy was continuously scanne d from 0.002-2 Hz during heating in or de r to obta in inform ation abo ut the cha rac ter of the gel from the slope log G' versus log f[ see Frequency dependence belo w (30)]. The slope of log G' versus log f decreased continuously from the start of the gelation at T = 61°e , wher e
462
Inhomogeneous f3.lactoglobulin gels
0.2 ,......., 0.15 0
0.... ....:::.:::
L...---J
C:J
0.1 0.05 0 50
60
70
80
90
T rOC] Fig. 5. Gelation of 14.6% f3-lactoglobulin at pH 7.5 at a heating rate ofO.017°C/min (1°C/h). G'rf) is shown for three frequencies: 0.002, 0.05 and 1 Hz.
6
Onm Fig. 6. Micrograph of a 12% f3-lactoglobulin gel heated directly to 70°C, held there for 1 h, and then cooled directly to 20°C without further heating.
G starts to increase, up to 90°, without inflections at the transient structure. This means that these rheological characteristics did not reveal any change in the microstructure at the peak. The transient structure appeared at temperatures higher than the denaturation temperature, Td , which is 63°C at pH 7.5 (31). The phase angle, 8, dropped to 8 = 10° at the start of gelation at 6PC. It then decreased to 8 = 5° at the second increase in G' at T> 80°C. Figure 6 shows a gel which was heated directly to 70°C, held there for 1 h, and then cooled to 20°C i.e. not heated up to 90°C. This heating was comparable to a heating rate of 0.1°C/min. The network was homogeneous with distinct strands in contrast to the thick strands formed when heating the sample at 0.1°Clmin to I
463
M.Stading, M.Langton and A.·M.Hermansson
90°e. The period of time when the gel is kept at -70°C seems to be important for the conformation of the strands , and the aggregation mechanisms need to be further studied. An explanation of the transient structure is that, at first , a homogeneous structure (see Figure 6) starts to form and G' increases, but at the maximum in G' the microstructure divides into a polymer-rich and a polymer-poor fraction, causing a decrease in G' after the maximum. The structure formation then continues and G' increases again as a result of the increasing strength of the network . When the gel is cooled to 20°C, the microstructure remains essentially the same , and the resulting inhomogeneous network structure is shown in Figure 2b. As mentioned in the introduction, this phenomenon has been referred to earlier as microphase separation (10) or microsyneresis (1 ,11). Frequency dependence The frequency dependence of the shear modulus for a gel is characteristic of the type of gel (30). G* of a gel with strong, covalent cross-links far away from the gel point is independent of frequency, whereas G* is slightly dependent on the frequency for a physical gel. The dependence can usually be described by G' oc G" cc f" , which gives a straight line with slope n, in a log-log plot. A strong gel has, consequently, a lower value of n than a physical gel has. For an entanglement gel, G' and G" strongly depend on the frequency and even show a cross-over at some frequency. The frequency dependence of the fine-stranded gels was studied (i) at pH 7.5 for different heating rates and (ii) at the shift between particulate and findstranded network structure at -pH 5.8. The frequency dependence was recorded after cooling the gels to 20°e. (i) At pH 7.5 the gels formed at 5°C/min were homogeneous, had the highest G' and were less frequency-dependent than the inhomogeneous gels formed at slower heating rates (see Figure 7). This means that the homogeneous gels had more of the character of strong gels. It could be speculated that these properties relate to the microstructure , i.e. depend on differences in the cross-links or perhaps in the dynamics of the cross-links, but unfortunately , micrographs cannot show this. The micrographs do, however, indicate a different character of the strands at fast heating rates, which may cause more elasticity in the strands resulting in less frequency-dependent gels, as shown in Figure 4. When the frequency dependence of the inhomogeneous gels (see 0.1 and O.017°C/min in Figure 7) is examined more closely , it becomes even more complex . The curves of G' ( f) consist of two slopes: one steep slope at low frequency and a shallower one at high frequency (see Table I). One explanation of this could be that the regions having different den sities dominate the response at different frequencies (see Model below for further explanation). (ii) The network structure shifts from particulate to fine-stranded at -pH 6: below 6 the structure is particulate , and above it is fine-stranded. Langton and Hermansson have earlier shown that the network structure just above the shift is inhomogeneous (26) . The electron micrographs of the inhomogeneous struc464
Iohomogeneous 13-lactoglobulin gels
10 ,..----, 0
0~
'----'
0 1 0.001
0.01
0.1
10
f [Hz] Fig. 7. The frequency dependence G'(f) of 14% 13-lactoglobulin gels at pH 7.5. The heating rates of the different curves are presented in DC/min. The lines are fitted to the experimental data.
Table I. The slope n in G' pH
ex:
f"
from the frequency curves of 13-lactoglobulin gels
Heating rate °C/min
7.5 7.5 7.5 7.5
5
5.58 5.81 5.97 6.33 6.50
5 5 5 5 5
0.8 0.1 0.017
n, first slope
second slope
0.2 0.2
0.03 0.06 0.07 0.1
0.1 0.1 0.1
n2
0.01 0.06 0.04 0.06 0.2
Data taken from Figures 7 and 8.
tures in reference 26 were taken of 13-lactoglobulin in another batch, which had the structural shift at pH 6 instead of at pH 5.8, and a heating rate of lOoC/min. Figure 8 shows that just above the shift (pH 5.81, 5.97, 6.33) these gels had a frequency dependence G' (f) consisting of two slopes. The behaviour of G' (f) is similar to that of the 13-lactoglobulin gels formed with a slow heating rate at pH 7.5 (Figure 7), even though the gels formed at the shift were heated at a fast rate. The gel at pH 5.58, which had a particulate structure, had a higher G' which was almost independent of frequency. At pH >6.33 the two slopes became less obvious, and at pH 6.5 there was only one slope. The slope is steeper (n is higher) at pH 6.5 for the concentration used (12%) because it is closer to the critical gel concentration than at lower pH (24). G decreased when passing the shift from a particulate to a fine-stranded gel structure, but was maximal at ~pH 6.0 before decreasing again at higher pH. I
465
M.Stading, M.Langton and A.-M.Hermansson
100
GI [kPa] 5.58 5.97
10
5.81 6.33
6.50
1
0.1 0.001
0.01
0.1
10
f [Hz] Fig. 8. The storage modulus as a function of frequency G' (f) around the upper shift between a particulate and a fine-stranded network structure for 12% 13-lactoglobulin gels heated at 5°C/min. The lines are fitted to the experimental data . • pH 5.58, 0 pH 5.81, 0 pH 5.97. 0 pH 6.33,. pH 6.50.
The maximum in G' at -pH 6.0 may depend on the rather coarse network occurring just above the shift (26). When the pH was further increased, the structure became more and more homogeneous, which explains the flattening out of the slope at low frequencies. Changes in the electrostatic forces. caused by, for instance, pH or salts, seem to have a stronger influence on the network structure than different heating rates. A change in pH may even change the network structure from finestranded to particulate, which is not possible by changes in the heating rate. Relaxation
Another way of expressing the concept of different regions being responsible for the different slopes of the frequency curve is to assume that the dense and the less dense regions have different relaxation times. The relaxation of an inhomogeneous gel at pH 7.5 and a homogeneous gel formed at pH 7.5 (see Figure 7, 0.017 and SO/min respectively) are shown in Figure 9. G(t) of the gel formed at 0.01 TCimin seems to consist of two components. The relaxation time spectra in Figure 9 show two peaks for the inhomogeneous gel, which also 466
Innomogeneous 13-lactoglobulingels
10
10
_ _-;-~ ....
1 \
0.1
:::r::
\ 0.1
++----f-+-----f---I----+-------.,f----t-
0.01
0.1
10
100
o.a1
1000 10000
time [5] Fig. 9. The filtered relaxation modulus G as a function of time for 14% 13-lactoglobulin at pH 7.5 heated at O.017"C/min (thick lines) and 12% 13-lactoglobulin at 5°C/min (thin lines). H is the relaxation time spectrum calculated using Alfrey's approximation.'
implies two dominant relaxation times. The spectra have to be treated with caution because they were calculated from limited time intervals. Relaxation times outside the intervals may very well occur, especially at longer times. It would therefore be desirable to continue the relaxation experiments to longer times but sample degradation and instrumental drift prevents this. The relaxation behaviour of the inhomogeneous gels is different from the homogeneous gels despite these experimental difficulties. Model. The frequency response of a material with two dominant relaxation times has also been modeled to find out if this really can cause a frequency curve with two slopes. Figure 10 shows the very simplified relaxation time spectrum used as a model. The two different relaxation times are represented by two peaks in the relaxation time spectrum, which was used to calculate a frequency curve, G' (f)' The calculated frequency curve was compared with the experimental results. The relation between G' and the relaxation time spectrum H(T) is (28)
(1) where w = 2'ITf, f is the frequency and T is the relaxation time. G' (w) was calculated by inserting the relaxa tion time spectrum H (T) shown in Figure 10 into eqn (1). G' was then determined by the constants H], H 2 , T" T2, T3, T4 in Figure 10 and non-linear regression was used to fit the constants to the measured values. The model gave a qualitative fit to the measurements (see 467
M.Stading, M.Langton and A.-M.Hermansson
H
Fig. 10. The relaxation time spectrum used to model the behaviour of the inhomogeneous finestranded gels.
10
0.1 0.001
~
0.01
0.1
__ --.-- b a
10
f [Hz] Fig. II. The frequency curve G'(f) of 14% 13-lactoglobulin at pH 7.5 heated at O.loC/min is indicated by The lines show the calculated frequency curves resulting from eqn (I) and the relaxation time spectrum described in Figure 10. Curves a and b are calculated using different sets of constants, as shown in the text.
+.
O.I°C/min in Figure 7) for HI = 150 kPa, H 2 = 160 kPa, TI = 13.3 s, T2 = 13.7 S, T3 = 140 S, T4 = 150 s as shown by curve a in Figure 11. These are all plausible values, which give a fair fit, but a perfect fit could not be obtained for any other reasonable values of the constants because the model spectrum is too simple. The real relaxation time spectrum is much broader, probably also broader than the 'measured' spectra in Figure 9. The two peaks in the relaxation time spectrum of the model (Figure 10) can be compared with the 'measured' relaxation time spectrum in Figure 9, and it can be concluded that the measured spectrum occurs at shorter relaxation times. When the constants are set to HI = 5 kPa, H 2 = 8 kPa, TI = 0.003 S, T2 = 0.02 S, T3 = 0.1 S, T4 = 10 s, the model 468
Inhomogeneous 13-lactoglobulin gels
spectrum becomes more similar to the measured spectrum. The calculated frequency curve then gets the right shape but is too exaggerated (see curve b in Figure 11). Other values of the constants may also give a different shape to the frequency curve. Weiss and Silberberg used a similar model to explain another frequency behaviour (32). They studied inhomogeneous polyacrylamide gels and found a plateau at low frequency and a rise at high frequency, i.e. the opposite to the results presented here. They found a qualitative agreement for their modelled relaxation time spectrum, which assumed a triangular peak at low frequency and a rectangular distribution at high frequency. Both the models are very simple and contain enough constants to fit both types of behaviour, but the models still show that a broken frequency curve may be caused by a relaxation time distribution with two peaks, i.e. different relaxation times in the dense and less dense regions may give a broken frequency curve. Conclusions
(i) 13-Lactoglobulin gels formed at pH 7.5 have an inhomogeneous microstructure when heated slowly but not when heated quickly. Inhomogeneities form during gelation as a result of microphase separati'on. (ii) 13-Lactoglobulin gels formed close to the shift from a fine-stranded to a particulate network structure at -vpl-l 6 also have an inhomogeneous network, even when heated quickly. (iii) The dense and loose regions of the inhomogeneous network have different relaxation times, which causes a broken frequency curve G' (f)' i.e. G'(f) forms two slopes. (iv) Heating rate influences the character of the gels formed at pH 7.5. The quickly heated gels have a high storage modulus which is not very frequency-dependent, whereas the slowly heated gels have a lower storage modulus which is more frequency-dependent. Acknowledgements
The authors thank Siv Kidman and Ina Storm for their skilled technical assistance. Financial support from The Swedish Council for Forestry and Agricultural Research and from the Nordic Industrial Fund is gratefully acknowledged. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
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