Starches in Semidilute Aqueous SolutionT. Aberle, and W. Burchard, Freiburg (Germany)Nine starches from different plants were studied in the semidilute concentration regime. The amylose content varied between 0% (waxy starch) and 76%. The applied concentration range of 5 to 30% (w/v) corresponds to typical concentrations used for thickeners in food and non-food industries. With the exception of the amylose rich starches the maximum concentration was at least 4 times larger than the overlap concentration. Up to a certain concentration a common master curve was found for all starches but at high concentrations this master curve was superimposed by association andaggregation phenomena. The aggregation is promoted by the presence of amylose. The onset of aggregation is shifted to lower concentrations when the amylose content in the starches was high. The aggregation proceeds in time. It could be followed by dynamic light scattering and quantitatively be evaluated. The time dependent ageing of the solutions and the finally formed gels gave evidence for a liquid-solid phase separation that is kinetically hampered by the presence of the branched amylopectin.1 IntroductionIn previous papers [1, 2] we reported the conformational properties of several starches which were fully dissolved in water after applying a well controlled pressure cooking. Such measurements were made in the highly dilute solution regime, where the individual macromolecules are well separated from each other. These studies were now extended to the semidilute concentration regime, which is a domain of particular interest to industrial application. The expression semidilute appears on a first sight as poorly defined and needs some explanations. Experimentally a marked change in behavior is observed when a certain concentration, c*, is exceeded. At c<c* the properties of individual macromolecules can be studied but at c>c* the individual macromolecules are no longer well separated from each other, and only an ensemble of many macromolecules is observed. The concentration c* is still very low (~10-2g/ml) and the solution is certainly to be considered as dilute. However, c* separates two dilute solution regimes of remarkably different behavior. To distinguish the higher concentrated one from the very diluted solutions the expression semidilute was coined [3]. The concentration c* has a simple physical meaning. In the dilute solution regime the coils are highly swollen, and the mean segmental concentration within a particle cint is rather low (<10-

2g/mL).When increasing the weighed-in concentration, a stage is reached at which c=cint=c*. At this point the segments of the coils start to overlap. For this reason c* is called the overlap concentration. Of course, the over-all concentration can be increased beyond c* but this is involved with drastic changes in the solution properties. Only two alternatives are conceivable: (i) the coils interpenetrate each other and form a transient network of entangled chains; or (ii) the coils resist against such interpenetration; then the coils have to be compressed or will be de-swollen by other interactions.The first case was suggested by de Gennes [3] for non-polar, flexible linear chains in non polar organic solvents. Such a solution of interpenetrating chains represents a many-body system in which the characteristic properties of the individual macromolecules lose their identity. Instead of the contour length now a correlation length £ [3], that describes the mesh size of the transient network, controls the behavior. The tran-sient network appears to be rather complex, and therefore the systems are often called complex fluids. Their properties may be difficult to describe quantitatively. However, by simple arguments de Gennes succeeded to derive universal relationships which are controlled by only one parameter, the reduced concentration c/c* [3].The de Gennes concept of interpenetrating chains has been very successful and the various predictions were verified by experimental findings with many types of flexible chain molecules. It is evident, however, that the original concept of de Gennes cannot be valid for all types of macromolecules because it neglects two basic facts. These are: (i) non-linear architectures, as for instance branched chains, and (ii) specific interactions among the macromolecules that may lead to association and gelation.

The effect of branching is demonstrated in Figure 1. Obviously interpenetration of the segment domains is possible only with the chains at the outside of the macromolecule. Thus, we expect another change in the properties when the

Figure 1. Scheme of partially interpenetrating branched macromolecules. The branching points form obstacles and prevent full interpenetration.

cores of non-interpenetrable segment domains start to touch each other. On further increasing the concentration, de-swelling of the core may occur. Macromolecules are soluble in water if the polymer carries polar groups which favorably interact with the water molecules. These polar groups have often the capability of forming hydrogen bonds or, in other cases, polyelectrolyte complexes. No universal behavior may be expected in this more concentrated regime.The present contribution deals with the attempt of deriving general rules for the various starches in this semidilute to moderately concentrated solutions which hopefully would reduce the discouraging complexity of the systems. In contrast to de Gennes'model suggestion we have to face three particularities with starches• the effect of a limited coil interpenetration due to branching,• the influence of specific interactions• the blend character of amylose with amylopectin.This outline demonstrates the immense difficulties one has with branched macromolecules in semidilute solutions. The various possibilities of branching offers serious problems already in the very diluted regime. Now, in addition, the influence of the interparticle interactions has to be taken into account. Because of the restricted coil interpenetration one has to question whether a change in the macromolecular conformation may be connected with this restriction.Fortunately, the very complex appearing behavior of semidilute solutions can also for the branched structures be cast into simple relationships by extending the scaling concept of de Gennes to branched systems. The technique works satisfactorily, as long as no change of the conformations is induced by the growing interactions when the concentration is increased [4]. However, pronounced deviations from universal behavior were often observed when the concentration was increased beyond a critical value. Such behavior was particularly striking with the starches from various sources studied in this contribution.The outline of this paper is organized as follows: At first a definition of the overlap concentration c*is given, and it is discussed how this concentration depends on the average molar masses of the various starches. Next, an overview is given on, which quantities can be measured by static light scattering and how the apparent quantities, obtained at finite concentration, are defined. It follows a consideration on the repulsive interactions and their effect on the apparent quantities. In the ensuing chapter the results from various starches are presented and discussed in connection to the amylose content. Finally the development of association with elapsing time is demonstrated with some amylose-rich starches at a selected concentration.

2 The Overlap Concentration c*As already mentioned c* represents an average segment concentration of individual coils. Such concentration is determined by the mass of the macromolecule and the volume that it occupies in solution

where M is the molar mass of the particle, VM its volume and NA is Avogadro's number. The molar mass can be deter-mined at infinite dilution by common techniques. However the volume of linear coils or highly swollen branched clusters' is not clearly defined since these objects have no defined surfaces. Nonetheless, well defined molecular volumes can be derived from three main considerations,

(i) Static light scattering measurements allow the determination of a radius of gyration, Rg, that is a geometrically defined radius. This radius gives a volume Vg=(4π/3)R 3

(ii) In hydrodynamics (viscosity, diffusion) the particles show behavior of equivalent hard spheres. Their volume may be denoted as Vhη, or VhD, respectively.

(iii) Thermodynamic interaction among the particles are dominated by a certain radius of action, and can be expressed by the strong repulsion of equivalent hard spheres. The corresponding volume be Veq.

An easy way to measure Vh results from the intrinsic viscosity, or viscosity number [η] that is given by the equation

which with eq (1) yields [5]

The definition of cη* is appropriate in discussing the hydro-dynamic properties of semidilute solutions. On the other hand, the thermodynamic interactions between two particles in solution are expressed by the second osmotic virial coefficient A2, that in terms of Veq is given as [6]

from which one finds

The second definition is especially adapted to the discussion of static properties in semidilute solutions [7, 8]. In the following mainly the data from static light scattering (LS) are considered. Since A2 can be directly obtained from the concentration dependence of the scattered light intensity, we will use here eq (5) as definition for c*. The two overlap concentrations of eq (3) and eq (5) differ in most cases [8]. For linear, flexible chains the dimensionless ratio (A2M)/[η]=c[η]*/cA2* in-creases first with M for short contour lengths but approaches a constant value of about 1.15 in the limit of large M [7, 9,10]. For branched structures the asymptotic plateau is reached apparently much earlier. Its value increases to 1.5-2.0, depending on the branching mechanism. For amylopectins in 0.5N NaOH a value of 1.5±0.2 was found [10].The second virial coefficient and the overlap concentration decrease with increasing molar mass for all polymer structures except for hard spheres for which it remains constant. This is a typical result of particles with a disordered internal structure that has to be dealt with statistical means. One re-cent approach of describing such systems is that of assigning a fractal dimension to the particle [11]. A structure is called a fractal when its mass follows the relationship

which gives

Table 1. Molecular Parameters of 9 Starches of Different Amylose Content.Mw

: weight average molar mass, Rg radius of gyration (z-average), p = amylose content (p = 1: pure amylose). The amylose content was estimated by the iodine binding capacity. cA2*: overlap concentration(eq (5)).

Eq (6) is a definition for the dimensionality of a particle. This is recognized when the Euclidean bodies of a sphere, disc and a rod are considered for which we find df=3,2, and 1, respectively. For polymers the dimension df is not an integer but can have values between 1 and 3. Thus, df is a fractal dimension. To give examples, the fractal dimensions for linear chains in a good solvent is df=1.67 and for randomly branched clusters in a poor solvent (reaction bath) it is df=2.5 [12]. The values of cA2* from a number of starches studied by us are collected in Table 1 together with some other characteristic molecular parameters. Figure 2 shows the plots of cA2* against Mw and amylose content p, respectively. There is a fairly large scatter of the data, and the dotted lines were drawn here to guide the eye. If according to eq (7) power law behavior is assumed one would obtain for the fractal dimension a value of df=1.42. This low dimension stands in strong contrast to the fractal dimension of about 2.3+0.15 that was determined previously by other techniques [13] for amylopectin.

3 Theoretical BackgroundThis chapter gives an overview of relationships which are already known to hold for semidilute solutions of non-associating macromolecules. These relationships are fairly complex but will be needed for a deeper understanding of the processes. On the other hand, the phenomena shown here are pronounced and will widely explain themselves. In a frist reading this chapter may be skipped and can be consulted later on.

3.1 Theoretical background:

Quantities measured by static light scatteringMolar masses can be efficiently determined by light scattering [14,15]. Less known is that also the interparticle interactions and the size and shape of the macromolecules can be obtained by the same technique. The relevant quantities are usually evaluated from Zimm plots [16]. Here the normalized reciprocal scattering intensity (Kc/R0), measured at different scattering angles 0, is plotted against q2+kc where q=(4πn0/λ0) sin(0/2) is related to the scattering angle 0; λ0 is the wave-length of the used light, c is the concentration and k is a suitable constant which prevents that the curves from the various concentrations fall upon each other. K is an optical contrast factor that depends on the difference in the refractive indices of the solution from the solvent. Finally R0 = r2i[(0)/I0] is the Rayleigh ratio of the scattering intensity, i(0), and I0 is the primary beam intensity; r is the distance of the LS detector from the center of the scattering cell.The Zimm plot yields a set of parallel straight lines for linear flexible chains. Such straight lines are easily extrapolated to zero scattering angle 0=O. This value from the so called forward scattering intensity is an important thermodynamic quantity [17] that is discussed in the next chapter. For

branched structures, however, the angular envelope is not linear in a Zimm plot but shows a curvature at small q-values that can cause difficulties in the required extrapolation [18]. In these cases a modification of the Zimm plot, first introduced by Berry [19], gives a linearization over a wide range of scattering angles. In the Berry representation the root of (Kc/R0) is plotted in the same manner as proposed by Zimm. (The differences between a Zimm and a Berry plot are collected in Table 2).The inset in Figure 3 gives a typical example for waxy maize in the dilute regime. Such a Berry plot (as well as a Zimm plot) has two limiting curves:(1) The one, 0=0, results from the extrapolation of the scattering curves to zero scattering angle. This curve is solely determined by the solution thermodynamics and gives quantitative information on the interparticle interactions [8, 17].(2) The second one, c=0 results form the extrapolation of the scattering data for each scattering angle towards the concentration c=0. The resulting angular dependence gives information on the size and shape of the individual macromolecules [14, 15, 18].Both limiting curves should intersect the ordinate at the same point that determines the molar mass (1/MW in the Zimm and 1/Mw

½ in the Berry representation). The initial

Figure 2. Molar mass dependence of the overlap concentration c* in a double logarithmic plot (above), and the corresponding dependence on the amylose content p (below). The dotted lines are drawn to guide the eye. The slope of the straight line, —1.12, in the upper part of the Figure would give a fractal dimension of df=1.15 (eq (7)) a result that is at variance to the fractal dimension directly obtained from the molar mass dependence of the radius of gyration [13].

Table 2. Difference Between a Zimm and a Berry plot. The Zimm plot is appropriate for the study of linear chains. For branched and globular structures it shows a curvature at small q-values. This part becomes linearized when using the Berry plot.

slope of the angular dependence of the curve c=0 gives the mean square radius of gyration, Rg2 in a

different way for the Zimm and Berry plots, respectively that are listed in Table 2. The slope for the Berry plot is

The mean square radius of gyration is geometrically defined. It is the mean square distance of the various segments from the center of mass of the particle.

Here, N ist the number of segments (monomer repeating units) in the macromolecule, rj the distance of the jth segment from the center of mass, and the angled bracket, < >, de-notes the average over all orientations and distance fluctuations around a mean distance. Thus, from the intercept the molar mass Mw and from the slope the radius of gyration R. are obtained.The parallel lines in the Berry plot of Figure 3 (inset) suggests to take the points at zero scattering angle for each concentration as a reciprocal molar mass, that now depends on the concentration. It will be denoted as Mapp(c). Similarly, the slope can be taken as a measure of a radius at this concentration but this again will be an apparent radius of gyration Rg,app(c). Instead of eq. (8) one now obtains for the slope

3.2 Theoretical background: the osmotic modulus and its influence on the apparent quantitiesAccording to Einstein [20] the forward scattering intensity (R0=o) is caused by concentration fluctuations. These can be expressed by the osmotic compressibility RT(δc/δπ) and is given by

in which π is the osmotic pressure and K the already defined optical contrast factor, that can be measured separately. For practical reasons it is often more convenient to use eq (11) in its reciprocal form

The right hand side of eq (11) is actually an inverse osmotic compressibility which conveniently we will call an osmotic modulus.The apparent molar mass Mapp(c): The osmotic pressure can be expanded as a power series in terms of the concentration

Figure 3. Berry plot of angular dependent scattering data for waxy maize in a wide concentration range up to 30% (w/v). The inset exhibits the behavior in the very dilute concentration regime (c<0.1%).

where A2, A3 etc. are the osmotic virial coefficients. The whole sum in the square brackets denotes the interparticle interactions [8,21,22]. Eq (13) demonstrates how the true molar mass is modified by the interactions. The term in the brackets can be simplified as follows.• A2MWC=C/ cA2* = X. (eq (5)).• the 3rd virial coefficient can be expressed in terms of the second virial coefficient [7, 8, 21]

where ga is a structure dependent parameter that is 0.625 for hard spheres but 0.269 for coils of flexible chains. Other examples will be shown in the chapter Results.• Eq (13) suggests that the interaction term is a unique function of c/ cA2* =X.Thus the apparent molar mass can be expressed in terms of a scaled concentration as [3, 22, 23]

in which f(c/ cA2* ) is a homogeneous function of the scaled concentration [23]. The universality of this scaling is seen in the fact that it does not make a difference whether the concentration or the molar mass is varied: the same function of Mw/ Mapp(c) is obtained whatsoever the molar mass of the sample may be when X≡c/ cA2* =A2Mwc is used as parameter. The apparent radius of gyration: The angular dependence of scattered light is caused by destructive interferences of scattered rays emitted by different points in the particle. According to the general theory of scattering [14,15] the initial part of the normalized scattering intensity can be developed in any case in a series with the universal initial slope

The function Papp(q,c) ≡ Papp(q,c) ≡ R0(c)/R0=0(c) is called an apparent particle scattering factor. The name originates from its dependence at large q2 that is characteristic of the particle structure. The true particle scattering factor P(q) is obtained by extrapolating Papp(q,c) to zero concentration, as it is done in a Zimm or a Berry plot. Since R0=o(c) ∞ Mapp(c) one finds with eq (13) and eq (16) and from the condition that the slopes of the curves remaine unchanged

where Rg(c) and Mw(c) are now the true radius of gyration and the true molar mass at the concentration c which are no more distorted by the intermolecular interactions. Both quantities on the left hand side of eq (17) are measurable. Therefore, if the ratio of the left side remains constant, no change in molar mass and structure will be observed when the concentration is increased.

4 Results and Discussion

4.1 The osmotic modulus

Five starches (waxy maize, potato, wheat, amylomaize and wrinkled pea) were investigated in detail. Their molecularta and the amylose content are listed in Table 1 together with the overlap concentrations. The results of these different starches will be discussed separately. A common conclusion will be drawn at the end.

Waxy Maize starch: The concentration was varied here from 0.01% to 30% (w/v). Figure 3 shows the Berry plot of the scattering data. The dilute regime (inset of Figure 3) is represented by the lines near the origin. Two facts are immediately recognized, (i) The angular dependencies form a set of parallel curves up to a concentration of about 0.4% (cA2* =0.31%). Then a strong downturn at small angles occurs which eventually dominates the angular dependence, (ii) The to zero scattering angle extrapolated points at first increase with the concentration but the curve flattens then off to a much weaker increase.These to 0=0 extrapolated data are l/[Mapp(c)]1/2 and the ordinate intercept is 1/[MW]1/2. Since also cA2* is known, we can plot MW/Mapp(c) against X=c/ cA2* . This is shown in Figure 4 as a double logarithmic plot. The Figure also contains the theoretical curves for hard spheres [25] and for flexible coils [26] and the experimentally determined curve for acid degraded potato starches in 0.5N NaOH [27], The curve for the reduced osmotic modulus is apparently well described by the curve from the degraded starches up to about X=c/ cA2* ; then the curve for waxy starch in water flattens off. The changes in behavior are even better demonstrated with the graphs of Figure 5 a where the ratio of the apparent mean square radius of gyration to the true mean square radius of gy-ration R2

g,app(c)/Rg2 is plotted against X. A drastic change in behavior occurs at about X=1.4 (c=0.45%). Figure 5b shows the same data but now corrected for the contribution of interparticle interaction (eq (17)). We see that the dimensions do not change up to the overlap concentration, but when the overlap concentration is increased a drastic increase of the dimensions is observed. Evidently some large heterogeneities are building up. Here it appears necessary to emphasize that this effect is not due to incomplete dissolution, because the results are obtained from different series of dilution starting with 0.1%, 10%, 20% and 30% stock solutions, respectively. Still the same curve was obtained.

Figure 4. Variation of the reduced osmotic modulus (Mw/RT)(δπ/ δc)=Mw/Mapp(c) as a function of the scaled concentration X=A2-Mwc=c/ cA2* . The solid lines correspond to theories for hard spheres [25] and flexible linear chains [26], the dotted line represents the behavior found for acid degraded starches in 0.5N NaOH [27].

Figure 5. (a) Dependence of the normalized apparent mean square radius of gyration Rg,app(c)/R| on the scaled concentration X=A2-Mwc=c/ cA2* (b) Plot as in (a) but now corrected according to eq (17).Potato and amylose rich starches: Potato starch differs from waxy maize starch by an amylose content of 22% and a weak substitution by phosphate esters [28,29]. The Berry plot is shown in Figure 6. A similar appearance as with waxy maize (Figure 3) is obtained up to c=0.3% w/v (c*=0.22%). Then, however, in contrast to waxy maize, the concentration dependence decreases again. The effect is better seen in Figure 7 where the reduced osmotic modulus [(Mw/RT)(δπ/ δc) =Mw/ Mapp(c)] is plotted. The downturn at moderately high concentrations indicates a strong increase in the molar mass Mapp(c). This effect results from a growth of the particle weight. Appar-ently association occurs, because at concentrations between 8 and 15% (depending on the molar mass) gelation occurs. This critical concentration of gelation agrees well with Theological findings [30].The behavior of the reduced osmotic modulus for the two amylose-rich starches follows at first again the universal curve, but deviations occur already at c>0.6% (X=0.4) for amy-lomaize and at c>0.15% (X=0.08) for wrinkled pea starch. Gelation sets in abruptly now already at concentrations of about 2% and 1.2%, respectively. Apparently the amylose content has a strong influence on the tendency to association. Wheat starch: The wheat starch displayed properties which deviate from this general picture. Similar as was done with the other starches, stock solutions were prepared by autoclaving suspensions of 0.1%, 1.0% and 5%, respectively. However, we did not succeed in a complete dissolution of the starch at high concentration. The molar mass of the starches changed from 63.8x 106 to 984x 106 as the suspension concentration was increased. The relevant particle parameters are shown in Table 3. In spite of the fact that all these parameters change with the particle weight the osmotic modulus exhibits one common curve (Figure 8) which agrees well with that of the other starches and confirms the universality of this function.

The best fit of the data from acid degraded potato starches in 0.5N NaOH is shown in Figure 7 by the dotted line that runs between those for hard spheres and flexible coils of linear chains. Two conclusions can be drawn: (i) The reduced osmotic modulus is evidently an universal curve for starches, independent of the solvent used, if the overlap concentration is not exceeded. It can be described by the fit equation [37]

(ii) There is a clear influence of the amylose content in the starches, which stimulates association and gelation. The point of gelation is shifted from >30% for amylose free starch (waxy maize) to ca 10% for potato starch down to about 0.3% for the amylose rich starches.The two observations may be commented as follows. As long as the concentration is smaller than the overlap concen-

Figure 6. Berry plot of the data from potato starch, (compare Figure 3).

Figure 7. Change of the reduced osmotic modulus for several starches (symbols). All other curves as in Figure 4.

Figure 8. Plot of the reduced osmotic modulus as a function of X=A2-Mwc=c/ cA2* for wheat starch. The data result from 3 different series with different overlap concentrations cA2* given in Table 3. Still the same curve is obtained that also agrees with the results from the other starches and with universal fit curve derived from degraded starches in 0.5N NaOH [27].tration there will be only a weak coil interpenetration. This in-terpenetration is not hampered because the chains at the outside of the starch particles contain no obstacles (branching points) and can interpenetrate to some extent. In this respect all starches are similar, and therefore universal behavior can be expected. The curve runs between those for flexible coils and hard spheres. This again is sensible, since the branched structure can be regarded as a spherical object but with a den-sity profile around the centre of mass that lies in between of the bell-shaped Gaussian distribution for linear chains and a homogeneous density for hard spheres. Waxy maize starch: Deviations are to be expected at larger concentrations because the chains from the various starches have increasingly difficulties to interpenetrate. Disregarding for a moment association, the system has under this constraint only the possibility to de-swell under the action of the osmotic modulus. One consequence of this de-swelling is an increase of the overlap concentration or a decrease of the effective Xeff=c/ceff*. Since no gelation was observed with the waxy maize, such a de-swelling seems here to be effective: The shift of the data to larger X is then actually due to a change in the overlap concentration (increase of the segment density) as a consequence of de-swelling. This reduced swelling can be approximated by the relationship

in which cA2*=l/(A2Mw) is the overlap concentration that was determined in the dilute regime and X= cA2*, while Xuniv governs the relationship of eq (17).The strong increase of the apparent radius of gyration Rg,app(c) when the overlap concentration is exceeded seems to contradict this interpretation. Here we have to mention that this radius is not necessarily the radius of an isolated particle but rather is a correlation length that describes the aver-age distance at which the segment density has decayed to 1/e of the segment concentration at a selected position in space. Thus, molecules which are randomly squeezed together may exhibit a large correlation length, that is measured by the interference effect in light scattering although there may be no association. A random packing of particles does not cause a change in the molar mass Mw and no change in the reduced osmotic modulus. Figure 9 shows the ratios of reduced swelling for the amylopectin molecules as a function of c. Of course, this curve represents an idealization; the osmotic modulus may very likely change towards a more hard sphere behavior, and association cannot be fully ruled out. Amylose containing starches: The quantitative interpretation of these starches is complex because of two facts. The one consists in the effect of association that is stimulated by the amylose, and the second one is the blend character of these starches i.e. the coexistence of fairly small linear amylose molecules with the extremely large and highly branched amylopectins.

Figure 9. De-swelling ratio of waxy maize starch at high concentrations. The data were calculated from the deviation of the measured data from the master curve [27] assuming that there is no association.

The overlap concentration would be a "simple" average of the overlap concentrations of both components if there were no association. The word "simple" should indicate well defined, although at present it is not fully clear which type of average is effective in the second virial coefficient. The actually existing association makes a definition in terms of both components even more complex. However association evidently occurs and becomes manifested by the occurrence of a critical concentration of gelation. Thus, cA2* has to be considered here only as an empirical parameter. Indeed, Figure 2 demonstrates that there is a correlation between the amylose content p and the overlap concentration, but no strict dependence. These findings agree with recent Theological measurements by Vorwerg and Radosta [30] who found an increase of the elastic modulus of formed gels for amylose containing starches, but not a clear relationship. As already outlined, the fractal dimension derived from the slope in Figure 2 (above) gave an unreasonable value which is now recognized as a result of the blend character of amlyose with amylopectin and a not yet fully understood aggregation process. Furthermore, the curve in Figure 2 (below) has a sigmoidal shape rather than that of a straight line. This curvature would indicate a certain coopera-tivity induced by the amlyose.In addition to the de-swelling we now have to consider also an increase in the true molar mass Mw(c) of the particle at the concentration c. Therefore, instead of eq (13) we have to write

where Mw and Mw(c) are the true molar masses at c=0 and finite concentration, c, respectively. This change of the molar mass due to association makes a quantitative interpretation very difficult although not unfeasible [8]. Qualitatively, we can make the following observation. The expression in the curled brackets is a weakly with the concentration increasing function; but a growth in the molar mass Mw(c) necessarily must cause a strong decrease in Mw/Mapp(c). Gelation occurs when Mw(c) increases beyond all limits where Mw/ Mapp(c) →0.

4.2 Time dependent associationA decrease of the reduced osmotic modulus also can be caused by a phase separation. According to basic thermodynamics, phase separation takes place when the expression in the curled brackets of eq (20) becomes zero (spinodal curve). Such phase separation is unlikely with pure amylopectin, because experimentally there was observed no pronounced turbidity that suddenly occurred and that was controlled by the temperature. A different situation exists, however, when amylose is present.Amylose does not form a stable aqueous solution. It can be dissolved in hot water when starting with an amylose in its disordered state [31]. However, this solution enters a metas-table state when the temperature is decreased below 80°C. The molecules undergo a disorder-order transition (double helix formation) [32] that is accompanied by aggregation [33].

Figure 10. Intensity time correlation functions from a 2% amylo-maize starch solution measured in time intervals of I5 min. The intercept of these curves decreases as a result of heterodyne scattering and simultaneously the curves are shifted to larger delay times, which indicates a slowing down of the translational diffusion.

These aggregates are not random in structure but form a crystalline phase. If this crystallization is sterically hindered it leads to gelation [34]. This gel is not in thermodynamic equilibrium and develops typical ageing effects during that further crystallization takes place.Therefore, we have to expect a liquid/solid phase separation also with the amylose containing starches, that is superimposed by aggregation phenomena. A typical sign for metas-table solutions is the effect of a slowly in time progressing aggregation or crystallization, where the rate of aggregation depends on how deeply the system has been conducted into the region between the coexistence curve and the spinodal decomposition. (Spinodal decomposition is defined by the con-dition that the osmotic modulus becomes zero, in the present case, by the condition Mw/Mapp(c)=0).We have performed dynamic light scattering measurements for the five starches with 2% solutions at 20°C. In dynamic light scattering a time dependent intensity correlation function is measured. This intensity time correlation function (TCF), <i((0)i(t)>, is formed by an autocorrelator, that essentially is a fast computer that multiplies the scattering intensity i(0) measured at a certain starting time with i(t) that was measured a very short time interval t later. When changing the time intervals t the TCF decays exponentially to a base line, and this happens around a characteristic relaxation time r0. This relaxation time is related to the translational diffusion coefficient D. The diffusion coefficient on the other hand is related to a hydrodynamic equivalent sphere radius Rh via the Stokes-Einstein relationship [35]

Thus, when the particle increases in size the diffusion proceeds more slowly, i.e. the relaxation time τ0 becomes larger. Figure 10 shows a set of such time correlation functions G2(t)=<i(0)i(t)> for a 2% amylomaize starch. The measurements have been made at 20°C in time intervals of 15min. Two observations can be made:(i) The curves become shifted to larger delay times. This indicates a growth of the particles.

(ii) The intercept of the ordinate decreases with elapsing time. This effect is known in dynamic light scattering as heterodyne scattering. Its value is given by the relationship [36]

Figure 11. Variation of the heterodyne contributions with ageing time for the five starches of this study at concentrations of 2% (lower part) and the growth of particles, expressed by their hydrodynamic radii Rh (upper part).

In this equation is β an equipment dependent constant, that has to determined separately, and x is the so called homo-dyne fraction of the dynamically scattered light. The fraction 1-x denotes the heterodyne contribution. It results from particles which move only very slowly and scatter strongly the light. In the present case it can be considered to arise from the aggregated particles. Its value depends on the product of the particle's molar mass and the mass fraction of these particles.Figure 11 shows how this heterodyne contribution changes with time for a 2% solution of the five starches of the present investigation. No heterodyne contribution was found for waxy maize and potato starches at this concentration. The two amylose-rich starches on the other hand developed a pronounced increase of this fraction with time. The increase of the relaxation times have been transformed into hydrodynamic radii which are shown in the upper part of Figure 11. We can conclude that both, the particle size and the mass fraction of aggregated particles, grow in time. We have not yet evaluated the kinetics of these processes, but the indications of these experiments are that a diffusion limited phase separation takes place.

5 ConclusionsSemidilute solutions comprise a concentration region between 5 to 30% (w/v). This range is typical for industrial application of thickeners in food chemistry and in the non-food area. The region of semidilute solutions of branched macro-molecules has not yet been much studied. This unexplored area of research was recently entered by our group [4,27, 37] and is continued here with native starches. No basic theory has been developed so far. The present study tried to establish a simplification of the very complex dependencies on many

parameters. The scaling concepts, successfully introduced by de Gennes [3] for an universal discription of linear and flexible chains is extended here to branched polymers. The concept led to universal behavior for the osmotic modulus as long as the overlap concentration was not much exceeded. From this observation a non inhibited interpenetration of the chains at the outside of the branched macromolecules can be concluded. Beyond this concentration deviations occurred that are characteristic of the various starches. Amylose free starches and amylose containing starches have principally to be distinguished.In pure amylopectin mainly an impeded interpenetration of the various branched macromolecules led to a shrinking of the molecular dimensions and thus to an increase in the overlap concentration. Gelation did not take place but a weak (reversible) association had also to be taken into consideration.Amylose containing starches, on the other hand, developed a pronounced tendency of (irreversible) aggregation. It occurred at lower concentration for amylose rich starches than for starches with low amylose content. No equilibrium state was reached. The aggregation proceeded in time until ge-lation took place. Even these gels were not in thermodynami-cal equilibrium but showed ageing. A diffusion controlled liquid/solid phase separation is evidently the driving force for the observed phenomena.The time dependent aggregation process could be quantitatively registered by dynamic light scattering. A slowing down of the diffusion coefficient was observed that indicated a growth of aggregated particles. Simultaneously the so called heterodyne fraction increased. It gave evidence for a strong increase also of the mass fraction of the aggregated clusters.

6 ExperimentalThe applied methods for characterization and the description of solution preparation are the same as given in a previous paper [1]. A difference exists only in the use of a Buechi autoclave, that is made of glass and could be used up to pressures of 12 bar. In contrast to the formerly used Roth autoclave the sometimes rather viscous suspensions could mechanically be stirred even during the process of gelatinization. Temperatures between 135 and 165°C were applied for 20 minutes. For convenience, to avoid cross checking with earlier papers, we repeat here some of the relevant details.

6.1 MaterialsThe number of starches was increased by three further types (wheat, barley and rice) such that now 9 different starches could be prepared. The optimum dissolution temperatures had to be found by trial and error. The dissolution process caused in most cases no serious difficulties, but wheat starches could be molecularly dissolved only for the very dilute suspensions (c<0.1%). Stock suspensions of higher concentration led to higher molar masses and the other parameters connected with it. This particularity was discussed in the main text.All starches were de-fatted with a mixture of n-propanol/ water=3/l at 80°C for about l0h. The propanol/water mixture was exchanged three times during that period. After filtration the suspension the starches were dried at room temperature under oil-pump vacuum.

6.2 Determination of the amylose contentThe amylose content was determined via the iodine binding capacity (IBC). The starches were titrated with a potas-

sium iodide/iodate solution and is described in detail by Banks and Greenwood [38]. An automated titrator was used (Titroprocessor 636, Dosimat E635, Polarisator E 585: all products of Metrohm, Herisau, Switzerland). The composition of the titration solution was: 0.084g NaHCC>3 dissolved water, 1.9362g KI was added. After dissolution 0.1783g KIO3 was added, and the whole solution was filled up to 1L H2O. The solutions was stirred in a brown flask. The IBC of 20.5% (w/w) for pure (synthetic) amylose was taken as basis for comparison with the starches.

6.3 Light scatteringMostly static light scattering measurements were made in this study. A modified SOFICA light scattering pho-togoniometer was used that was fully computer driven (Baur Instrumentenbau, Hausen, Germany). A 2mW HeNe laser was the light source (λ0=632.8nm). Measurements were made at scattering angles between 30° and 145° in steps of 5° at 20" °C. For calibration of the Rayleigh ratios (normalized scattering intensity) the data of ref. [39] were taken. All characteriza-tion started with the dilute regime (c=0.1%) from which the molecular parameters Mw, Rg and the second virial coefficient A2 were obtained and the overlap concentration cA2* = l/ (A2Mw) was derived. The concentrations were then increased. In all cases stock solutions of different concentrations were prepared by autoclaving. These were diluted to prepare 5 to 10 different concentrations. In most cases the same concentration dependence was found for the osmotic modulus. Only wheat starch displayed characteristic deviations which were discussed in the main text. Even for this starch the same master curve as for the other starches was obtained when Mw/ Mapp(c) was plotted against c/ cA2* .

AcknowledgementThe one of us (W. B.) is indebted to Dr. W. Vorwerg and Dr. S. Ra-dosta, Fraunhofer-Institute for Applied Polymer Research in Teltow, for revitalizing his interest in the intriguing structural problems of starch. As members of the Amylose Association (Amyloseverbund) the work was partially supported by the Federal Ministry of Education and Research (BMBF).

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Address of authors: Dr. Thomas Aberle and Professor Dr. Walther Burchard. Institut fur Makromolekulare Chemie, Universitat Freiburg. SonnenstraBe 5, D-79104 Freiburg, Germany.

(Received: April 4, 1997).