Comment on the structure of amorphous starch as derived from

precursors of crystallization: the role of the entanglement network

R.K. Bayer*, F.J. Baltá Calleja

Instituto de Estructura de la Materia, CSIC, Serrano 119, 28006 Madrid, Spain

paper submitted to J. Macromol. Sci.- Phys.

February 2005

Keywords: Amorphous starch, SAXS long period, entanglement network, structure development.

*Permanent address: Universität Gesamthochschule Kassel, Mönchebergstr. 3, D-34125 Kassel, Germany

Correspondence to: F.J. Baltá Calleja (e-mail: embalta@iem.cfmac.csic.es)

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ABSTRACT

A model based on data about the critical entanglement molecular weight is proposed to

derive the statistical chain segment length, ls, of amylose. This value is somewhat larger than

one turn of the single helix molecule. This implies a high mobility of the amylose molecule,

leading to a statistical shape in which the V – helix of the amylose molecule is subjected to a

local varying extension. On the one hand, the model proposed explains the structure of the

amorphous state; on the other it allows the understanding of the formation mechanism of a

double helix from two single helices. Discussion of results assumes the formation of chain

entanglements through rapprochement of statistical single helix molecules. The direct

distance = 15 nm between entanglements in the amorphous phase can be calculated from

the ls value. It is shown that can be determined from X-ray scattering data which

characterize the early state of crystallization of amylose. Crystals are formed within the

amorphous matrix in the entanglement-free regions. Since some of the first crystals are

organized in lamellar stacks, as evidenced by SAXS results, their long period L provides a

first indication about the average distance between entanglements. The crystals appearing

during the first stages of crystallization, giving rise to the SAXS maximum, model therefore,

the distance between entanglements, which are segregated into the amorphous layers.

Previous X-ray experiments performed on injection molded potato and pea starch yield a

characteristic value of L = 15–16 nm during the early state of crystallization of amylose, in

accordance with the above-mentioned calculated value (The crystalline fraction remains

within the range of 7 – 12%). Results indicate that the entanglement network of an

amorphous starch melt is transferred into the solid state. The critical temperature is about

120 – 130ºC. The melt entanglement network thus, is a precursor of the amylose network of

the solid state. A second component of the amylose network, which leads to a densification

of the entanglement network, is also discussed. This secondary network develops from net-

points of double helices at lower temperature (70ºC) and defines the characteristic

temperature of gelatinization of native starch in water.

INTRODUCTION

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Starch, the polysaccharide of cereals, legumes and tubers, is a renewable and widely

available natural material suitable for a variety of industrial uses [1]. The two starch

polymers, amylose and amylopectin are structurally different and give rise to very complex

crystalline structures. X-ray diffraction of semicrystalline starch is characterized by the

presence of both relatively sharp reflections and broad diffuse maxima [2]. The former are

the result of coherent scattering from crystalline order and the latter originates from

incoherent scattering caused by disordered material. Recent investigations on amorphous

starch show that the WAXS – pattern consists of a superposition of various amorphous

components [3, 4]. Our own results reveal that the X-ray pattern of amorphous starch can be

decomposed into three symmetrical Gauss – curves [5]. By means of computer simulations

of the scattering of amylose molecules in different conformations, Müller [4] demonstrated

that two of the amorphous components can be attributed to single helices in statistical

random conformation, while the remaining component emerges from a statistical

conformation of left handed double helices. On the other hand, we suggested that double

helices aggregate into network regions that are connected by single helices [5]. On the basis

of this analysis, directly from the WAXS diagram, it was possible for the first time [5], to

quantify the amount of network regions in starch, previously postulated by Gidley [6]. This

author also suggests the possibility that the amylose network should not only arise by double

helix formation but also through development of entanglements [6]. Furthermore, Gidley

points out that the gelatinization of starch may be described solely by the formation double

helix regions. Nevertheless, one may question why entanglements should not play a role in

the formation of the starch network. Carriere, [7] Hulleman [8] and Jauregi et al [9] suggest,

indeed, that starch molecules may form entanglements too; Jauregi et al. even quote a

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critical molecular weight [9] for the distance between two entanglements along the amylose

molecule. Since, as mentioned above, starch molecules tend to bind themselves by

formation of double-helix complexes, one can imagine that analogous mechanisms would

lead to a strong chain coupling when helical molecules entangle with each other. This

should be the case, especially when molecular mobility is as low as in the solid state.

It has been suggested that the density of entanglements within a polymer, does not change

after crystallization from the bulky melt (as in the case of injection molding) into the solid

state [10]. In a previous study [11] we showed that superstructures of entanglements (knots=

multi-chain coupling) are transferred from the melt into the solid state leading to the

formation of the amorphous layers of thickness la segregated between the lamellar crystals

with an average thickness lc. The occurrence of regular lamellar stacks can be described by

the long period, L, which is the sum of the average values of la and lc. The L-parameter that

can be derived from SAXS, is correlated by means of la in a characteristic manner to the

structure of the melt. We proposed that the lc-value cannot grow beyond the maximum

extension of an entanglement mesh (in case of polyethylene, for example, lcmax = 25 nm

during rapid crystallization [11]). However, this straightforward correlation of lc to the melt

structure is affected by the influence of the crystallization conditions: in case of increased

cooling rates from the melt, thinner crystals are formed, exhibiting besides entanglements

also chain folds on the crystal surface. If the density of entanglements after crystallization is

preserved, then at high supercoolings the long period decreases and, as a result, the number

of folds at the crystalline–amorphous interface, increases.

The crystallization of starch in the A- and B– polymorphic modifications is attributed to

parallel portions of extended double helices. However, it does not seem reasonable to

assume that immobile double helices could form folds on the crystal surfaces. It seems more

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meaningful that the limiting factor of amylose crystallization is caused by the net-points of

the three-dimensional amylose network. In this case the crystalline structure of amylose

corresponds probably more to a fringed micelle than to flat lamellae. Therefore, the long

period of semicrystalline amylose could be related directly to the distance between net-

points, i.e. average spacing between crystalline domains.

The aims of the present work are:

- To analyze previous results on the long period derived from SAXS – patterns of

crystallized starch.

- To examine the influence of the entanglements on the amylose network. Special

emphasis will be made on the structure transfer from the polymeric melt into the

solid state.

- The early state of crystallization is of particular interest, because the limitations

of crystallization in this case are only due to molecular obstacles of the melt

structure and not due to already existing crystals, as in later states of

crystallization (formation of inter-lamellar secondary crystals).

- To detect the contribution of entanglements within the starch network. For this,

the structure of the amorphous material will be analyzed in the vicinity of the

molten state when the first regularly arranged crystals are formed, by the “probe”

formation of crystallization. As entanglements are preferentially localized outside

of the crystals, the crystals themselves model the entanglement free regions of

the melt.

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RESULTS AND DISCUSSION

To carry out a first elucidation on the issues in question we have analyzed preceding X-ray

scattering results concerning the behavior of long period, L, and crystallinity, Xc during the

first stages of crystallization [5]. These results can be summarized as follows:

- During retrogradation of amorphous potato starch in a saturated humid atmosphere,

after 10 min at room temperature (RT), L 16 nm, showing at longer times small

changes. The value of L 16 nm is typical for the early state of amylose

crystallization (Xc 7%).

- Crystallization of potato starch at RT (20 days) in a humid atmosphere leads to a

crystallinity of 65%. This structure melts at 85ºC. Short before the last crystal

disappear ( 80ºC) a long period L = 15.6 nm has been measured.

- Pea starch (amylose content: 76%) is treated in the same way (20 days in a humid

atmosphere at RT) leading to a final crystallinity of 25%. When the sample prepared

in this manner is heated up to 40ºC, a crystallinity of 12% still remains and a long

period L = 15 nm is measured.

It is noteworthy [12], that the amylose component of potato starch crystallizes before the

amylopectin fraction. In summary, a limiting value of L = 15.0–16.0 nm is found for the

various stages of crystallization of amylose in the vicinity of the completely amorphous

state.

Flexibility of Single – Helix – Amylose Molecules

Let us recall that the entanglement network of amylose is defined by the critical molecular

weight Mc, i.e. the relative molecular mass of the chain between two entanglements:

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Mc = 29.400 [9]. The monomer unit of starch (anhydrous-glucose, AHG) has the molecular

weight, MAHG = 162. Therefore, the critical molecular weight, Mc , corresponds approximately

to 182 starch monomers. On the other hand, according to Wu & Sarko [13] the length of the

monomer (virtual bond length VB) may be set as: VB = 0.425 nm. From the Mc-value the

curvilinear length sc between two entanglements is derived as sc = 182 x 0.425 nm = 77.4 nm.

From our previous calculations [11, 14] sc is correlated to the length ls of the statistical chain-

segment through the expression:

sc = ls (1)

where = 27 is Rault’s degree of interpenetration of chain molecules, which is derived from

the statistical shape of the molecular coils in the melt [15]. The parameter is a universal

constant and, thus, can be applied to the molecules of starch. This yields for the statistical chain

length of linear amylose a value: ls = 2.87 nm, corresponding to 6.74 AHG units and 1.12 turns

of the single helix. This result suggests that the single starch helix apparently can be easily

bent. Fig. 1 shows a schematic representation of a 180º bending of the single helix which

involves freedom of rotation about six single backbone bonds between the saccharide

monomers. As an approximation, ls is shown here, as one turn of the single helix, starting at

point A and ending at point E.

If one turns the single helix at point 0 by 180º, the final point E changes to E’. If a smaller twist

is applied, the end of the helix turn is located on a circle perpendicular to the plane of the

paper. If the twist is delocalized from 0 to any point of the turn, between A and the end, every

chain direction has the same probability to be reached with respect to the initial direction at A.

This picture shows descriptively, that the condition ls = 1 turn of the helix, fulfills the definition

of the statistical chain segment. Hence, the derived value for ls seems meaningful. Following

Müller [4], if one considers a collapsed, energy minimized single helix, then the number of

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monomers per helix-turn increases from 6 to 6.2. Hence, the calculated value of ls

approximates the conformation of one helix turn.

Formation of a double helix from two single helices

In a preceding X-ray scattering study we proposed that [5] single helices should be capable

of approaching each other in such a way as to coalesce into double helices, leading finally to

their organization into double-helix crystals. In what follows we wish to discuss why the

180º - bent state of the double helix is a meaningful forerunner for the formation of double

helices from single helices.

According to Zobel [16], one turn of the single helix is characterized by a projected distance

of 0.82 nm (see Fig. 1, from A to E). V–crystals of starch consist of regular packings of

ordered single-helices. Immelmann and Lichtenthaler [17] obtain for the diameter of the

single helix a value of 1.35 nm, which leaves in the center a hollow channel with a diameter

of 0.54 nm. Zobel [16] calculates for the longitudinal periodicity of the double-helix a

distance of 2.14 nm. The diameter of the double helix is calculated to be 1.03 nm [19], i.e.

much smaller than the diameter of the single helix. Single helices within the double helix

are, hence, much more extended than the regular single helix. The elongation ratio from the

lengths of the respective helix-turn lengths yields:

= 2.14 nm / 0.82 nm = 2.61 (2)

The - value entails two contributions: If one assumes that two equal spiral springs (as in

Figure 1 for the regular single-helix) interpenetrate within the diameter of one spiral spring,

then both springs have to be stretched by a factor 2. The resulting double-helix would

exhibit the same packing density as the single helix. Obviously, due to strong molecular

interactions, this state is not stable, which leads to a complete disappearance of the inner

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hollow channel. This provokes a lateral contraction, as well as an additional elongation

above 2. Since the electron density of the starch molecule remains constant during this

process then: = 2V = 2.61, which leads to:

V = 1.31 = 1 + V and: V = 0.31 (3)

where the draw ratio V results from the complete disappearance of the inner (hydrophobic)

channel of the single helix.

Let us next test the above conclusion. The shrinkage of the inner-volume during the

penetration of two single helices is equal to:

V / V= - (0.54 nm /1.35 nm)2 = - 0.16

V / V= 2 q + (4)

where is the elongation due to the shrinkage of the inner-volume. The lateral contraction q

derives from:

q = (1.03 nm / 1.35 nm) - 1 = - 0.24 (5)

Using equations (3-5) and taking into account equation 3 one obtains:

= V / V - 2 q = - 0.16 + 0.48 = 0.32 (6)

This value is approximately equal to that of V in equation (3). Therefore, the additional

extension V = 0.32 corresponds precisely to the volume contraction V / V = -0.16.

After turning the single helix shown in Fig. 1 by 180º from point A to point E’ it maintains its

helical nature. If one now uses the data of the single helix conformation within the contracted

volume (diameter: 1.03 nm; longitudinal periodicity 1.31 x 0.82 nm = 1.07 nm), one obtains

from Fig. 1: AE’ = 2.17 nm which corresponds to the periodicity of the single helix as part of

the double helix (2.14 nm, [16]) as mentioned above. As a result, the completely wound-off

single helix of the amorphous state corresponds to the conformation of the extended single

helix within the double helix. If 180º wound-off single helices approach to each other, there is

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no more change in the conformation besides the shrinkage of the inner channel necessary to

form a double helix. In our preceding study [5] the approaching single helices were considered

as forerunners of a double helix. In this case, they should be visualized as 180º twisted single

helices; i.e. single helices, which form a double helix, first must change their conformation

towards 180º wound-off single helices.

Finally, to justify the proposed value of ls it is necessary to postulate a strongly wound up

single helix structure. This is confirmed by the conformation of the single helix belonging to a

double helix. In other words, the formation of a double helix requires an easy extensibility of

the single helix.

Entanglement development from single helices

The high flexibility of the single helix, which is determined by the size of l s , has a serious

consequence on the conformation of a single helix in the amorphous state. Fig. 2 depicts

schematically the shape of a single helix, with its helix-turns statistically wound up. In spite

of its helical character the starch molecule sketched in Fig. 2 exhibits a statistical shape.

This conformation, based on the ls-size, explains why Zobel [16] correlates the disorder of

the amorphous state to the single helices and why Waigh et al. [18] postulate a transition

between the double helix and the disordered single helix. The molten state of amorphous

starch consists of statistical chain molecules as illustrated in Fig. 2. Similarly to the case of

other linear polymers, such molecular conformations caused by the entropy increase must

form entanglements. Statistically wound-up starch single helices form a fluctuating network

of entanglements (Lodge elastic liquid [19]). In the foregoing we have seen that the distance

between entanglements, along the molecule, is 74.7 nm [section 2.1]. The direct distance

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from one entanglement to the next one is given in ref [11, 14]. By using the known values

for ls and one obtains:

= 1/2 lss = 14.9 nm. . (7)

As crystallization does not significantly change the radius of the coiled polymer molecule

[20], the long period L should correlate with (see introduction)It has been shown that

the early crystallization state of amylose leads to values for L = 15–16 nm, which are

close to

The net-points of the amylose network, which control the crystallization process, seem

hence to correspond to regions of entanglements in the melt. The control of the

entanglement network by the processing conditions (processing temperature, rate of cooling,

amylose content, etc) should, thus, influence the swelling and the solution behavior of

processed starch, which is characterized by the amylose network. This will be the object of a

forthcoming publication.

Fixation of Entanglements

The idea of a fixation of entanglements can be derived from the following experiments:

Birefringence measurements on thin cuts of injection-molded starch allow to draw

conclusions on the flow during the mold filling process [21]. When the injection temperature

is below 130ºC, the melt viscosity increases markedly. The initial laminar flow transforms

itself into a heterogeneous one. The corresponding change of the starch network also yields

a transition of mechanical properties of the solid injection moldings.

Bernazzani [22] shows from FTIR – experiments that the starch network develops below

120ºC. This critical temperature is somewhat lowered, due to a 10 hour annealing process at

various temperatures, which causes a relaxation of the network. Since the entanglement

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network does not change during solidification of the melt, it is reasonable to expect a

fixation process of the entanglements. On the other hand, at temperatures above 120ºC a

thermal dissociation of the fixed entanglements can be expected. Bernazzani [22] further

reports that another discrete densification of the network takes place in the temperature

region below 70ºC. In ref. [5] we mention that this phenomenon is related to a

rapprochement of single helices giving rise to double-helix net-point regions (secondary

network). The formation of a network connected by double-helix regions is also reported

Gidley [6]. We have observed that drying of amorphous starch increases the secondary

network [5]. The essential difference between both types of chain couplings (primary

network of fixed entanglements, secondary network of double helices) is that the higher

temperature stable component is formed at 120ºC by the entanglement of two chains, while

the secondary coupling (formed below 70ºC) is built up by a bare rapprochement of

neighboring single helices. We have shown that this type of coupling is sensitive to an

unraveling process [23]. In the latter case, due to the free dissociation of the double helix, a

high melt entropy SM should be detected. However, after thermal dissociation a chain

entanglement still exist, giving rise to smaller melt entropy. If one assumes, that the

energetic effect (HM) is not much less for the fixation of an entanglement than for double

helix bonding, then from TM = HM / SM the elevated thermal stability of the network of

fixed entanglements emerges.

CONCLUSIONS

1. From data of the critical molecular weight between two entanglements of the amylose

chain, the flexibility of the single helix chain has been estimated. It turns out that the

statistical chain segment ls of amylose is approximately equal to one turn of the helix. From

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the definition of ls one can attribute a high molecular mobility to one turn of the single

amylose helix

2. Analysis of data indicates that single helices within the amorphous state show a disordered

conformation. Single-helix crystals (V – crystals) exhibit, on the other hand, a regular chain

conformation.

3. Due to their easy extensibility amylose molecules can pack easily into double helices.

Molecular attraction leads to an increase of the elongation ratio above 2. However, the

extension is restricted by the disappearance of the inner (hydrophobic) channel of the single

helix. Single helices are densely packed within each double helix, as there is no inter-space

left between them.

4. The maximum possible entropy induces an expansion of the molecular coils in the molten

state, thereby facilitating an interpenetration (described by Rault’s degree of

interpenetration ) of the chains leading to the formation of entanglements.

5. It is shown that the mean distance between entanglements in the molten state is controlled

by the chain flexibility (size of ls ). The distance can be directly correlated to the X-ray

long period during the early stages of crystallization of amylose.

6. Results favor the concept that the entanglement network occurring in the melt is transferred

into the solid state. Below 130ºC the entanglement network transforms to an amylose

network of stable net-points. When the temperature decreases below 70ºC, a further

densification of the network takes place, which is related to double helix formation through

rapprochement of single helices.

ACKNOWLEDGEMENTS

Grateful acknowledgement is due to the MEC, Spain (grant FIS2004-01331) for the generous

support of this work. One of us (RKB) gratefully acknowledges the Secretaría de Estado de

Universidades e Investigación, MEC, and the “European Social Fund” for the award of a

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Sabbatical Grant (SAB2003-0131). RKB also thanks the DFG (Deutsche

Forschungsgemeinschaft) for the support of this work. The SAXS and WAXS data discussed in

this work were derived from measurements carried out at HASYLAB, DESY, Hamburg, under

project II-04-029 EC. The IHP-Contract HPRI-CT-1999-00040 of the European Community

funded this project. The Arburg Company in Lossburg, Germany is thanked for kind supply of

the injection-molding machine used. We wish to thank Prof. P.H. Geil for his valuable

comments and suggestions.

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FIGURE CAPTIONS

Fig. 1 Schematic representation of a single helix turn of the starch molecule (from A to E)

and a 180º - twist of the helix (from A to E´).

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Fig. 2 Schematics of a single helix showing seven turns in a statistical conformation. One turn

corresponds to one ls unit. Dotted line: inner channel of the single helix.

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Fig. 1

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Fig. 2

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