CRYOBIOLOGY12,340-352

(1975)

Comparative

Crystallization and Aqueous EVA-MARIA

American

Foundation

for Biological

Behavior Solutions AMRHEIN

1975. Schoenstatt Center, W 284 Waukesha, Wi 53186. by NIH Grant RR-05’740. 340

Copyright All rights

Q 1975 by Academic Press, Inc. of rqmduction in any form reserved.

1

Research, 2 Rt 5, Madison, Wisconsin 53704

The object of this paper is to point out some significant similarities and differences between the crystallization behavior of organic polymers and that of aqueous soIutions of substances of various moIecular weights. Fart I gives a short introduction to the crystallization behavior of Iong-chain molecules (polymers). When this behavior is compared with that of aqueous solutions, it is found, as the main result, that the noncrystallizing parts of a macromolecule restrict the polymer crystallization, like the soIute, in aqueous solutions, hinders the crystallization of water. Part II presents a series of photomicrographs of the three main crystal patterns of polymers and of aqueous soIutions, characterized as regular polyhedra (single crystals), irregular dendrites, and spheruIites by Luyet and Rapatz (9). The final morphologies are, in many respects, similar in the two systems. In a qualitative way, the similarities in the crystal morphology are traced back to similar conditions of nucleation and growth. The three patterns of CrystalIization depend on the degree of supercooling and on the solute concentration as would be predicted by the classical theory of crystallization, A comparison of the melting and recrystallization behavior of the two systems will be published in a subsequent paper. Received April 7, 1 Present address: N 698, Cherry Lane, 2 Work supported

of Polymers

I. MODES

OF CRYSTALLIZATION IN POLYMERS

A. Nuci!eation and Crystal Growth 1. The liquid structure. The basic unit of all polymer systems is the macromolecular chain. The macromolecule has, for average degrees of poIymerization, a ratio of length to diameter between 10’ and 106. In the following we will restrict ourselves to simple synthetic polymers, i.e., to linear moIecuIes with chemically simple repeat units ( polyethyIene, polyoxymethylene, polyethyleneglyco1, etc. ). The chemical bonds along the “backbone chain” are usually of the covalent type; the interchain bonds are of the van der WaaIs type or hydrogen bonds. Covalent bonds allow a more or less free rotation, e.g., around the C-C bond axis. Therefore, the macromolecular chains can assume very different conformations, and resemble, in their behavior in the liquid state, that of flexible, randomly coiIed threads. Each chain may pervade a volume more than 100 times as large as the actual chain volume, and the volumes “occupied” by different chains penetrate each other (except for dilute solutions of polymers, which are characterized by “noninterpenetrating occupied volumes”), A rough visualization of this structure is given by the “amorphous” parts of the model sketched in Fig. I. For a more detailed introduction to the structure of macromolecules we refer the reader to P. J, Flory

POLYMERS

AND

AQUEOUS

(3), F. W. Billmeyer ( 1), and other polymer textbooks. 2. A&Zeus form&m. If a liquid polymer is to crystalhze, parts of the threadlike molecules must be incorporated into a regular lattice. This imposes two conditions: First, the chain must consist of periodically repeated units of identical geometry, which means that the chain backbone assumes either a pIanar zigzag or a helical conformation. Secondly, these regular chain segments must align one beside the other, to form a region of crystallike order. If this region is Iarge enough for further stable growth, it becomes a “nucleus” of the new sohd phase. The resulting crystal symmetry depends on the symmetry of the moIecuIe. For further information on the crystallographic data of polymers see P. H. Geil (4), L. Mandelkern (12). Usually the nucleus is much smaller than the average molecular chain length. In forming a nucleus, a chain must either fold back and forth (like a fire hose), or it traverses the nucleus once or several times and then, like a fringe, enters the liquid zone again, AccordingIy, nuclei with very different types of surfaces can

FIG. I. Sketch of a partially crystalhne structure: “fringed micelle model.” “A” chain segment crosslinking the crystallites

polymer marks a 1 and 2.

SOLUTIONS

341

FIG. 2. Schematic representation of various types of polymer crystallization. Those parts of the chains that are incorporated in the crystal lattice are marked by thicker lines. (- - - -) In&c&es the lateral crystal surfaces. Fig. l(A). The two extreme cases: folded chain (a) and extended chain (b) crystals. In (a) the surface is built up by “adjacent chain reentries”; in (b ) chains do not reenter tie crystal but form “fringes” in the surfaces. Fig. 2( B ) . An intermediate case, “switchboard model” or “nonadjacent reentering of chains.”

be formed. Their growth leads to different types of poIymer crystals. 3, Folded-chain and extended-chain cystals. Models of the various types of polymer crystals are sketched in Fig. 2. Figure 2A.a shows a nucleus buih up by reguIarly folded chains. In this way lamellar “‘folded-chain crystals” develop, Their thickness corresponds to the average “fold length” of the chains, and their surfaces are “regular fold planes.” In the case shown in Fig. 2A.b the chains traversing the crystalline region do not reenter the nucleus. The two major (1ateraI) surfaces, then, have “fringes” consisting of those parts of the chains which are not incorporated in the lattice. These nuclei form “extended-chain crystals.” Usually, their growth is soon restricted by the entangled mass of fringes at the crysta1 borders. The resulting crystallites are like “micelles” embedded in a remaining amorphous phase. They are illustrated by the “fringed micelle model” of Fig. 1. Figure 2B shows how chains can reenter the nucleus after having formed loops or irregular folds. The resulting surface structure and the fmal crystal morphology are

342

EVA-MARL4

FIG. 3. Electron crystallized at 89°C from a dilute tetralin

micrographs of linear polyethylene (m, = 50,000): from a dilute tetralin solution and (b) isothermally solution. (Micrographs courtesy of Dr. R. V. Rice.)

intermediate between 2A.a and 2A.b. Most of the real cases of solid polymers are, in the present state of our knowledge, represented by this model. According to F. P. Price, “‘At present there is a significant trend to meld the two models (folded-chain and extended-chain crystals) and to describe crystalline aggregates in polymers as chain-folded lamellae which are tied together by molecules running from one crystal to another” ( 15). B. The Resulting

AMRWEIN

Morphology

Extended-chain as well as folded-chain nuclei develop into crystallites of limited particle size. Figure 1, though it refers mainly to “extended-chain crystals,” is a model typical of the resulting structure. No polymer shows complete crystallinity; there is always a remaining amount of amorphous phase and/or of interphase boundaries. This follows from the inherent hindrances to crystallization that are characteristic of long-chain moIecuIes: first, crystal growth is usuaIly restricted to the lateral surfaces, which leads to Zamellar crystals; secondly, not all material

(a) isothermally crystallized at 60°C

is CrystallizabIe and this holds for the remaining amorphous phase; thirdly, crystallizing and noncrystallizing components are tied together by covalent bonds, and this factor mainly determines the structure of the soZid-liquid boundaries. 1 I The restriction to lateral growth, leading to ZameEZar crystals. The great difference between the chemical bonds along the chain axis and those perpendicular to it (covalent and van der Waals type, respectively) is reflected in a large anisotropy of the surface tensions of polymer nuclei. The free energy of the surface perpendicular to the chain axes (the “fold planes”) is about ten times that of the “lateral” interfaces. The thermodynamically most stable polymer crystal, therefore, would be one with a minimum of high surface energy faces, i.e., an extended-chain crystal with all molecules aligned over their whole chain length. The kinetics of crystallization, however, impose the restriction to a lamellar growth and chain folding. Starting from the picture of a randomly coiled threadlike molecult one can envision that the “easiest”

POLYMERS

AND

AQUEOUS

FIG. 4. Electron micrograph of melt crystallized linear polyethylene. By permission of J. Polymer Science, John Wiley and Sons (2 )

way to arrange this chain in a regular manner is by folding it back and forth rather than by straightening it completely. FoIded-chain nuclei are the fastest growing nuclei and therefore dominate in all practical (normal pressure) crystallizationthough they do not lead to the “ideal” extended chain crystal, but to lamellae, with fold periods corresponding to about the critical nucleus dimensions (see below, part II, B). The investigation of polymer crystallization provides a typical example of the way in which the kinetics of a overplays crystallization process static equilibrium considerations and Ieads to finite, restricted crystal sizes. The restriction to lamellar growth is common to the crystallization of polymers both from solution and from the melt. Figs. 3a and 4 show two examples. In dilute solution the Iateral growth proceeds

Bf!&?$$ $ffjJ D

8

b

FIG. 5. Model of macromolecules with noncrystallizing components: A, regular, crystalhzable chain segments; B, bulky noncrystallizable side group; C, branching point; D, Loop. Fig. 5 (a) represents the liquid state, and Fig. 5( b ) represents the partially crystalhe state.

343

SOLUTIONS

FIG. 6. Hexagonal ice formations obtained at high subzero temperatures, Solute-bovine serum albumin, Concentration-35%. Temperature: Photographs (a) and (b): -1.5”C; photographs (c) and (d): -2” and -2.9, respectively. Thickness approx 0.01 mm. X58. By permission of Biodynamica (9 ).

by a rather unrestricted, regular chain folding and leads to the Iozenge-shaped 1ameIIae shown in Fig. 3a. Under all other conditions the Iateral growth, too, is restricted; the crystallites might remain as small as the “micelles” in the sketch of Fig. 1, due to the other inherent hindrances to crystallization in polymer systems. 2. The presence of noncrystallizable components, leading to a limited crystal content. A “crystallizable component” of a polymer system in the strict meaning of the word is not, or is very seIdom, the macromolecular chain as a whole, but rather a sequence of stereoregular repeat units of the long chain molecule. A chain molecule inevitably shows irregularities OT “‘impurities” which cannot be incorporated into the crystal lattice.3 They are called “chemical impurities,” if bound chemically to the macromolecule in the polymerization process, Iike branching points and foreign side groups (C and B impurities,” if in Fig. 5), or “physical formed by physical processes, Iike entanglements ,and loops (D in Fig. 5). Since these “impurities” cannot enter the 3 Stereoirregularities like the subsequent chain units are not paper; for information we refer textbooks (1, 3, 4, 12).

“atacticity” of discussed in this you

to polymer

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EVA-MARIA

crystal lattice, they form a “boundary layer” of high defect concentration at the crystal surface. 3. The interlinkage between crystalline and amorphous regions, A pecularity of the long chain structure of polymers is that crystallizable and noncrystallizabIe components are tied together in one dimension by covalent bonds; they are part of one and the same molecule. This again reduces the number of crystallizable chain units. As illustrated in Fig. 5, a regular chain segment A’ between two impurities B, which is shorter than the corresponding nucleus dimension “A”, ~also becomes “noncrystallizable.” Besides this, the main effect of the intrachain bonding is a strong reduction of the molecular mobility in the course of crystallization. Because the noncrystallizable components that accumulate at the crysta1 borders cannot diffuse away, a concentration gradient is built up which rapidly increases the effective viscosity at the cry&a1 growth front. In addition a “cross-Iinking” of the whole material takes place, if parts of one and the same chain are incorporated into different crystallites (like chain segment “A” in Fig. 1). This again reduces the mobility of the system. Finally crystal growth stops completely, either because of the sterical hindrances at the crystal borders and/or because of the solidiflcation of the amorphous material by a “glass transition.” The final result is a “two-phase system,” consisting of small crystallites embedded in an amorphous matrix. The structure of the interfaces may vary from the “smooth” surface of regular foIds to the very irregular fringed or “switchboard-like” surfaces of Figs. 2.B and 5( b ) . In some cases (lamellae from dilute solutions) the surfaces will be the onIy “amorphous phase” present, in other cases they are even considered as a “third phase” between the regular crystals and the melt or glass.

AMRHEIN

C. Similarities

to the C ystallization

in

Aqueous Solutions 1. The question of a basis for compari801~.To make the comparison meaningful, some features in the crystallization behavior of polymers must also apply to the freezing of aqueous solutions. The basic chemical units in both systems-macromolecules on the one side and the H 0 molecules on the other-do not seem ?to have any similarities. If, nevertheless, crystal patterns are found in the two fields which are strikingly similar (see Figs. 3-IO), the underlying physical conditions of crystallization must show a close resemblance. These comparable physical conditions and their influence on the resulting crystal patterns shall be stressed in the fohowing sections, Before doing so, those aspects of the crystallization behavior of aqueous solutions which serve as a basis for the comparison, are shortly reviewed. For further information reference is made to the investigations of Luyet and co-workers (10, 11, 16). 2. The conditions of cystullization in aqueous solutions. The second component of the solutions considered in this comparison is a high or low molecular weight organic compound, like glycerol or polyvinylpyrollidone [for a summary see Luyet (lo)]. In all casesof practical interest the crystalbzation of the solute can be neglected. The solute influences, however, the crystallization of the water in a twofold way: (1) due to a strong interaction with solute moIecuIes part of the water molecules become “nonfreezable”; so that the final crystal content is pemzanently restricted; (2) the crystallization is temporarily hindered, due to an increase in viscosity and, in some cases, to concentration gradients at the crystal boundaries. Like in polymer systems the result is a “two-phase-system” of crystalline and amorphous materia1 with crystal-liquid interfaces. “The frozen sohrtions . . . con-

POLYMERS

FIG. 7. Photographs, in cerol solution, illustrating units at increasing cooling (a) -6O’C; (b) -70°C;

AND AQUEOUS

SOLUTIONS

34ri

polarized light, of spherulites formed in thin layers of a 5 M Glythe increasing number and decreasing size of the crystallization rates and decreasing temperatures. Temperature of freezing bath: (c) -75°C. ~85.5. By p ermission of Blod~namica ( 18).

sist of a framework of ice, often of very fine structural design, interpenetrating a nonfrozen phase of considerable total volume, often finely divided and therefore separated from the ice by enormously large contact areas; steep concentration gradients may be maintained for long periods of time in the narrow channels of nonfrozen material” (8). 3. The similarities in the modes of crystallization. The common features in the modes of crystaIIization of polymers and aqueous solutions, then, can be summarized as follows: (a) Only one component is crystallizable, the water molecule or a regular repeat unit of the macromolecular chain. (b) Part of the water molecules are “trapped” between the solute and become nonfreezable, similar to the manner in which regular chain units of a macromolecule are “trapped” between irregularities that prevent the incorporation into a crystal lattice. (c) The noncrystallizing components (the solute in one case, and the impurities of the polymer chain in the other) ac-

cumulate (during crystal growth) at the crystallite borders, and lead to an increased viscosity and to concentration gradients. (d) The ice crystals, like polymer crystals, have a restricted particle size. In both cases the resuhing morphology is typical of a hindered, partial crystahization. II. COMI’ARISQN OF THE CRYSTAL PATTERNS IN POLYMERS AND IN AQUEOUS SOLUTIONS

A. Patttiw of Cystallization ferent Conditions

Under

Dif-

Crystal patterns of polymers and aqueous solutions resulting from various conditions of nucleation and growth, are illustrated in Figs. 3-10. The selection follows approximately the cIas&cation by Luyet and Rapatz (16), in their paper “Patterns of Ice Formation in Some Aqueous Solutions .” They distinguish three patterns; regular polyhedra, irregular dendrites and spherulites. These patterns are shown subsequently as functions of the degree of supercooling, AT, which one may define

FIG. 8. (a) Photomicrograph of high density polyethylene after brief treatment at 350°C followed by rapid crystallization in thin film form. X150. (b) SampIe of polyethylene showing spherulites in granular background after complete crystallization at constant temperature. X150. By permission of St. Martin’s Press (18).

as the difference between the temperature of crystallization and the equilibrium melting point, and of the concentration of noncrystallizing components. 1. Small supercooling, low concentration, Figures 3(a) and 6(a) demonstrate the growth behavior under the condition of small under-cooling AT and dilute solutions. “Dilute solution” means a high concentration of water on one side, and a high dilution of the polymer molecules on the other; in both cases this condition refers to a high mobility of the crystallizing components. The growth habit is that of Tegaih~ single crystal growth; the shape of the crystals reflects the crystallographic symmetry (hexagonal and orthorhombic symmetry for ice crystals and polyethylene crystals, respectively). Figure 3(a) shows many single transparent lamellae precipitated from the solution and lying at random one upon the other, Except for the small lozenges which resulted from spiral growth on the primary, larger ones, they have regular plane surfaces (probably “reguIar fold planes”). These single crystals are characteristic of the crystallization of polymers in dilute &&on, but the restriction to lamellar growth is typical of all polymer crystals. Lamellae that crystallized from a polymer melt are shown in the electron micrograph of Fig. 4 for comparison. The region re-

produced in Fig. 4, however, is part of a spherulitic aggregate and belongs to the type of crystallization in a highly viscous liquid (Section 3). 2. Increasing supercooling, low concentration. Figures 3(b) and 6(b-d) show the effect of lowering the temperature of crystallization under otherwise identical conditions. The crystal pattern changes remarkably and dendritic forms develop. The primary crystal branches out into many subunits. In the polymer the subunits still show the orthorhombic symmetry. In the case of ice formation, the branching follows the crystallographic angle of 60”, but the units become more and more needlelike. 3. Increasing mpercooUng, high concentration. Figures 7 and 8 represent the case of large supercooling and high viscositythe conditions essential for “spherulitic growth,” There is remarkably little difference in the appearance of the ice and polymer spherulites under crossed nicols. Figure 7 also ilIustrates that the number of growth units increases when the temperature is lowered-corresponding to an increased nucleation rate. In the case of Fig, 7(c) the temperature of homogeneous nucleation was reached (17). The many small units correspond to a high number of nuclei formed homogeneously at very

FIG. 9. Spheruhtes grown at 125°C in isotactic polypropylene blended with the following amounts of atactic polypropylene (HMA): (a) OR, (b) ZO%,, (c) 40%, and (d) 90%. Crossed polarizer, X204. By permission of Journal of AppZied Physics, American Institute of Physics (6).

low temperature. This might also explain leads to coarser spherulites or irregular fibriIIar growth. the granular background in Fig. S(b) . 4. Medium. supercooling, increasing concentration, Irregular fibrillar growth is il- A. Relation of the Diferent Cystal lustrated in Figs, 9 and 10. As will be Patterns to Different Conditions of Growth shown below, spherulitic growth is caused A ModeZ for Describing Crystal Growth This section attempts to describe the by large amounts of noncrystallizable material, which restrict more and more the various growth habits and their depenlateral growth rate of the crystal until the dence on the crystallization temperature needlelike growth of spherulite radii starts. and concentration on a unified basis, Only AI1 kinds of transition forms between one crystaIIizing unit is considered. The influence of the number of crystallizing the regular dendritic growth and the polycrystalline spherulitic growth can be ob- centers that appear per unit of time and tained by varying the concentration of volume, i.e., of the nucleation rate, on the noncrystallizabIe components, This is il- final shape and size of the crystals is not discussed in detail. It is evident, for inlustrated in Fig. 9(b-d) and Fig. lO( b). “Atactic” polypropylene (see Fig. 9) is a stance, from a comparison of Fig. 7 (a).stereoirregular moIecule that cannot crys- (c)1. Distinction of successioesteps in cystallize; if it is added to the “isotactic” polytal growth. Each step in crystal growth mer, it has the same effect on the crystal morphology as an increased PVP concen- consists of the addition of a small new entration has on ice formation in aqueous tity of ordered material to the growing solutions [see Fig. lO( b ) 1. In both cases nucleus. For an estimate of the growth rate according to the classical theory of the high concentration of ‘impurities”

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crystahization each step must be specified, so that the work required for the addition of the new unit can be calculated from the molecular symmetry, heat of fusion, and surface tensions. A simple example of this procedure is given in Fig. 11. It shows a (cubic) crystal growing in a-direction by compIetion of monomolecular growth planes on the b-c face, one after another. Three different growth steps, G., Gb, and G,, with three different rate constants, can be distinguished. Usually growth steps “G,” are faster than those of type “Gb,” and these again are faster than those of type -Gg” (less new interfaces must be formed), so that the h-c plane is completed before the next growth plane is “nucleated.” Then G,, the “secondary nucleation rate,” determines the overall crystal growth rate. Growth of this kind is called nucleation controlled growth (20). Each growth plane develops from a “coherent surface nucleus,” 4 on the previous growth pIane (the “substrate” is the growing crystal itself).5 An illustration, taken from studies on polymer crystalhzation, is given in Fig, 11 (b) . It shows a model for the growth of a “folded-chain crystah” The fold pIanes are the b-c planes, and the chain axes lie in c-direction (a “coherent” surface nucleus must have the chains aligned in the same direction as in the undedying plane). The G,-steps, then, simply mean the aligning of subsequent chain segments, while growth steps “Gb” demand the folding of the chain. G,, the rate of “nucleation” of the next fold plane, was calculated for this model from the work of formation of the surface nucleus “coherent nucleus” has the same lattice 4A symmetry as the underlying plane, so that X-rays, diffracted from both planes, show definite phase relations or “coherence”; coherent nucleation is essential of single crystal growth. s Another type of crystal growth, f.i., would result from screw dislocations. These, and other defects acting in a simiIar way, are rare in polymer crystals; therefore, nucleation controhed growth k the outstanding one in polymer crystallization.

AMRHEIN

dependent on its fold Iength ‘Y, and convincing arguments for the (actually observed) kinetic preference of growth steps with about constant fold length could be given (5, 8, 14, 15 ). ‘Y” is related to the critical nucleus dimensions. The essential for the following discussion is that the relative magnitudes of G, compared with Gbr and of G,, compared with G, determine the final shape of the crystallite. As Iong as G, is much smaller than the lateral growth rates, the borders of the crystallite are its crystallographic planes. If, for some reason, growth in cdirection is restricted (as in thin film samples, or by the condition of constant average fold length in polymers), a high ratio of Gb to G, leads to a platelike crystal (lamellae), a lower ratio to a ribbonlike crystal; whiIe a reduction of both G, and G, Ieads to needlelike growth. The factors that determine the relative magnitudes of G., Gb, and G,, are again given by classical crystallization theory. 2. Estimate of the growth rates. Any growth rate “G” is determined by two exponential factors ( 19), one relates to the work of formation, AG', of a nucleus of critical size (that is, large enough for stable growth) and one accounts for the transport of molecules or crystallizing units to and across the crystal-liquid interface. G

=

The work

G,

e-AU*/RT

e-D/RT

of formation is proportional energies of the new interfaces. The sketch of Fig. lla shows that growth steps of type ‘