Spherulites

Spherulites are to be distinguished from dendrimers, which also have spherical form. A dendrimer is a single molecule of a special kind of polymer which spreads from a nucleus by repeated branching. 

Spherulites with diameters between 5 pm and a few millimeters can be studied with an ordinary polarizing microscope, and those with diameters below 5 im with an electron microscope or by small-angle light scattering. In 

The differences in the speed of the light result from differences in the refractive index. If the highest refractive index is in the radial direction, one talks of positive spherulites. Negative spherulites show the highest refractive index in the tangential direction. Thus, information about the microstructure of the spherulites can be gained from their optical properties. 

Spherulites show an imperfect crystalline structure, since the melting point of the spherulite usually lies considerably below the thermodynamic melting point (see Chapter 10). Even then, a further increase in X-ray crystallinity can also be observed when the spherulites have filled the volume. Localized orientation of the crystalline region leads to the characteristic 

Spherulites make films and foils opaque when their diameters are greater than half in wavelength of the light and when, in addition, inhomogeneities exist in relation to the density or to the refractive index. Spherulitic poly(ethylene), for example, is opaque, but spherulitic poly(4-methyl-pentene-1) is glass clear (at room temperature), even when the latter has the same number of spherulites with the same dimensions as poly(ethylene). 

100 im are characteristic of polymers crystallized from the melt in the absence of significant stress or fiow. It is now believed that spherulites form as a consequence of certain general crystal growth conditions specific to polymers. It has to be emphasized that spherulitic texture is essentially independent of textures of lamellar units built into them. 

The most prominent structural entity in a material crystallized from a polymer melt is the spherulite. Electron microscopic evidence clearly shows that sphemlites are aggregates of lamellar crystallites and the lamellar structure persists throughout the body of spherulites. Spherulites are spherical 

The Avrami equation [Eq. (2.11)], which was derived in the general context of phase changes in metallurgy, has provided the starting point for many studies of polymer crystallization and spherulitic growth. The equation relates the fraction of a sample still molten, 6, to the time, t, which has elapsed since crystalhzation began, the temperature being held constant  

For a given system imder speci ed conditions, Z and n are constants and, in theory, they provide information about the nature of the crystallization process. Taking logarithm twice in succession 

A plot of In(-lne) against Int should thus be a straight Une of slope , making an intercept of InZ with the vertical axis. In practice, this method of evaluating n and Z is very prone to error. So curve tting methods using Eq. (2.12) and the raw data are usually preferred. 

The Avrami exponent, n, has a theoretical value of 3 when crystallization takes the form of spherulitic growth of nuclei that came into being at the same instant in time. Integral values of n ranging from 1 to 4 can be attributed to other forms of nucleation and growth (Hay, 1971). The spherulites formed from a melt have different sizes and degrees of perfection, and they completely 11 the volume of a well-crystaUized material. 

Examination of thin sections of semicrystalline polymers reveals that the crystallites themselves are not arranged randomly, but form regular birefringent structures with circular symmetry. These structures, which exhibit a characteristic Maltese cross-optical extinction pattern, are called spherulites. Although spherulites are characteristic of crystalline polymers, they have also been observed to form in low-molar-mass compoimds that are crystallized from highly viscous media. 

Spherulites are classified as positive when the refractive index of the polymCT chain is greater across the chain than along the axis, and negative whrai the greater refractive index is in the axial direction. They also show various other features sueh as zigzag patterns, concentric rings, and dendritic strucfirres. 

The intermission and resumption of growth are inevitably involved in a system where there is an imbalance between the diffusion rate and the growth rate and a critical value such as the energy barrier is involved. When growth resumes, the particle size is small and the density is high, but the size increases and the density decreases as growth proceeds. Since the impurity concentration will also vary, the color intensity will be different. 

Spherulites are formed if geometrical selection takes place on a spherical substrate particle. Substrate particles maybe a completely different material from those materials forming the spherulites, such as a sand grain, or a spherical particle of polycrystalline aggregate of the same species formed under a higher driving 

This helps to confirm that nucleation, crystallization rate, and spherulite size are strongly influenced by the presence of fillers. It is still uncertain what role a filler plays in the mechanism of nucleation. 

In one publication, an extensive morphological study was conducted on the effect of TiO2 on the morphology of crystallized PP and HDPE. The authors did not find any evidence of a modified morphology around the particles and concluded that spherulites grew until they were stopped by the surface of the filler unless the 

The filler affects spherulite size only if cooling rates are low At a high cooling rate (e.g., 20°C/inin), the nucleating role of the filler becomes much less significant. 

While the presence of a filler affects the way a matrix crystallizes, the opposite is also true. In studies of in situ formation of calcium carbonate in different copolymers, different crystalline forms of calcium carbonate were found. Calcium carbonate crystallized without a polymer had a rhombohedral morphology. When crystallized in the presence of polyethylene oxide its morphology remained rhombohedral because the polymer does not interact with the crystal of calcium carbonate as it 

Problem 2.16 Using the Avrami equation calculate approximately the extent of crystallization of polyethylene during cooling from the melt, if the melt is cooled in 1 s by quenching. Use = 3 and Z = 5 (for time in seconds) as the average rate constant over the range of temperature in question. 

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Figure 4.12 Spherulites of poly( 1-propylene oxide) observed through crossed Polaroid filters by optical microscopy. See text for significance of Maltese cross and banding in these images. [From J. H. MaGill, Treatise on Materials Science and Technology, Vol. lOA, J. M. Schultz (Ed.), Academic, New York, 1977, with permission.]...

They possess spherical symmetry around a center of nucleation. This symmetry projects a perfectly circular cross section if the development of the spherulite is not stopped by contact with another expanding spherulite. 

A system of mutually impinging spherulites develop into an array of irregular polyhedra, the dimensions of which can be as large as a centimeter or so. 

The individual spherulite shows up by the characteristic Maltese cross optical pattern under crossed Polaroids, although the Maltese cross is truncated in the event of impinging spherulites. 

Spherulites have been observed in organic and inorganic systems of synthetic, biological, and geological origin, including moon rocks, and are therefore not unique to polymers. 

A larger number of smaller spherulites are produced at larger undercoolings, a situation suggesting nucleation control. Various details of the Maltese cross pattern, such as the presence or absence of banding, may also depend on the temperature of crystallization. 

The molecular chain folding is the origin of the Maltese cross which identifies the spherulite under crossed Polaroids. The Maltese cross is known to arise from a spherical array of birefringent particles through the following considerations ... 

The ordered polymer chains are consistently oriented perpendicularly to the radius of the spherulite. 

Figure 4.13 Schematic illustration of the leading edge of a lathlike crystal within a spherulite.

Items (1) and (2) mean that the refractive index in the tangential direction of the spherulite is generally greater than that along the radius. 

If the Polaroid filters are held fixed and the sample rotated between them, the Maltese cross remains fixed because of the symmetry of the spherulite. 

The presence of spherulites or smaller crystallites is comparable to cross-linking and affects not only the moduli and compliances, but also the ultimate properties such as yield strength and ultimate elongation. 

Practical appHcations have been reported for PVP/ceUulosics (108,119,120) and PVP/polysulfones (121,122) in membrane separation technology, eg, in the manufacture of dialysis membranes. Electrically conductive polymers of polyaruline are rendered more soluble and hence easier to process by complexation with PVP (123). Addition of small amounts of PVP to nylon 66 and 610 causes significant morphological changes, resulting in fewer but more regular spherulites (124). 

Figure 3.6). This theory known as the fringed mieelle theory or fringed crystallite theory helped to explain many properties of crystalline polymers but it was difficult to explain the formation of certain larger structures such as spherulites which could possess a diameter as large as 0.1 mm. 

The properties of a given polymer will very much depend on the way in which crystallisation has taken place. A polymer mass with relatively few large spherulitic structures will be very different in its properties to a polymer with far more, but smaller, spherulites. It is thus useful to consider the factors affecting the formation of the initial nuclei for crystallisation (nucleation) and on those which affect growth. 

Polymers below the glass transition temperature are usually rather brittle unless modified by fibre reinforcement or by addition of rubbery additives. In some polymers where there is a small degree of crystallisation it appears that the crystallines act as knots and toughen up the mass of material, as in the case of the polycarbonates. Where, however, there are large spherulite structures this effect is more or less offset by high strains set up at the spherulite boundaries and as in the case of P4MP1 the product is rather brittle. 

The greater the percentage crystallinity the higher the yield point and tensile modulus. It has also been shown that by raising the quench temperature the spherulite size is increased and that this greatly decreases the impact toughness. 

In the case of the polycrystalline polyester thermoplastic rubbers the simple domain theory does not seem to apply. With these rubbers it would appear that they contain spherulitic structures consisting of 4GT radial lamellae with inter-radial amorphous regions that are mixtures of PTMEG soft segments and noncrystalline hard segments. 

The polymer is liable to depolymerisation at temperatures just above T. In the case of pure polymer there is a tendency for the few spherulites to grow to sizes up to 1mm diameter. Spherulite size may be reduced by the use of nucleating agents and by fast cooling. 

Amorphous stereotactic polymers can crystallise, in which condition neighbouring chains are parallel. Because of the unavoidable chain entanglement in the amorphous state, only modest alignment of amorphous polymer chains is usually feasible, and moreover complete crystallisation is impossible under most circumstances, and thus many polymers are semi-crystalline. It is this feature, semicrystallinity, which distinguished polymers most sharply from other kinds of materials. Crystallisation can be from solution or from the melt, to form spherulites, or alternatively (as in a rubber or in high-strength fibres) it can be induced by mechanical means. This last is another crucial difference between polymers and other materials. Unit cells in crystals are much smaller than polymer chain lengths, which leads to a unique structural feature which is further discussed below. 

Figure 8.1. (a) Spherulites growing in a thin film of isotactic polystyrene, seen by optical microscopy with crossed polars (from Bassett 1981, after Keith 196.3). (b) A common sequence of forms leading to sphertililic growth (after Bassett 1981). The fibres consist of zigzag polymer chains. 

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