Structure of Negative Spherulites of Even–Even Polyamides

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Structure of Negative Spherulites of Even−Even Polyamides. Introducing a Complex Multicomponent Spherulite Architecture B. Lotz* Institut Charles Sadron (CNRS and Université de Strasbourg), 23, Rue du Loess, 67034 Strasbourg, France

S. Z. D. Cheng Downloaded via DURHAM UNIV on July 5, 2018 at 14:52:03 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States

C. Y. Li Department of Materials Science and Engineering, Drexel University, 3141 Chestnut Street, Philadelphia, Pennsylvania 19104, United States S Supporting Information *

ABSTRACT: Even−even polyamides are known to grow as positive spherulites, which implies that the radial, fastest growth direction is parallel to the a-axis and hydrogen bond direction. However, after annealing/self-seeding close to Tm, crystallization in a limited Tc window (down to ≈20 °C below Tm) yields profuse negative spherulites and, frequently stemming from the latter, less frequent and ill-defined entities named “spherulitic aggregates”. The detailed structure and origin of these two entities, and especially of the negative spherulites, are still not clearly established although they were first observed some 70 years ago. The recent recognition that polymer spherulites (specifically, spherulites of PVDF in its γ phase) are made of scrolled, radiating lamellae and the observation and analysis of solution grown, scrolled nylon-66 single crystals provide useful guidelines for a renewed analysis of this structural puzzle. The present analysis relies heavily on the approach and on the detailed diffraction data obtained by Lovinger in the late 1970s. It strongly supports the contention that negative spherulites of even−even polyamides are made of scrolled lamellae. The hydrogen bonds are oblique to the spherulite radius. Twinning parallel to the hydrogen-bonded sheets generates two different orientations of the unit cell that helically wind around the scroll axis. These two cell orientations plus a contribution of aggregate-like lamellae that grow inside the radial scrolls account for the apparent lack of orientation of the unit cell in these negative spherulites. This model explains also the birefringence variation of negative spherulites with Tc and their melting point identical to that of aggregates. Negative even− even PA spherulites thus illustrate an original spherulite architecture in which one population of lamellae generates a scaffold within which a second population develops in a confined but oriented frame. It appears to be applicable, perhaps with variants, to the spherulite structure of other types of polyamides.

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INTRODUCTION AND BACKGROUND The crystal structure at the unit-cell level of nylons has been established early on: Bunn and Garner determined the structure of nylon-66 in 1947.1 The organization at the spherulite level has beenand still isa much more complex issue, especially for m,n polyamides, i.e., for polyamides based on the condensation of a diamine and a diacid. Seminal works on the optical properties and structure of m,n polyamides spherulites (mostly for polyamides with m and n even, e.g., PA 6,6 and 6,10) are due to Khoury, Keller, Magill, Mann, RoldanGonzales, and Lovinger.2−9 These contributions have been summarized in the latter and most comprehensive work. Nylon-66 forms normally spherulites with radiating lamellae in which the radial, fastest growth rate is parallel to the hydrogen bonds, and lies, expectedly, along the spherulite radius. These spherulites are optically positive owing to the polarizability of the hydrogen bonds and their radial © XXXX American Chemical Society

orientation in the spherulites. However, other types of spherulites have been reported and analyzed. These additional entities are optically negative spherulites and spherulite aggregates. Contrary to many (but not all) other cases of spherulitic polymorphism, these different spherulites are based on the same triclinic unit cell as the positive spherulites. The polymorphism thus rests solely on a different organization and/or orientation of the unit cell in the lamellae and/or of the lamellae in the spherulite. In this sense, we are dealing with a “spherulitic pseudopolymorphism”,8 whereas a “true” spherulitic polymorphism is associated with crystalline polymorphism, i.e., with different chain conformation and/or unit-cell geometry and/or symmetry. Negative spherulites and Received: April 29, 2018 Revised: June 25, 2018

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Macromolecules

different (acid on one lamellar surface, amine on the other), and identical again, but for a stem length one c-axis (and chemical) repeat unit longer. This sequence of balanced/ unbalanced/balanced opposite folds surfaces translates, for increasing Ts, in a sequence of flat, scrolled, and flat single crystals. In the present context, the focus will be on the scrolled lamellae with their opposite surfaces in which the folds have different chemical structure and encumbrance, even though the structural details remain to be established. Further work on solution-grown crystals by Cai et al. dealt with more concentrated solutions of PA66, also in glycerin.13 This work yielded more compact, but isolated, crystalline morphologies that could be recognized as negative and positive spherulites and as spherulitic aggregates. Relatively little work has dealt in recent years with the texture and morphology of polyamides spherulites. Most work has concentrated on the so-called Brill transition. A series of 31(!) even−even polyamides have been investigated by Atkins and co-workers.16 This systematic analysis helped apprehend “the competitive interplay between the nylon chemistry, the crystal structure of the lamellar core, and the nature of the folds”. Cooper et al.17 and more systematically Tashiro and coworkers18−20 compared the behavior of even−even polyamides and their oligomeric models. From a detailed X-ray and IR analysis, they conclude that above the Brill transition the hydrogen-bonded sheet structure is maintained in spite of the higher mobility/libration of the aliphatic segments. In fact, the major segment mobility is located in the NH-aliphatic connection of the repeat sequence. Taking into account the Brill transition in structural analysis of polyamides is relevant since crystallization takes place above the transition and observation is usually made at room temperature. The present contribution attempts to combine the structural information gained on negative spherulites of PA66 on one hand and the insights gained on PA66 solution grown lamellae on the other. To this aim and in a first part, earlier works are summarized and illustrated with some of their most significant figures. Only a few experiments, made mostly for illustrative purposes, are reported. This part may be skipped for readers familiar with the history of structural investigations on polyamides. In a second part, the scrolled single crystals produced in solution are analyzed. The results of this analysis are used as guidelines to reconsider the structure of negative spherulites. In essence, it is suggested that negative spherulites of PA66 are made of scrolled lamellae similar to those produced in solution. As such, this structural model is still unsatisfactory. However, when combined with an unexpected guest that develops within the first-formed scrolled texture, the resulting “two-phases model” accounts for many of the as yet little understood features of negative PA spherulites. Such an intricate coexistence of two different structural entities within the same spherulite is probably unprecedented. The specific, possibly transient conditions that may be involved in the formation of negative spherulites (i.e., impact of the Brill transition) are discussed. The present contribution should provide useful guidelines for a renewed analysis of these unorthodox spherulites and spherulitic aggregate morphologies of even m,n polyamides.

the more sporadic spherulitic aggregates are produced when, after annealing first formed positive spherulites near their melting temperature, crystallization takes place in a narrow range (≈20 °C) below the annealing temperature. Many aspects of the negative spherulites are known. As indicated by their simultaneous nucleation and their similar size, they result from a self-seeding process taking place at the annealing temperature. They have an “extremely fine fibrillar texture” with “the macroscopic appearance of fibrils a few tenths of a micrometer in width”.9 Their structure has remained a puzzle for a long time. Their negative birefringence indicates that contrary to positive spherulites, the hydrogen bond direction is not radial. A significant advance in the structural analysis of these entities was made by Lovinger, who used directional solidification (or zone solidification) in a steep temperature gradient. This technique allows development of macroscopic samples in which the fastest growth rate direction (the radial direction in spherulites) becomes the controlling factor in determining the crystalline morphology. Since their growth rates are sufficiently different, the positive and negative spherulites and the spherulitic aggregates could be analyzed separately and moreover, as indicated, as oriented entities. The corresponding diffraction patterns resemble fiber patterns in which however the “fiber” axis corresponds to the fastest, radial growth direction. The directional solidification experiments led to some major advances in the structural analysis of these entities. In particular, they helped establish and/or confirm that the unit-cell orientation (to be detailed later) in negative spherulites and spherulitic aggregates differs significantly from that of positive spherulites. Major structural details remain to be worked out. In particular, several puzzling features are not accounted for by the available models of negative spherulitesmost prominently the fact that as indicated by their negative birefringence the hydrogen bond direction cannot be the radial growth direction as in the standard positive PA spherulites. Moreover, as pointed out by Khoury,2 Magill,5 and Lovinger, the birefringence of the negative spherulites varies with crystallization temperature. It is virtually zero at the two extremes of the 20 °C interval indicated above and reaches a minimum near the middle of that interval, at ≈255 °C for nylon-66 and at ≈225 °C for nylon-610. Work on these puzzling structural entities has remained virtually at a halt since the seminal papers published by Lovinger in the late 1970s. More recent work on the morphology of polyamides dealt with single crystals produced from solution. Single crystals of polyamides are known since the early 1950s.10,11 However, Cai et al. reported that PA66 solution grown single crystals exist in two different morphologies, either flat or scrolled.12−14 Production of the scrolled and flat lamellae does not depend on the temperature of crystallization, Tc, but on the temperature of annealing, Ts, prior to crystallization at Tc. As developed later, a plausible interpretation of this observation suggests that the lamellar morphology reflects the thickness of the seeds produced during the annealing step that preceded crystallization. The two morphologies would then reflect the existence of two different fold surface types, associated with the periodic, diamine-diacid chemical sequence of PA66 (and as a matter of fact of all m,n PAs). Folds may be made at either the amine or the acid part. When the stem length increases, folds at opposite stem ends may be identical (e.g., both in the amine part or, as advocated by Atkins et al.,15 at the acid part),

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EXPERIMENTAL SECTION

The sample of PA66 used in this study is of commercial origin (Aldrich) used without further purification. B

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Macromolecules The various spherulite types were produced by crystallization of a thin (several tens of micrometers) film of PA66 sandwiched between glass cover slides. Crude thermal treatments, as applied by sliding the sample on a Kofler bench, are sufficient to produce the spherulites of interest. The thermal gradient helps cover a wide range of annealing and crystallization temperatures in a single experiment. Since the various spherulite types are easily recognizable under a polarizing microscope, complex experimental procedures are not necessary. However, more controlled thermal histories were also applied with the help of a Linkam LTS 420 stage under nitrogen flux. The samples were examined with a Zeiss Ultraphot optical microscope under polarized light. A sensitive plate was used to determine the positive or negative optical character of the spherulites and aggregates. Extensive molecular modeling and calculation of the diffration patterns were performed with the relevant modules of the Cerius 2 program (formerly Accelrys, now owned but no longer supported by Biovia Academic, Cork, Ireland, a subsidiary of Dassault Systems). The diffraction patterns expected for the different radial growth directions are easily generated by calculating “fiber” patterns in which the fiber direction is the radial growth direction. For this purpose, the unit cell must be redefined in the “Builders” module with the radial direction becoming the c-axis. This transformation has one limitation: the h, k, and l indices of the initial cell are limited to 20 when defining the c-axis of the new cell. This (minor) limitation may lead to radial caxis (mis)orientations that are at most 3° away from their “ideal” orientation but do not invalidate the approach used, as will be seen in e.g. Figure 11. Review of Earlier Works. This section is organized in several parts. First, the earlier works on the structure of PA spherulites are described and analyzed. This part is essentially a review of existing knowledge and interpretations and draws heavily on the data and analyses due to Lovinger since they provide the most useful frame to describe PA spherulites. A similar analysis on single crystals follows. In both cases, diffraction data and imaging techniques are considered almost exclusively, since the interpretations provided later rest on such information. Also, these earlier works dealt (mostly) with either PA66 or PA610. The spherulites are essentially similar for the two polymers. Analysis of their diffraction patterns uses exclusively the major hk0 reflections (100, 010, and 110) and the 002 reflection. The spacings and orientations of the hk0 reflections are identical in the two spherulites; the orientations of 002 are identical, and only the spacings differ. Since their diffraction patterns are virtually identical, the distinction between the two polymers will not be made any further in the details of the discussion. For the same reasons, PA66 will be used in the following as a generic and convenient short hand form to refer to most (possibly all) m,n polyamides with m and n even. Bulk Crystallization. The Structure of Polyamide-66 Spherulites. In this section the experimental results obtained by Lovinger, mostly on PA610, are recalled briefly. They are by far the most detailed ones since they are obtained in samples formed by directional solidification in a temperature gradient. The fastest growth direction is aligned with the gradient, and the sample becomes a macroscopic array of parallel radii of spherulites. Positive Spherulites. The structure of the positive spherulites is recalled mostly for comparison purposes. However, it will feature also in the later analyses. The diffraction pattern shows an arc of strong 100 reflections oriented nearly radially. In addition, the 002 reflection is nearly normal to the radius. The diffraction pattern indicates that the a-axis is radial. The spherulites are made of lamellae elongated in the radial growth direction as is usual for polymers with hydrogen bonding. Under the optical microscope, the birefringence is clearly positive due to the prevailing contribution and orientation of the hydrogen bonds to the optical anisotropy. The spherulites are observed in virtually the whole crystallization range of PAs. They are by far the dominant and most representative morphology of bulk crystallized polyamides. Although not systematically observed, lamellar twisting may be an

additional ingredient in the structure of positive spherulites and shows up as concentric extinction rings in the polarizing microscope.

Figure 1. Diffraction pattern of positive spherulites. The a-axis is radial. In this and in all later figures, the radial growth direction is vertical. Reproduced with permission from ref 9. Copyright 1978 American Institute of Physics. Negative Spherulites. The history and structural analysis of negative spherulites are developed in more detail, since they are the major topics of this contribution. Negative spherulites were reported for the first time in the late 1940s by Brenschede.21 They are observed only when specific thermal histories are applied. Heating well above the melting range results in the formation of positive spherulites only at lower Tc crystallization. When heating within or slightly above the melting region followed by crystallization in a slightly lower temperature range, negative spherulites are formed. To quote: “Negative spherulites crystallize neither at low temperatures nor after even minimal superheating in the melt, but only through meltrecrystallization from positive spherulites”.9 Khoury points out a nucleation process via self-seeding: crystalline remnants survive the heating process leading to predetermined nucleation and resulting negative spherulites all of the same size. To quote Khoury’s analysis: “The simultaneous formation and constant size of the negative spherulites [of PA66] at any temperature (for a given time) between 256−264°C indicates that they are initiated from predetermined nuclei...These centers are predominantly due to microscopic aggregates of polymer rather than foreign particles”.2 Figure 2 illustrates this feature for a PA66 sample. The negative spherulites have “an extremely fine fibrillar texture”.8 This has been a puzzle for many years. Several reports indicate the possibility of small entities but without further qualification.

Figure 2. Negative spherulites of PA66 produced after partial melting. Note the similar size of all spherulites, suggesting a self-seeding process. The finer birefringence is due to positive spherulites produced when quenching the sample after partial crystallization at Tc. In the black, nonbirefringent areas, there is no polyamide. C

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Macromolecules The structure of negative spherulites appears all the more puzzling that in spite of their well-defined spherical shape, early investigations failed to recognize any smaller structural entity (e.g., lamellae) such as exist in their positive counterparts. In addition, no clear-cut unit-cell orientation could be established for a long time, which led at times to suggest that negative spherulites had no (or a random) crystal orientation.5 The X-ray analysis of negative spherulites grown in a temperature gradient challenged this view. As shown in Figure 3 taken

Figure 4. Variation of birefringence for PA66 and PA610, as synthesized by Magill.7 The negative spherulites are produced between T1 and T2. Ringed spherulites are indicated by vertical bars. Their spacing illustrates the variation of the rings spacing with temperature. The upper curve illustrates the observed (full line) or extrapolated (broken line) melting temperatures for the positive spherulites produced at low Tc (below T1). Note: for nylon-6.10 the small domain of ringed positive spherulites just below T2. Reproduced with permission from ref 7. Copyright 1966 John Wiley and Sons.

for Tc = 251 and 264 °C, respectively. This variation is very neatly illustrated when crystallization is performed at different Tcs including steps at the zero birefringence temperatures. At these specific stages, isotropic crowns develop, the existence of which is only revealed under the polarizing microscope when further growth at a different Tc generates an additional, birefringent ring. Note again that similar birefringence variations are observed for a number of m,n polyamides (cf. Figure SI3). The existence of lamellar crystals in the PA66 negative spherulites does not seem to be clearly established through small-angle X-ray scattering (SAXS). However, Cannon and Harris analyzed the infrared spectrum of the folds in negative spherulites and concluded that very well developed chain folding does exist in these spherulites.22,23 A final word about negative spherulites deals with their melting characteristics. The melting temperature of negative PA66 spherulites is “considerably higher” than that of the positive spherulites produced at the same Tc. For PA66, Tm ≈ 271 °C versus 265 °C.9 Similar or even larger gaps in Tm have been recorded for other even−even polyamides by Magill (cf. later, Table 1).7 Spherulitic Aggregates. The nucleation, growth, and structure of spherulitic aggregates are in many respects even more mysterious than those of negative spherulites. There is no systematic way to produce such spherulitic aggregates only. Their nucleation is more erratic. They are formed in association with negative spherulites and frequently (but not exclusively) stem from those negative spherulites, especially in the lower Tc range of the latter. The aggregates have faster growth rates than positive and negative spherulites. Therefore, when initiated in a zone solidification process, they are maintained and even grow at the expense of the spherulitic counterparts. This faster growth rate helped generate “pure” and oriented aggregates, yielding clearer diffraction data. The available information and insights into the structure of spherulitic aggregates are briefly indicated: • Initiation of aggregates occurs frequently via a growth transformation mechanism from negative spherulites rather than via primary nucleation. • Aggregates grow faster than negative and positive spherulites (up to 2 times faster). However, zone solidification reveals that the growth rate is “totally variable”. “Individual aggregates constantly alter their growth velocity, initiate and terminate growth at random, and display a very coarse and uneven texture”.9

Figure 3. Diffraction evidence for negative spherulites. Reproduced with permission from ref 9. Copyright 1978 American Institute of Physics. again from Lovinger’s work, a densitometry analysis of the diffraction arcs or rings indicates a nonuniform distribution of intensity. The decomposition in different reflections is shown in Figure 3, together with a possible indexing of the observed reflections, assuming that the radial direction is normal to the ac plane and is thus [010]*. If the radial direction is normal (or nearly so) to the chain axis, the 002 reflection is no longer equatorial, as observed in the diffraction pattern. The positions of all the reflections relative to the growth axis (vertical) are accounted for as indicated by their calculated position. The model as derived is consistent with the diffraction evidence. It has two unusual features. First, the hydrogen bonds orientation is very nearly tangential to the spherulite surface; that is, it is roughly at right angles to their orientation in “normal”, positive spherulites that nucleate and coexist with their negative counterparts. The negative character of the spherulites is therefore explained by and associated with this unusual orientation of the hydrogen bonds. Second, the 00l reflections are not normal to the radius of the spherulite. Assuming that the lamellae are radial, this would imply that the lamellar fold surfaces are no longer parallel to the ab plane or that indeed the lamellae are not oriented radially. In spite of its merits and as developed later on, a curious feature of this model is the unexpected tangential orientation of its hydrogen bonds. In all polyamide crystals, the hydrogen bond direction corresponds to the fastest growth direction, i.e., the radial direction in spherulite growth. (A notable exception, probably not sufficiently taken into account in earlier works, is the b-axis growth in the spherulitic aggregates considered next.) Several more features of negative spherulites need be mentioned. As already indicated, the birefringence of the negative spherulites is not constant. It changes with Tc in a very specific way, as investigated in much detail by Khoury and Magill for a number of PAs. The variation for PA66 and PA610, borrowed from Magill’s work, is shown in Figure 4 (his full diagram with other PAs is reproduced in the Supporting Information, Figure SI3). For PA66 it indicates a maximum of birefringence for Tc = 255 °C, and a progressive decrease at both higher and lower Tc, with zero birefringence reached D

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Macromolecules • Melting of the aggregates parallels that of negative spherulites. (cf. later, Table 1). Upon melting, aggregates “disintegrate into needlelike structures, 50−200 μm in length”.8 The aggregates have a very coarse, most probably lamellar texture. Their birefringence is mixed, with extinction at ≈45° to the polarizers and analyzers. Two variants of aggregates exist that according to Mann and Roldan-Gonzalez are produced in thick and in thin films.5 In the temperature gradient experiments, Lovinger describes them as aggregates of type I and of type II. They differ by their birefringence. Type I is made of coarser domains, and type II has a finer and more oriented structure. However, their structure is similar: the b-axis is the direction of fastest growth. The coarser domains of aggregates of type I show up in a wider spread of the reflections in the diffraction pattern (Figure 5).

The diffraction pattern establishes that the b-axis is parallel to the fastest growth direction in both aggregates, in agreement with Mann and Roldan-Gonzalez, and Magill’s analyses. This structural scheme accounts for the position of the major diffraction arcs and especially for the equatorial orientation of both the 100 and 002 reflections. This specific orientation of the 002 reflection is a major criterion: it establishes that the ab plane is parallel to the radius, which in turn implies that the chains are tilted relative to that radius at a very high angle: 49°but as seen later, the hydrogen bonds are nearly perpendicular to the radius. Mann and Roldan-Gonzalez show also that in thin films the ab plane tends to lie preferentially parallel to the substrate. Also, the Maltese cross in a polarizing microscope is rotated at some 45° to the polarizer and analyzera result of thin film growth.5 To summarize, the overall situation with aggregates is even more complex and varied than for the negative spherulites. These entities represent major challenges that in many respects have not yet been solved. Crystalline Entities Produced in Solution Crystallization. The growth of polyamide single crystals from solution has a long history. Early works date back to the first days of polymer single crystals: lozenge-shaped single crystals of PA6 are shown in Phil Geil’s book, published in 1963.10 Single crystals of PAs with very diverse sequential chemical structures have been produced later on.24 The present account does not attempt to review all these works. Rather, it focuses on insights gained (a) by Khoury in an extensive investigation (mostly unpublished in an extended form) and (b) by Cai and Li et al. when investigating the impact of self-seeding on the single crystals morphology and structure of specifically, PA66. However, the procedures and results should be valid for other even−even PAs as well or possibly for m,n PAs in general. The present short summary highlights structural aspects that will be important in the subsequent analysis of the negative spherulites. Single Crystals Produced in Dilute Solution. Besides the “conventional” single crystals of the alpha phase that will be described for the sake of completeness, a number of original crystal morphologies have been uncovered and investigated in earlier works by Khoury and by Cai and Li et al.: they are most importantly scrolled crystals and very rare tube-like crystals and less frequent “lancelet-like” (cf. later) and triangular crystals. Alpha Phase Single Crystals. The familiar, flat single crystals of αPA6,10 are illustrated in Figure SI1 together with their electron

Figure 5. Spherulitic aggregates. Diffraction patterns of type I and type II on the top left and right, respectively. Bottom: orientation of the unit cell. The b-axis is radial. Reproduced with permission from ref 9. Copyright 1978 American Institute of Physics.

Figure 6. From left to right: (a) Scolled crystal of PA66 produced in glycerin, sedimented and flattened on a mica substrate, and shaddowed. Reproduced with permission from ref 12. Copyright 2004 Wiley. (b) A similar crystal with its edges decorated on cooling by additional growth of some uncrystallized material left at Tc. The additional growth indicates the orientation of the hydrogen bonds in the scroll. Reproduced with permission from ref 13. Copyright 2004 Elsevier. (c) Structural origin of the scrolled morphology of asbestos chrysotile fibers. Top: cross section of an asbestos fiber seen in transmission electron microscopy. The spiral-like growth of the layer is underlined (white broken line). Note the central hole left because the curvature of the layer reached a limit. Bottom: the crystal structure of asbestos chrysotile. Reproduced with permission from ref 26. E

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Macromolecules diffraction pattern. The (010) plane and the hydrogen bonds are parallel to the long axis of the crystal. Scrolled and Tube-like Crystals. Scrolled PA66 crystals had been occasionally observed by Geil, but Cai et al. could determine the highly specific annealing/dissolution conditions under which scrolled (and flat!) morphologies are produced.12−14 Formation of flat and scrolled crystals depends on the annealing temperature Ts of flat αPA66 crystals produced in a first crystallization and not on the actual crystallization temperature Tc used when recrystallizing the sample. Thus, for PA66 in a glycerin solution, the crystals produced at one and the same Tc (172 °C) are (mostly) flat when Ts is 202 °C, scrolled when Ts is 206 °C, and flat again when Ts is 208 °C. Scrolled crystals wind up in a cylinder-like morphology with a diameter of ≈350 nm. When sedimented, they break along their long axis and flatten, as illustrated in Figure 6, left part. The lamellar thickness, determined by AFM, on such crystals is ≈9.4 nm. Figure 6 also includes information on well-known scrolled crystals of a mineral, namely asbestos chrysotile.25 It is a bilayer. Scrolling is induced by the smaller unit-cell dimensions of an inner hexagonal silica layer compared to the larger cell dimensions of a brucite (magnesium hydroxide) layer to which it is chemically linked. In the “hollow tubes formed by rolled-up sheets” of chrysotile fibers, the inner diameter is ≈3 nm, the outer one ≈20−25 nm, and the stress-free, “ideal” diameter is 8.8 nm.26 At an even smaller length scale, scrolled variants of carbon nanotubes have been observed and analyzed.27,28 The flat-scrolled-flat lamellar morphology sequence for one and the same polymer crystallized at one and the same temperature has no precedent in polymer science. It indicates that the thickness of lamellae produced at Ts acts as a structural memory imprinted in the seeds, and this thickness dictates the lamellar thickness and morphology of crystals produced at Tc. Thicker seeds are produced at higher Ts. If the flat-scrolled-flat crystals sequence is determined by the seeds thickness, a logical structural picture emerges.12 Two different units build up the chemical sequence of PA66: a diamine with six CH2 units and a diacid with only four CH2 units. Folds may be made at the diamine or at the diacid parts. This possibility is illustrated in Figure 7. As is evident from this figure, the folds have different conformations and encumbrance in the diamine and diacid parts since the number of CH2 units differs.

more, or they are less, crowded (Figure 7). The structural unbalance generates different surface stresses and induces the lamellar scrolling. More details on the PA66 scrolled crystals’ structure are provided by the hydrogen bond decoration technique.12,13 The crystals’ tip in Figure 6a shows two faces, oblique but nearly symmetric to the scroll axis, much like a square cloth folded along one of its diagonals. These faces are however very different. Figure 6b illustrates a decoration process that highlights the hydrogen bonds orientationin short a hydrogen bond decoration technique. Since its contribution will be an essential ingredient in the later analysis, some of its characteristics must be described and underlined. The elongated shape of single crystals of PA66 as illustrated in Figure SA1 indicates the orientation of its hydrogen bonds. If these crystals are nucleated on an apparently smooth crystal surface that however features arrays of oriented H-bonding CO or N−H units, these arrays will act as orienting nucleation sites for the growth of the elongated PA66 crystals. The orientation of the “decoration” indicates the existence and orientation of the underlying crystal H bonds. The method is quite general. In an unpublished work, a similar technique was applied to reveal the orientation of crystalline domains on the surface of silk fibers, using regenerated silk as the decorating material. It helps in particular assess the existence of small domains in which the H-bonded sheets are not parallel to the wild silk fiber surface (cf. SI2). In the present case, crystallization of PA66 single crystals is not completed at Tc when the solution is further cooled down. The remaining crystallizable material forms elongated αPA66 crystals nucleated preferentially on the hydrogen bonds of the crystals formed at Tc. The decoration reveals that the H bond direction is nearly normal to only one growth face: the apparent morphology symmetry of the scroll actually hides a true structural asymmetry. This asymmetry is borne out by the analysis of the diffraction pattern to be detailed later. Tube-like crystals appear to be a morphological variant of scrolled crystals. They are extremely rare. They appear to be formed when after half a turn around the scroll axis, the two lips of the scrolled crystal come in (coplanar) contact on the opposite side of the scroll.12 This morphology-generated twin creates a reentrant angle that is a favorable nucleation site and induces faster growth along the generatrix of the scroll. A similar impact of a reentrant angle on the growth rate is well documented for 110 twinned crystals of polyethylene. Lancelets and Triangular Crystals. For the sake of completeness, but these morphologies will not feature in the later analyses, it should be mentioned that under the same crystallization conditions another type of crystal morphology is frequently encountered: flat, elongated, slightly bent crystals with a smooth inner edge and the opposite, outer edge crennelated or sawtooth like. These crystals have been described by Khoury as “lancelets”a terminology that refers to the shape of Middle Age weapons.

Figure 7. Amine (left) and acid (right) folds in a hydrogen-bonded sheet of polyamide 66. These models are only illustrative, although they have been minimized with the “Clean” function of the 3Dsketcher in the Cerius Crystal Building module.

Depending on the seed stem length, the lamellar thickness may be such that folds are made at two (say) amine parts of the molecule, which generates similar fold surfaces on opposite sides of the lamella. The lamella should be flat. If, however, the stem length is such that folds are produced at an amine part and at an acid part of the chain, the fold surfaces are chemically and structurally differentthey are

Figure 8. Triangular crystals and “lancelets” (in the upper right part of (b)) produced in dilute solution of glycerin. Note the different edges profiles of the triangular crystals and lancelets as well as their different hydrogen bonds decoration patterns. Reproduced with permission from ref 13. Copyright 2004 Elsevier. F

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• Spherulitic aggregates (Figure 9d; two of them stem also from the negative spherulite displayed in Figure 9b) are again made of relatively large lamellae, with no clear-cut or even a seemingly scattered orientation relative to the parent entities. Structural Analyses. Postulate: Negative Spherulites Are Made of Scrolled Crystals. The variety of PA66 spherulite and solution grown lamellar morphologies, all based on the conventional αPA66 crystal phase, implies varied structures and possibly growth processes. In the present section, we attempt to provide further analyses and possible structures and growth mechanisms for the negative spherulites. In this approach, we transfer knowledge gained on solution-grown crystals and crystalline entities to the more complex spherulites. More specifically, we postulate that negative spherulites are made of scrolled crystals. This postulate rests on the following: (a) The analogous thermal treatments used to generate scrolled single crystals in solution and negative spherulites in the bulk. In both cases, these entities are produced after self-seeding/annealing near the dissolution or melting temperature of first formed entities. The lamellar thickening that generates the unbalanced folds is not limited to solution crystallization and could apply for the bulk crystallization of PA66 as well. Actually, it is even generic to the structure of all even− even polyamides, provided that folds can be made at the diacid and diamine segments. (b) Although the exact (lamellar?) structure of negative spherulites is not known, all descriptions mention very fine structures with small, narrow entities or fibrils elongated in the radial direction. Submicrometer dimensions in the 200−300 nm range are frequently indicated. These descriptions are consistent with a scrolled lamellar texture. (c) The negative spherulites of even−even polyamides share the same fineness of texture under the optical microscope with the only other known spherulites made of radiating, scrolled lamellae, namely spherulites of γPVDF. This scrolled morphology was first diagnosed by Vaughan30 and later31 explained in molecular terms by an imbalance of folds constitution on opposite γPVDF lamellar surfacesan explanation that set the frame for the analysis of the scrolled single crystals of PA66. Basing our approach on the above postulate, the following parts will (a) analyze the structure of the scrolls produced in solution. This part was left open in the first reports on scrolled PA66 single crystals12 (b) Having established the structure of the individual scrolls, the diffraction patterns expected from spherulites made of scrolled crystals are computed. They are compared with the patterns obtained by Lovinger in the zone solidification experiments. This part deals with an unusual challenge in structural investigations, already tackled by Lovinger. The challenge is to explain why and how a well-oriented morphology can give rise to a near powder-like diffraction pattern. As will be seen, this structural oxymoron is neatly resolved by recognizing that the simple morphology hides a complex crystallography since the spherulites examined at room temperature combine three (and possibly four) different unit-cell orientations. Structure of Scrolled Single Crystals. The analysis of scrolled crystals produced by self-seeding in a glycerin solution by Cai and Li et al. establishes one of the foundations of the present contribution. As already indicated, the electron micrographs shown in Figure 6 illustrate that when deposited and sedimented, the scrolled crystals break and flatten and have a constant width of ≈550 nm. The diameter of the scroll is thus ≈350 nm. The lamellar thickness determined by AFM is ≈9.4 nm. The crystals are limited by growth faces oblique to the scroll axis. Hydrogen bonds decoration indicates that the H bonds are tilted to the scroll axis. This orientation is supported and complemented by selected area electron diffraction. Figure 10 reproduces in part the figure of the tip of a (sedimented) scroll. The associated electron diffraction is remarkably, taken from the very tip of the crystal, where only one layer has been selected. If taken further down the scroll, where top and bottom parts of the scroll are superposed, the diffraction pattern would look as arising from a twinned crystal, with the scroll axis acting as a morphological twin plane.32 This diffraction pattern shows two pairs of 100 reflections of the PA66 unit cell, whereas only one pair of these reflections is expected for “conventional” single crystals of PA66.

Selected area electron diffraction on the lancelets locates the 100 spots at some 23° to the direction of fastest growth, parallel to the long, smooth edge of the crystal [Khoury, F., personal communication]. The detailed structure remains uncertain. The small triangular crystals coexist with scrolled crystals. Their structure is not understood yet. They display, very characteristically, one smooth edge and two more serrated growth faces. This morphology is highly original and has, to our knowledge, only one precedent in polymer science, also not yet understood. It is the socalled “hour watch glasses” crystals of poly(β-benzyl aspartate) produced in hexafluoroisopropanol. They are also limited by smooth and serrated facesin this case by two smooth faces and only one serrated face.29 To summarize, scrolled crystals are rather frequent when melting/ annealing and recrystallization conditions are adequate. They coexist with less frequent triangular crystals and very rare tube-like crystals. The finer crystallographic details (cell orientation, possible twinning, etc.) of these different crystal forms have not been worked out yet. Morphologies Produced in More Concentrated Solutions. When applied to more concentrated solutions, thermal histories that imply annealing in the dissolution range yield morphologies that are very reminiscent of the spherulites produced in the bulk. These crystalline entities provide an elegant means to apprehend the lamellar organization of the spherulites. In addition, these entities are large (in the tens of micrometers) and offer the possibility to correlate the optical properties with their morphology. Figure 9, reproduced from ref 14, gathers the spherulite morphologies observed for negative spherulites, positive, and zero birefringence spherulites and spherulitic aggregates.

Figure 9. SEM images of the different morphologies of PA66 obtained in concentrated solution in glycerin: (a) initial stage of a positive spherulite; (b) negative spherulite (the round sphere) with development of spherulitic aggregates on its surface; (c) spherulites with zero birefringence; (d) spherulitic aggregate. Reproduced with permission from ref 14. Copyright 2004 Elsevier. Useful information provided by these SEM images is as follows: • Positive spherulites (here developed in only one direction, i.e., not having reached spherical symmetry yet) are made of large, elongated, fanning lamellae, as is well-known in polymer crystallization. • Negative spherulites are very different. They are “spherical” and made of a very dense population of crystalline entities. These entities cannot be resolved at the resolution of the SEM. Zero birefringence spherulites have the same texture/structure as negative spherulites, as already inferred long ago (to quote: “the different birefringence [between negative and zero birefringence spherulites] indicates a difference of degree, not of structure”). G

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Figure 10. A sedimented, flattened scrolled crystal of PA66 (left part), the electron diffraction pattern of the selected area (middle), and its analysis in terms of a (010) twin (right part). The twin plane is parallel to the hydrogen-bonded sheet and at 30° to the scroll axis. The growth direction indicated by the hydrogen bond decoration (cf. Figure 6, middle) is parallel to the twin plane and also at 30° to the (apparent) growth direction indicated by the scroll axis direction. Reproduced with permission from ref 12. Copyright 2004 Wiley.

Figure 11. Calculated patterns expected for a PA66 negative spherulite made of twinned, scrolled, radial lamellae. Note the slightly different positions of the 010 spots in the top and bottom models. They should be at identical places on the pattern (the hydrogen bonded plane is common in the two models). They are 3°−4° apart, which illustrates the minor approximations of the calculation indicated in the Experimental Section. Beyond these morphological, rather qualitative analogies, a more critical test rests on the comparison of the available diffraction data and the diffraction pattern expected for a spherulite made of scrolled lamellae. The model must account not only for the position of the reflections, as is usually the case. It must also explain the curious spread of the diffraction pattern that is not expected from a wellordered morphologythe pattern was once considered to be a powder pattern. It must also provide a plausible explanation for the observed variation of birefringence illustrated in Figure 4. In this approach and analysis, the methodology developed by Lovinger is highly relevant. We consider the orientation of the different unit-cell reflections and compare them with the data obtained by the zone solidification method. As it turns out, the pattern is indeed a “fiber” pattern (with the radial direction as the “fiber” axis), but it combines three (and possibly even four) different unit-cell orientations. Two of them stem from the analysis of the scrolled single crystals illustrated in Figure 6; the other(s) is (are) quite unexpected as they are a morphological consequence of the lamellar scrolling. Transfer of the Scrolled Crystals Structure to Negative Spherulites. In PA66 scrolled crystals, the (010) twin plane is oriented at ≈30° angle to the scroll axisthe angle made by the bisector of the four spots with the scroll axis. In solution crystallization, the lamellae wrap the hollow cylindrical interior. The

The 54° angle between the pairs of 100 diffraction spots indicates that the twin plane is the (010) plane of the unit cell, that is, the hydrogenbonded sheet. This additional information is a major ingredient in the structure analysis to come: the lamellae that build up the scrolls are twins, and they share a common H-bond direction. The H-bonded sheets are parallel to the bisector of the 54° angle, that is, at nearly 30° to the scroll axis, and to the growth direction. This information is a key in deciphering the structure of negative PA spherulites. Structure of Negative Spherulites. The lamellar shape of “conventional” (flat) PA66 crystals (cf. SI1) and of scrolled single crystals differs markedly, even though they have the same unit cell. Similarly, positive and negative spherulites have the same unit cell, but their lamellar organization and internal structure must differ. Are the different spherulite optical properties due to different orientations of the crystallographic axes only, as is known for example in poly(ethylene adipate), or do they also indicate a different lamellar shape? If so, a potential candidate would be scrolled lamellae. For PVDF in its γ phase, solution grown crystals and spherulites are both made of similar scrolled lamellae. For γPVDF, recognition of lamellar scrolling by Vaughan30 was first made on lightly etched spherulites and only later reported for solution grown crystals. For the PA66 case, the chronology iswill beexactly opposite. H

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Figure 12. Diffraction pattern expected for a radial b-axis orientation and, on the right, for a combinaton of all three unit-cell orientations considered so far. tilt of the stems in the lamellae is difficult to determine from the limited data available. Only two sets of 100 reflections are imaged in Figure 10, which indicates that at least after sedimentation and flattening, the stems are not exactly normal to the lamellar surface other hk0 reflections would be present. A small tilt is likely. We will assume nevertheless at this stage, in agreement with Lovinger’s analysis, that the stems are normal to the lamellar surface. This assumption is also supported by the fact that when polyamide fibers produced at lower temperature are heated above the Brill transition, near the melting domain of PA66, the lamellar surface becomes oriented normal to the stems.33 If the scroll is a building element of the spherulite, its long axis will be radial. The corresponding diffraction pattern expected from the arms of such a spherulite will be a fiber pattern since the lamella winds around the scroll and radial axis. This winding is more organized than a random azimuthal orientation of the unit cell around the radius. Diffraction-wise it translates in a very conventional fiber, even though the apparent randomness hides a more orderly (scroll) origin. In the present case, two unit-cell orientations need be considered. Following the procedure described in the Experimental Section, crystallographic vectors with orientations close to the scroll axis can be defined for the two cells in Figure 10. They are [6 8 −2] and [15 −9 1], respectively. In the following, they will be labeled cell I and cell II, respectively (awaiting, later on, a cell III). For cell I, the scroll axis is very nearly parallel to the [6 8 −2] direction of the α phase unit cell. This orientation and the expected diffraction pattern are illustrated in Figure 11, top row. The reflections are indexed in a quadrant calculated with an orientation half-width (ohw) of 2°. A complete pattern with an ohw of 5° helps better locate the reflections and gives a feeling of the actual pattern. A probably more realistic, but less “readable” pattern with an ohw of 10° will also be shown later on. The pattern calculated for this cell orientation bears, curiously, very strong similarities with the pattern retained by Lovinger to explain the spherulite structure (Figure 3). The 002 and 100 reflections are oblique to the fiber axis, and two reflections indexed as 010 and 110 with very similar spacing and intensities are located along the fiber axis/spherulite radius and tilted to it. However, the indexing of these 010 and 110 reflections is opposite for the scroll and the earlier model, which reflects the different orientation of the H-bonded sheets relative to the spherulite radius. The above structural model follows the standard analysis of spherulite structures in that it assumes a single radial crystallographic direction with a fiber-like rotation of the unit cell around that axis. In the present case, however, a fraction of the scrolls are in twinned orientationwith the twin plane oblique to the scroll axis. For this case II, the scroll axis is now nearly parallel to the [15 −9 1] direction of the unit cell. The patterns are illustrated in Figure 11, bottom row. They differ markedly from Figure 11, top row, in the expectedvery different locations of similar reflections relative to the “fiber” axis. In particular, the 100 reflections calculated for the two cell orientations are located very near and away from the scroll axis, which reproduces their position in the diffraction pattern of the solutiongrown scrolled crystal (Figure 10). The diffraction pattern of a PA66 spherulite made of radiating, twinned scrolls could be a combination of the two patterns, as

illustrated at the right of Figure 11. Clearly, the coexistence of two different unit-cell orientations results in a significantly more uniform distribution of intensities than for a single cell orientation. Combined with a wider spread of unit-cell orientations, and taking into account the fact that the populations of the two orientations may not be equal, the model of radial scrolled lamellae might account for the puzzling “full rings” patterns recorded for negative spherulites. Introducing an Additional Component in the Negative Spherulites Structure. As developed so far, the composite pattern illustrated in Figure 11 has however one significant weakness. The densitometric trace of the experimental pattern indicates that the 100 reflection is stongest near the equator (Figure 4). The two cell orientations associated with the scroll do not account for this feature. A third orientation of the unit cell must be involved. A logical third orientation is provided by the spherulitic aggregates that crystallize under the same conditions as the negative spherulites. In these entities, the b-axis is the fastest growth and radial direction. In the “fiber” diffraction pattern calculated for such a cell orientation, the 100 reflection is located on the equator (Figure 12). This orientation is a significantly better candidate than a radial a-axis, for which the 100 reflections are way off the equator (cf. later, Figure 16). Addition of this third unit-cell orientation results in a very even distribution of reflections for both the 100 reflection “ring” and for the combined 110/010 ring. Figure 12 (right side) illustrates the different reflections expected to contribute to the “composite” structure made of three different unit-cells orientations that following the present analysis build up the negative PA66 spherulites. It should be reemphasized at this stage that this analysis can only deal with the positions of reflections in the “fiber” pattern. The relative intensities of reflections depend on the weight of the different unit-cell orientations in the spherulite. Why should and how can a b-axis oriented component intervene in the structure of negative spherulites made of radial scrolled crystals? The answer is essentially morphological. Upper and lower limits of the surface tensions that the scrolled crystals can bear result in tolerable upper and lower lamellar curvatures. These limitations are best illustrated by the cross sections of chrysotile fibers illustrated in Figure 6: their core is empty, and the maximum diameter is ≈20 nm. Transposing the same limitations to the structure of scrolled lamellae of polyamides yields interesting insights. The geometry of the solution-grown PA66 scrolls provides useful data to illustrate the argument. Their diameter is 350 nm, and the lamella thickness is ≈10 nm. Assuming a hexagonal close-packed assembly of such monolayer, tube-like scrolls, the crystal represents only 10% of the total volume, 10% is ouside the scroll, and 80% is the scroll interior. In bulk, and for a spiral-like growth that generates a multilayered wall as illustrated in its early stage in Figure 6a for the PA66 scrolls and in its late or final stage in Figure 6c for asbestos, radial, cylinder-like zones of molten material remain at the scroll center, because the lamellae have reached their tolerable bending limit. In these tubes, crystallization in a scroll-type morphology is prevented. The only possibility left is a crystallization process along the scroll axis. This is precisely where the aggregate-type b-axis growth intervenes. I

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Macromolecules Crystallization in a confined space is well documented in polymer science.34 Crystallization along tubes, that is, in a 2D confinement, is observed (but this is only one example among many others) in the much narrower cylinders (13.7 nm) of the PEO sequence of a PEO-bPS diblock copolymer blended with PS homopolymer.35 Interestingly, the PEO chain axis tilt relative to the growth direction varies from 45° to 90° with Tc increasing from −30 to 0 °C and remains at 90° at higher Tc. In polyethylene, the highest chain tilt (also 45°) is reached at high Tc in very thin films, that is, in 1D confinement.36 In the present case, the geometric constraints that result in a radial and confined b-axis lamellar growth explains another, frequenty reported and puzzling feature of these entities. If and when these lamellae emerge from the radial cylinders/scrolls at the negative spherulite outer surface, they have the exact structure and orientation needed to initiate the development of spherulitic aggregates. Such a nucleation process of entities with a different morphology and structure is vividly illustrated in Figure 9b. At this stage, it might be worth mentioning that a further development of this model will be detailed in the Discussion section, when dealing with the variation of the birefringence with Tc. In the continuity of the logics developed so far, we stay for the present with this model and explore it at the crystallization temperature. Backtracking the Formation of Negative Spherulites at the Crystallization Temperature. The above analysis of the negative PA66 spherulites has one feature that appears curious. The unconventional orientation of the scroll axis does not make much sense in terms of its crystal structure. How can exotic crystallographic directions like [6 8 −2] or [15 9 −1] be singled out as scroll axes? The answer is in the well-known impact of the Brill transition in polyamides. The indexing rests on data obtained at room temperature and does not reflect the situation at Tc. In the polyamides case, crystallization takes place above the Brill transition. With increasing temperature, the intersheet distance increases, and at the Brill transition and above, the unit cell becomes pseudohexagonal in c-axis projection. For PA66, according to Hirschinger et al., the cell remains triclinic above 190 °C with parameters a = 0.491 nm, b = 0.587 nm, c = 1.650 nm, α = 55.7°, β = 80.7°, and γ = 60.1°.37 The c chain axis becomes slightly shorter (less than one Å) due to the introduction of gauche conformations at high Tc, mostly in the diamine segments. The b-axis parameter increases by 0.35 Å from its RT value (0.552 nm), which indicates a weakened interaction between the hydrogenbonded sheets.37 The model considered so far based on the room temperature cell geometry is thus inadequate. A more realistic model should use the high-temperature cell parameters and the hexagonal unit-cell projection. This amended version, based on the unit-cell parameters of Hirschinger et al., is illustrated in Figure 13 and is compared with the scroll axis case I (axis [6 8 −2]). Strikingly, the [110] plane of the high-temperature unit cell is nearly parallel to the scroll axis determined at room temperature (probably within the approximations of the modeling mentioned in the Techniques part). This observation suggests a much simpler relation between the scroll morphology as built up at Tc and the unit-cell orientation. At Tc, the scroll axis lies in the plane parallel to the bisector of the a* and b* axes, i.e., (1 −1 0). In addition, it is kept normal to the chain axis direction, which leads to a [4 4 −1] indexing. Figure 14 illustrates the diffraction pattern expected at Tc based on this scroll axis. The companion diffraction pattern expected at Tc for the b-axis component of the spherulite is also included. Both patterns are much less informative than the room temperature one since the three major hk0 reflections are not differentiated. Combined contribution of the two componentsnamely addition of the two right patterns with a 10° orientation half-width results in a virtually uniform distribution of intensities on a single ring. This is illustrated in Figure 15 which compares Lovinger’s experimental data and the (re)created patterns at 25 °C and at Tc based on the present structural model. The figure also illustrates in perspective the different cell orientations considered in this contribution.

Figure 13. Comparison of the scroll axes orientations at room temperature and at the crystallization temperature, above the Brill transition. In both cases, the scroll axis is assumed normal to the stems and thus the complex indexing. The molecular model shown for the high temperature form is not meant to represent the true structure, which has not been determined so far. The shaded area represents its pseudohexagonal cell projection. In this illustration, the hydrogen-bonded sheets orientation (horizontal) is supposed to remain unaffected by the expansion of the lattice. The room temperature scroll axis is rotated by ≈6° counterclockwise, as is the rotation of the b-axis (here at 1 o’clock). As it turns out, crossing the Brill transition on cooling is not detrimental but actually helps uncover two “hidden” features of the negative spherulites. First, the near-matching of the high Tc [4 4 −1] axis and room temperature [6 8 −2] applies only for that specific scroll axis. No similar connection applies for the second room temperature scroll axis indexed [15 −9 1]. On this basis, the buildup of the scroll at Tc rests mostly or exclusively on a single scroll axis of the more symmetrical unit-cell prevalent above the Brill transition. The case II orientation observed at room temperature appears to be created during the cooling process below the Brill transition. It is probably absent at Tc when the scroll and the negative spherulites are formed. Second, and perhaps more importantly, since only one scroll axis is involved, the surface stresses that generate the scroll have their resultant oriented exactly at right angle to the scroll axis, that i,s in the (1 1 0) plane of the high-temperature unit cell. Such an orientation makes much mechanical sense. This insight should help analyze possible molecular aspects of the folds. They will be addressed briefly in the Discussion section.

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DISCUSSION The development of the negative spherulites model presented above follows the intellectual process that lead to it. It blends structural features determined in single crystals and several assumptions, admittedly questionable but also reasonable. It was triggered by the need to explain the very unusually spreadout diffraction pattern of negative spherulites. The model reaches more or less such an agreement and is compatible with the spherulite texture. With its two populations, the model is not new. Magill7 mentions the hypothesis made by Cannon et al.23 back in 1963 about the structure of the zero birefringence spherulites. To quote: “It has been suggested [by Cannon et al.] that these spherulites arise as a result of a “mixing” together of crystallites of positive and negative orientations”. At best, the present model provides a firmer structural basis for this assumption, and of course considers it as valid beyond the sole zero birefringence spherulites. However, explaining a nearly unoriented diffraction pattern may be takenrightlyas an insufficient experimental J

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Figure 14. Top: diffraction pattern expected at Tc for a PA66 spherulite made of scrolls with the scroll axis in the (110) plane and normal to the chains (indexed [4 4 −1]). Bottom: diffraction pattern expected for the second spherulite component with radial b-axis orientation.

Figure 15. Top: experimental data (microbeam X-ray pattern and its densitometric trace) due to A. J. Lovinger on zone solidified negative spherulites of even−even polyamides (here, a PA610 sample) and the patterns calculated for the model developed in this contribution, assuming an orientation half-width of 10°. The patterns expected at room temperaure and above the Brill transition (at Tc) are illustrated. The different orientations of the unit-cell generate a very spread-out diffraction pattern although the texture is a very organized one. The distribution of intensities modeled here is not realistic. It will depend on the relative amounts of the different populations. Bottom: the four unit-cell orientations considered in this contribution. It should be reminded that in the two left diagrams the chain axis orientation shown normal to the scroll axis is most certainly only an approximation.

support for any model. Indeed, the pattern could beand in fact has been taken (or mistaken?)for a powder pattern or, alternatively for a radial b-axis oriented pattern, that is, for spherulites made of only one of its present ingredients. The present discussion considers whether the many unusual charateristics of the model supportor notand can explainor notother features of these negative spherulites.

In a second, more speculative part, molecular features of the lamellar structure are considered. In this approach, elements from a comparable analysis of spherulitic aggregates, still underway, are needed and will be briefly introduced. A Spherulite with Two Constituants: Optical Properties. The defining characteristic of these spherulites is their optical propertiestheir negative character. However, deterK

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character even though they are composed of two populations of lamellae at right angle to each other. The birefringence of the domains therefore depends on their orientation relative to the optical path. When the radial lamellae have their chains parallel to the light path, their negative contribution is canceled. What is left is only the positive contribution of the radial chains in tangential lamellae: domains of positive birefringence coexist with negative domains.38,39 The situation seems to be similar for the PA66 spherulitic aggregates, with additional features that further muddy the picture: branches growing at 45° to the aggregate axis, chain tilt. In short, when in a given domain the hydrogen bonds are nearly parallel to the optical path, their negative contribution to the birefringence is annihilated. Formation of near-single-crystal-like domains as exist for the aggregates cannot take place for the b-axis component in the scrolls. This population is truly fiber-like due to its orientation imposed by the radial scroll and its dispersion in many scrolls, which ensures a “clean” azimuthal spread around the radius. In addition, since the b-axis component’s growth is confined within very narrow domains (inside but also probably outside the scrolls: b-axis growth may “leak” outside the scrolls at e.g. branch points, etc.), the impact of branching is limited or even totally hindered. The scrolls house only the spines, or the branch-less “trunks” of the aggregates. In short, the “in-filling” b-axis “guests” located inside the scrolls set the negative character of the spherulite. Scrolls Component. In the scrolled component, the Hbonds are oriented at ≈30° to the spherulite radius, as determined on the single crystals. This is only 30° away from the radial H bond orientation in the positive spherulites. When partitioning the same refractive index of the scroll between its radial and tangential contributions, the “positive”, radial part is n × sin 60°, i.e., 0.87n. This limited 13% decrease maintains the positive character of spherulites that would be made of scrolls only. It should be noted that the optical properties are not very sensitive to the twinned nature of the scrolls at room temperature (with scroll axes parallel to [6 8 −2] and [15 9 −1]). In the twin, the chain (c-axis) and hydrogen bonds (aaxis) orientationsthe major contributors to the optical indicatrixare maintained. The tilts of the two b-axes are symmetric to the contact plane, which induces a (probably minor) “symmetrization” of the optical properties. Optically, the twinned components of the scrolls behave as a single species. The scrolls that build up the “skeleton” of negative spherulites are positive. Variation of Birefringence of Negative Spherulites. A continuous variation of spherulite birefringence with Tc as illustrated in Figure 4 is highly unusual in polymer science, especially when considering that there is no impact of crystal polymorphism. The only example known so far is provided againby spherulites of isotactic polypropylene in its most common alpha phase (αiPP). Its origin is well understood and is again linked with the lamellar branching. The variation of spherulite birefringence depends on the likelihood of lamellar branching as a function of Tc. At high Tc (above 145 °C), epitaxial deposition is reduced; it becomes virtually absent at 160 °C. The spherulites are mostly made of radial lamellae and are negative. At low Tc ( 226 °C, positive and fibrillar between 224−226 and 200 °C, and negative and possibly ringed again at Tc < 200 °C. Even though the sign of the birefringence is reversed, its variation suggests crystal-

For PA1010 the ring spacing is ≈1.2 μm at 160 °C, 3.5 μm at 180 °C, and on its way to a further sharp increase with Tc. PA 610 and all other positive spherulites show the same trend, as illustrated in Figure 4 and in the Supporting Information. By contrast, the ring spacing in these specific positive spherulites is clearly in the submicrometer range. Such discrepancies point to a structural origin significanly different from the “conventional” banding and lamellar twist in positive spherulites. Is this different structural origin connected in any way with the development and structure of scrolls? Can the scrolls introduce a periodic variation of the birefringence? At this point, the recent analysis made by Ivanov et al. on the structure of poly(propylene adipate) (PPA) banded spherulites appears highly relevant.40,41 These authors have established that in PPA spherulites the lamellae rotate uniformly about the growth axisthey form helices. Recognition of this new morphology of banded spherulites built up with helical lamellar ribbons “broke a paradigm” in the analysis of spherulite architecture. Optical banding had been explained thus far only with the familiar “lamellar twisting” that is geometrically and by contrast a helicoid. In the present context, the feature of interest is that lamellar helices can pack in registry and in phase and result in the spherulites’ optical banding. The finely banded polyamide spherulites fit in the same logics of a structure made of or impacted by “helical lamellar ribbons”, at a much smaller scale than observed in PPA. The polyamide scrolls are no more than a variant of the helical lamellar ribbons. In the polyamides case indeed, and contrary to the scrolled crystals of γPVDF, the scrolls result from a helical winding of lamellae around the central scroll axis. Both helical ribbons and scrolls have the same optical properties periodic optical extinction in a polarizing microscope. The troubling analogy of the bandwidth in the spherulites and the “helical pitch” of the scrolls supports this correlation. The scrolls/cylinders illustrated in Figure 6 have a diameter of 350 nm. The a-axis of the unit cell is oriented at 30° to the scroll axis. A full turn of the scroll is therefore completed when the unit cell has traveled 1.9 μm along the cylinder axis. Optically, this corresponds to two band widths, which sets the putative “bandwidth” of the PA66 solution grown scroll at 0.95 μm. Reversing the reasoning, and assuming scrolls with the same structure for the other PAs, the bandwidth would tell the scroll diameter. The 0.5 μm PA610 bandwidth would then indicate a scroll diameter of ≈184 nm. Following the reasoning developed earlier to evaluate the volumes of the scroll and its interior in a hexagonal close-packed model of scrolls, and assuming again a “single walled” scroll 10 nm thick, the outer part is ≈10%, the wall volume is ≈20%, and the scroll interior is ≈70%. If the scroll wall has two additional layers, the relative volumes would be ≈10% outside, ≈50% for the scroll wall, and ≈40% for the scroll interior. Increasing the positive contribution of the scroll walls at the expense of the negative contribution of the scroll interior will result in, to quote Magill, “ringed positive spherulites with low birefringence”. The more important contribution of the scrolls may also explain the lower melting temperature observed by Magill. The same scheme can explain the formation of some negative ringed spherulites, also reported by Magill. Negative spherulites are usually unringed “with the exception of spherulites formed in nylon-210 and -106, which exhibit a perceptible ringed structure of about 1 μ spacing or less”.7 The N

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The other major observationagain a constant feature in the PA negative spherulitesis that their melting temperature may be “considerably higher” than that of positive spherulites. As illustrated in Table 1, the positive versus negative Tm gap

lization and orientation processes that remind those considered for the even−even polyamides spherulites. Transposition of reasonings held for even−even PAs is tempting but must take into account the structural constraints set by the chemically different PAs: even−odd, odd−even, or odd−odd materials. The difficulty to establish a “clean” sheetlike pattern of hydrogen bonds, the existence of two hydrogen bond orientations in PA65, or, for example, a different orientation of the fast growth direction relative to the scroll axis, etc., will impact the morphology. A more detailed structural investigation with determination of the cell orientation(s) is clearly called for perhaps using the above elements as guidelines. The task will not be easy. On one hand, and as analyzed long ago, the optical properties are hard to use in any quantitative way: the birefringence of spherulites is systematically much weaker than anticipated from the refractive indices of the unit cell.3 On the other hand, judging from the present even−even PAs case and the coexistence of several different cell orientations, zone solidification experiments supplemented by modern microbeam X-ray investigation techniques will still result in the counterintuitive (and incorrect) conclusion reached earlier that “the X-ray method is rather insensitive to the actual orientation present”.4 The technique is not at fault; the problem is with the sample! Curiously, the different melting temperatures of the various elements may helpor at least may help recognize the complexity of the structures. Melting of Negative Spherulites and Spherulitic Aggregates: the b-Axis Component. Melting of negative spherulites has always been reported as being “higher” than that of positive spherulites. The (optical) melting temperatures for nylon-210, -66, -610, -106, and -1010 determined by Magill are reproduced in Table 1. The table illustrates the systematic observation mentioned in all reports: negative spherulites and spherulitic aggregates have identical melting temperatures within 1 °C or so. This similarity fully supports the dual populations model of the negative spherulites with a b-axis component similar to the spherulitic aggregates. In both cases, the melting is that of a baxis material, either as part of the negative spherulite scrolls or in “pure” form in the spherulitic aggregates. The higher Tm is also in line with a longer stem length associated with a higher Ts. The formation of the b-axis component inside the scrolls remains an open issue: confinement? The higher end of the Mw distribution depleted in the initial growth of the scrolls; that would result in lower actual undercooling? The different thermal stability may be used as an advantage to reveal the existence of different species. Several examples are at hand. For PA610, Lovinger observes that “at about 5−10°C below their melting points, these aggregates were seen to disintegrate into needle-like structures, 50−200 μm in length, oriented parallel to the direction of solidification”.8 Are these needle-like entities scrolls? In a different work, Magill reports that for nylon-49 positive and negative low birefringence spherulites coexist at T ≈ 236 °C.7 “Some of the spherulites change sign during heating and cooling on the hot stage”, a process that can be repeated in cycles. The birefringence may revert or not depending on the subsequent cooling rate. All these features point to a complex structure with different constituents, one of which can be explored in the small temperature gap when the other one is melted.

Table 1. Optical Melting Temperatures Determined by Magill7 for Several Even−Even Polyamides in Their Three Characteristic Morphologies polymer

positive spherulites

negative spherulites

aggregates

nylon-210 nylon-66 nylon-610 nylon-106 nylon-1010

284 265 225 250 207

269−271 238−240 257−259 210−212

270−272 238−240 258−260 210−213

varies between 3 and 5 °C for nylon-66 and -1010 but is significantly larger for the two polymers for which the diamine and diacid segments lengths differ most, namely nylon-610 and -106: 13−15 °C and 7−9 °C, respectively. In line with the increased stem length, the increment in lamellar thickness is larger for longer alkyl segments, thus, possibly, the larger gap in the melting temperature. Molecular and Structural Aspects of the Scrolls. The structure of the negative spherulites as developed in this contribution emphasizes the major role played by the scrolled crystals first in the initial buildup and second in directing the additional growth of the b-axis component. In this last section, we compare features that generate lamellar scrolling in polymers and point out possible further work on polyamides. Molecular Aspects. In asbestos, the molecular origin of the scrolling lies in features of the crystal structurenamely the different lattice spacings of two different but chemically linked chemical species that result in a splay of crystal planes.25,26 In polymers, the splay has its origin in differences in fold volume and/or fold conformation, which makes its analysis much more complexwith one exception. The exception is the scrolled crystals of γPVDF. They provide the clearest illustration of the impact of a fold volume difference, certainly the illustration least “spoiled” by differences in conformation. In γPVDF the folds on opposite lamellar surfaces have an identical (odd) number of carbon atoms and the geometry of the points of emergence of the folds (e.g., bond orientations at the crystal-fold boundary) are identical, which suggests similar or identical fold conformations. The folds differ by their chemical constitution: say three CH2−CF2 units plus either one CH2 unit (volume: ≈35 Å3) or one CF2 unit (volume: ≈45 Å3). The fold volumes differ by only ≈10 Å3 for a total volume of ≈300 Å3. The resulting minute difference in fold cross sections generates a slight but cumulative splay in a plane normal to the fold direction, thus the resulting scrolling.31,45 The geometry of the scroll is also quite simple: the folds orientation and growth faces are parallel to the b-axis, that is also the scroll axis. γPVDF nanoscrolls recently produced in solution have dimensions very comparable to the PA66 ones: their diameter is 400 nm. In a recent detailed analysis of the scroll geometry the splay of crystal planes ≈5 Å apart was determined to be 0.14°.46 Isotactic poly(1-butene) (iPBu1) in its form III has an orthorhombic, chiral crystal structure made of helices with a 4fold symmetry. In bulk, it forms ringed spherulites with twisted lamellae, contrary to the conformationally achiral forms I and II. Solution crystallization generates also scrolled crystals, O

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Macromolecules frequently stemming from split edges of flat or pyramid-like single crystals.47 The splitting breaks the symmetry imposed by the single crystal growth and reveals the unbalanced surface stresses of the lamellae. A tentative analysis of the twist (and by implication of the scroll) emphasizes the different symmetry of the helices and the unit cell.45 Four different points of emergence and reentry of the folds are possible for each stem. They are segregated/selected by the orientation of the growth faces. The unbalanced surface stresses would thus result from differences in constitution (fold length) and conformation but with no means to quantify or apportion these contributions. The PA66 scrolls are structurally more complex. Even though the details of the fold are not established (in the absence of clear indication of the chain tilt in the lamellae), a geometrical analysis of the scroll is of interest. Let us recall that the scrolls have a diameter of 350 nm and the hydrogen bonds are at 30° to the scroll axis direction. The lamellar thickness is 10 nm, and we assume that it is fully crystalline. We evaluate the different splay observed in a cross section of the scroll versus the splay along the H-bonded sheet and conclude with a scroll chirality issue. For the Cross Section. After one turn, the path difference between the outer and inner lamella surface is π (350−330) nm, i.e., 63 nm or 630 Å. This path difference is split between ≈2250 stems 4.9 Å apart in the (110) plane (Brill structure, cf. Figure 13). Therefore, the difference between outer and inner stem distances in lamellae 10 nm thick is 0.28 Å. (Note that the 4.9 Å periodicity involves two (2−20) layers and is not the classical “inter-hydrogen-bonded layer” distance in polyamides). The interstem distance difference of 0.28 Å at opposite ends of the 10 nm long stem is significant: 5.7% of the crystallographic parameter. The splay between stems in the scroll cross section (that does not depend on the crystallinity assumed for the layer) is 0.16°. These figures for PA66 scrolls are very similar to the recent reevaluation of the γPVDF solution-grown nanoscrolls due to Burks et al.46 The scroll diameters and cell parameters are comparable. This similarity would suggest that the mechanical properties of the polymer lattice govern the scroll geometry more than the specific molecular origin leading to scrolling. Such a conclusion may be hasty. In this context, it is worth reminding that the “helical lamellar ribbons” in poly(propylene adipate) spherulites have a much larger diameter of ≈6 μm.40 For the H-Bonded Sheets. The H-bonded sheets travel over a longer distance in the scrolled lamella before completing one full turn. With its 30° angle to the scroll axis, the outer part of the sheet travels (350π/sin 60), i.e., 2200 nm or 22 000 Å. The inner part travels only (330π/sin 60) nm, i.e., 20 720 Å or 128 Å less. This distance corresponds to 4500 H-bonded stems ≈4.9 Å apart located in successive (2−20) planes (cf. again Figure 13). The length of the a parameter therefore differs on the outer and inner fold surfaces by 128 Å/4500 or 0.028 Å. This path difference results in a splay between successive stems of arcsin(0.028 Å/100 Å) or 0.016°, a figure that again is independent of the crystallinity index. The interlayers 0.16° splay is therefore ten times larger than the 0.016° intra-H-bonded layer splay, which reflects the different strength of interstem interactions in the two directionsthey are especially weak in the interlayers above the Brill transition. The absolute values of the splaysin the tenths or hundredths of a degree range−also illustrate how and

why morphology only can reveal these very minute, but cumulative, splays. Scroll Chirality. In Figure 10, the H-bonded sheets are oriented at 30° clockwise to the radial growth and scoll axis. Selection of only one orientation (clock or anticlock) indicates that the scrolls have a structural chiralitythey are helical ribbons. Related observations have been reported for lamellar twistthe two morphologies are induced by unbalanced surface stresses. The chirality of twisted lamellae of polyethylene is introduced by the clockwise or anticlockwise tilt (in the ac plane) of the PE stems relative to the lamella fold surface normal. Growth in +b and −b directions results, in thin films, in oppositely bent lamellae and, in spherulites, in lamellae with left- or right-handed twist.45 In the present PA66 scrolls, the chirality appears to be linked with the low symmetry unit cell. Referring to Figure 13, exchanging the a- and b-axes or considering growth in the reverse direction creates as situation in which the a-axis is symmetrically oriented to the scroll axis. The link between opposite growth directions and morpholology has already been analyzed for the sense of lamellar twist in poly(trimethylene terephthalate) by Rosenthal et al. (to quote: “the polarity of the growth axis has a crucial impact on the lamella handedness” and “reveal a one-to-one correlation between the handedness and growth axis polarity”.48 Note however that the chirality of twisted lamellae is “visible”. In sharp contrast, revealing the chirality of the PA66 scrolls growth is a much more challenging task since it is nearly “hidden” in the resulting near-cylindrical symmetry of the scroll. In the present case, it could only be revealed by the selected area diffraction pattern shown in Figure 10. Polyamides Scrolls and Original Lamellae Shapes: Specificity of Surface Stresses Origin? Further Insights? Twisted and scrolled polymer lamellae are, as a rule, observed for specific polymers only and moreover, if polymorphic, frequently for only one of their crystal structures. It is therefore difficult to draw general conclusions from their analysis. For example, the stem tilt in the poly(trimethylene terephthalate) twisted lamellae is only 4° which, if chain tilt is the determining factor, precludes any meaningful correlation at a molecular scale with the selection of twist−right or left. A 4° tilt is to quote “too faint to be the primary source of the surface stresses required for twisted lamellar growth”.40 (It should be added that the chain of this polymer is nonplanar, which might play a role also.) The polyamides appears to offer a wider range of materials of interest to investigate the role of crystal structure and/or fold constitution and conformation in the generation of unbalanced surface stresses. A variety of PAs with different chemical constitutions (even−even, even odd, odd−odd) display different spherulite types. Also, different lamellar morphologies (flat, scrolled, lancelets, triangles) may help decipher the different crystal structure(s) or growth modes and balance/imbalance of surface stresses involved. Some guidelines are provided in the following. They will need further support, both from experiment and from detailed molecular simulation. The first objective of these investigations is clearly to reach beyond the easy but first-order explanation of scrolling in PA66 (and other even−even polyamides) resting on the volume difference between amine and acid aliphatic parts. For PA66, the volume difference between the two folds is 70 Å3. For the γPVDF scrolls it is 10 Å3. Yet, the scrolls of the two polymers P

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opposite fold surfaces and of course scrolls with different folds (amine versus acid). These more detailed analyses, to be completed, will and must take into account information provided by the other highly specific morphologies (triangles, lancelets, etc.) formed by even−even polyamides under similar crystallization conditions.

both produced in solution are comparable (diameter, lamellar thickness). The fold volume is only part of the game. In PA66, conformational adjustments are needed to limit the splay of adjacent stems. The volume issue could be tackled by using a variety of different PAs. For the family of 30+ even−even polyamides investigated by Atkins and collaborators,16 “unconventional” lamellae types may be found including, possibly, scrolls by using annealing/partial melting protocols. PAs with short aliphatic segments would be of interest given their tendency to form folds reminding the β-turn of antiparallel stems in pleated sheets of proteins. PAs with equal length acid and amine segmentsso-called “nylon isomer pairs”would be of particular interest. To quote: “Nylon isomer pairs with inverted amides (nylons X Y and Y-2 X+2) form sheets with the same hydrogen-bonded lattice parameters; however, these pairs usually exhibit different sheet stacking and behave differently on heating.”16 The fold conformation issue is more difficult to tackle. Historically, and much in the spirit of polyethylene and cyclic parafins, help was sought from the conformation of cyclic models of PAs, which must fold. Northolt has investigated the structure of several cyclic monomer and dimers of PA6 and PA66.49−51 These systems turn out to be of little help as models of folds. As shown in Figure SI5, the dimer of PA66 forms extended rings that would at best correspond to loops linking second-nearest-neighbor stem. (In the analysis of scrolled morphologies, they are believed to play a secondary role.) The cyclic monomer of PA6 forms a protein-like β-turn at the acid moiety, but the near-extended C6 segment of the amine moiety shifts the amine groups well over 5 Å apart unacceptable in a H-bonded polyamide sheet and thus not representative. The dimer of PA6 also is essentially a double protein-like β-turn. Two major features are common to all these systems: (a) nearby amide moieties are antipolar; (b) hydrogen bonds are oriented at right angles to the plane of the aliphatic stems (in a protein-like “β-turn” type). Both features are inconsistent with the prevalent hydrogen bonding within the chain-folded sheets in even−even polyamide crystals: the conformation and stacking of rings obeys different rules than polymer chain folding. The different crystal structures formed by chemical sequences that impose departures from the trans−trans conformation provide other insights, as illustrated with the work on PA65. The hydrogen bonds directions are no longer confined within a single sheet.43 Above the Brill transition, such intersheet hydrogen bonding cannot be excluded in even−even polyamides, as advocated long ago by Atkins.52 This may apply in particular for the amide groups next to the folds where molecular mobility differs from the crystal interior. It would also be compatible with NMR37 and IR17,19 data mostly indicating both preservation of the low temperature sheet structure and mobility of the aliphatic segments above the Brill transition. In ultimate analysis, the existence of interlayer hydrogen bonding, whether partial and/or temporary or more permanent (which raises the issue of a possible metastable crystal phase), appears to be a major ingredient in the buildup of PA 66 scrolls. Such H-bonds help “glue” the “critical” (110) planes normal to the scroll axis. They have the required structural/ conformational versatility. They can be located at acid and amine folds and generate flat crystals with similar folds on

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CONCLUSION

The complexity and variability of the polyamide negative spherulites optical properties cannot be accounted for by any “standard” spherulite structure model based on a single component. The complex composite structure introduced in the present work does provide the necessary versatility required to meet this challenge. It differs from all previous models in that it combines twoor more!populations of crystalline entities. The scrolled morphology of the first formed lamellae generates a confined, oriented frame or scaffold within which a second, in-filling material develops. The composite structure thus created introduces new variables: different cell orientations of the two populations with competing optical properties, possibility of variable (weight) proportions of the two populations with the crystallization temperature, and even the possibility for the in-filling population to crystallize with two different cell orientations (b- or a-axis orientations) with negative and positive contributions to the global optical properties of the spherulite. The scrolled lamellae explain the very fine texture of the negative spherulites and provide a structural basis for the submicrometer dimensions indicated in many reports. They also explain the absence of optical banding (i.e., of twisting lamellae) in most of these spherulites. Conversely, the “helical lamellar ribbon” nature of the scrolls can explain the formation of banded spherulites with a very short band spacinga feature that “is not connected” with the more common lamellar twist of positive spherulites. The b-axis in-filling component of negative spherulites has the same structure as the spherulitic aggregates, which explains that their melting temperatures are systematically identical. In the lower part of the “negative” domain, a progressive intrusion of an a-axis in-filling growth may explain in a very “natural” way the variation of birefringence and the smooth transition from negative to clear positive birefringence while keeping the same, scrolled architecture. Further work is required to draw all the consequences of this composite spherulite architectureunderstanding the “reversed” optical properties of even−odd or odd−odd polyamides, connecting the negative spherulites and the spherulitic aggregates, analyzing the optical properties in a more quantitative way, understanding the more detailed molecular aspects, etc. The initial postulate of scrolled lamellae in negative spherulites, transferred from the investigation of solution grown crystals, may lead to further developments. For the time being, we are tempted to conclude this contribution by borrowing Keith and Padden’s words about their concept of unbalanced surface stresses to explain lamellar twisting. The proposed multicomponent architecture of negative spherulites of even−even polyamides “...commands attention because deductions based upon it appear to represent a significant advance in interpretation of diverse and hitherto unexplained morphological observations in a reasonably coherent way”.53 Q

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(5) Mann, J.; Roldan-Gonzalez, L. Orientation in Nylon Spherulites: A Study by X-Ray Diffraction. J. Polym. Sci. 1962, 60, 1−20. (6) Magill, J. H. Spherulitic Crystallization. Part I. “Odd-Even” Polyamides: Nylon 56 and 96. J. Polym. Sci., Part A: Gen. Pap. 1965, 3, 1195−1219. (7) Magill, J. H. Formation of Spherulites in Polyamide Melts: Part III. Even-Even Polyamides. J. Polym. Sci. A2 1966, 4, 243−265. (8) Lovinger, A. J. Crystallographic factors affecting the structure of polymeric spherulites. I. Morphology of directionally solidified polyamides. J. Appl. Phys. 1978, 49 (10), 5003−5013. (9) Lovinger, A. J. Crystallographic factors affecting the structure of polymeric spherulites. II. X-ray diffraction analysis of directionally solidified polyamides and general conclusions. J. Appl. Phys. 1978, 49 (10), 5014−5028. (10) Geil, P. H. Nylon Single Crystals. J. Polym. Sci. 1960, 44, 449− 458. (11) Geil, P. H. In Polymer Single Crystals; Interscience Publishers: 1963; p 82. (12) Cai, W.; Li, C. Y.; Li, L.; Lotz, B.; Keating, M.; Marks, D. Submicrometer Scroll/tubular Lamellar Crystals of Nylon 6,6. Adv. Mater. 2004, 16 (7), 600−605. (13) Li, C. Y.; Cai, W.; Li, L.; Lotz, B.; Keating, M.; Marks, D. On the crystal structure and morphology of nylon 6,6 from single crystals to spherulites. Polym. Mater. Sci. Eng. 2004, 91, 188−189. (14) Li, L.; Li, C. Y.; Cai, W.; Lotz, B.; Keating, M.; Marks, D. Nylon 6,6 scroll/tubular single crystals. Polym. Mater. Sci. Eng. 2004, 91, 495−496. (15) Atkins, E. D. T.; Keller, A.; Sadler, D. M. Structural Analysis of Chain Folded Lamellae Polyamide Crystals from X-Ray Diffraction. J. Polym. Sci. A2. 1972, 10, 863−875. (16) Jones, N. A.; Atkins, E. D. T.; Hill, M. J. Comparison of Structures and Behavior on Heating of Solution-Grown, ChainFolded Lamellar Crystals of 31 Even-Even Nylons. Macromolecules 2000, 33, 2642−2650. (17) Cooper, S. J.; Coogan, M.; Everall, N.; Priestnall, I. A polarized μ-FTIR study on a model systemfor nylon 6 6: implications for the nylon Brill structure. Polymer 2001, 42, 10119−10132. (18) Yoshioka, Y.; Tashiro, K. Structural changes in the Brill transition of Nylon m/n (1) Nylon 10/10 and its model compounds. Polymer 2003, 44, 7007−7019. (19) Yoshioka, Y.; Tashiro, K.; Ramesh, C. Structural changes in the Brill transition of Nylon m/n (2) Conformational disordering as viewed from the temperature-dependent infrared spectral measurements. Polymer 2003, 44, 6407−6417. (20) Tashiro, K.; Yoshioka, Y. Conformational disorder in the Brill transition of uniaxially-oriented nylon 10/10 sample investigated through the temperature-dependent measurement of X-ray fiber diagram. Polymer 2004, 45, 6349−6355. (21) Brenschede, W. Sphärolithische Struktur synthetischer Hochpolymerer. Colloid Polym. Sci. 1949, 114, 35−44. (22) Cannon, C. G.; Harris, P. H. Chain Folding and the Structure of Nylon 6.6 Spherulites. J. Macromol. Sci., Part B: Phys. 1969, 3 (2), 357−364. (23) Cannon, C. G.; Chappel, F. P.; Tidmarsh, J. I. Temperature dependence of birefringence of nylon 6.6 and the structure of spherulites. J. Text. Inst. Transactions 1963, 54, T210−T221. (24) Franco, L.; Puiggali, J. Structural data and thermal properties on nylon-12,10. J. Polym. Sci., Part B: Polym. Phys. 1995, 33, 2065− 2073. (25) Monkman, L. J. In Applied Fiber Science; Happey, F., Ed.; Academic Press, Inc.: London, 1979; Vol. 3, Chapter 4, pp 163−196. (26) Virta, R. L. “Asbestos: Geology, Mineralogy, Mining, and Uses”, U.S. Department of the Interior, U.S. Geological Survey: Open-File Report 02-149. (27) Ruland, W.; Schaper, A. K.; Hou, H.; Greiner, A. Multi-wall carbon nanotubes with uniform chirality: evidence for scroll structures. Carbon 2003, 41, 423−427.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00915. SI1: diffraction pattern and electron microscopy bright field image of a single crystal of polyamide 610; SI2: hydrogen bond decoration of Bombyx mori L. and Tussah (wild) silk fibers; SI3: birefringence characteristics of spherulites of even−even nylons as summarized by Magill; SI4: fold structure and organization in scrolled crystals of poly(vinylidene difluoride) gamma phase; SI5: conformation of cyclic models of PA6 and PA66, as determined by Northolt; SI6: brief summary of contributions by Mitomo et al. [J. Polym. Sci., Polym. Phys. Ed. 1977 and 1978) on polyamide-66 single crystals annealing and lamellar thickness stepwise increase by 1/2 monomer unit length (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (B.L.). ORCID

B. Lotz: 0000-0001-8091-9014 S. Z. D. Cheng: 0000-0003-1448-0546 C. Y. Li: 0000-0003-2431-7099 Notes

Note Added in Proof. After submission of this article, we came across contributions by H. Mitomo, K. Nakazoto, and I. Kuriyama [J. Polym. Sci., Polym. Phys. Ed., 1977, 15, 915; Polymer 1978, 19, 1427−1432] that report on an investigation of mats of PA66 single crystals (in 1977) annealed in the presence of glycerol (in 1978). Specifically, these authors observe that “the...lamellar thickness [of nylon-6,6 crystal] increased stepwise by 1/2 monomer unit length with increasing annealing temperature or annealing time”. The observation of PA66 lamellar thickness increases by half a chemical unit length is way ahead of and more systematic than our analysis of lamellar scrolling. We apologize for these earlier and present oversights. More details are given in SI6. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are deeply grateful to Andy Lovinger and Freddy Khoury for their advice, for sharing unpublished information, and for their friendly criticisms that helped bring this work to fruition. S.Z.D.C. acknowledges the support of National Science Foundation (DMR-1409972).

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REFERENCES

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DOI: 10.1021/acs.macromol.8b00915 Macromolecules XXXX, XXX, XXX−XXX