Cyclic and Linear Tetrablock Copolymers Synthesized at Speed and Scale by Lewis Pair Polymerization of a One-Pot (Meth)acrylic Mixture and Characterized at Multiple Levels.

Cyclic block copolymers (cBCP) are fundamentally intriguing materials, but their synthetic challenges that demand precision in controlling both the monomer sequence and polymer topology limit access to AB and ABC block architectures. Here, we show that cyclic ABAB tetra-BCPs (cABAB) and their linear counterpart (lABAB) can be readily obtained at a speed and scale from one-pot (meth)acrylic monomer mixtures, through coupling the Lewis pair polymerization's unique compounded-sequence control with its precision in topology control. This approach achieves fast (<15 min) and quantitative (>99%) conversion to tetra-BCPs of predesignated linear or cyclic topology at scale (40 g) in a one-pot procedure, precluding the needs for repeated chain extensions, stoichiometric addition steps, dilute conditions, and postsynthetic modifications, and/or postsynthetic ring-closure steps. The resulting lABAB and cABAB have essentially identical molecular weights (Mn = 165-168 kg mol-1) and block degrees/symmetry, allowing for direct behavioral comparisons in solution (hydrodynamic volume, intrinsic viscosity, elution time, and refractive indices), bulk (thermal transitions), and film (thermomechanical and rheometric properties and X-ray scattering patterns) states. To further the morphological characterizations, allylic side-chain functionality is exploited via the thiol-ene click chemistry to install crystalline octadecane side chains and promote phase separation between the A and B blocks, allowing visualization of microdomain formation.

Enzymatic Degradation Behavior of Self-Degradable Lipase-Embedded Aliphatic and Aromatic Polyesters and Their Blends.

Over the past decade, the preparation of novel materials by enzyme-embedding into biopolyesters has been proposed as a straightforward method to produce self-degrading polymers. This paper reports the preparation and enzymatic degradation of extruded self-degradable films of three different biopolyesters: poly(lactic acid) (PLA), poly(butylene adipate-co-terephthalate) (PBAT), and poly(butylene succinate) (PBS), as well as three binary/ternary blends. Candida antarctica lipase B (CalB) has been employed for the enzyme-embedding procedure, and to the best of our knowledge, the use of this approach in biopolyester blends has not been reported before. The three homopolymers exhibited differentiated degradation and suggested a preferential attack of CalB on PBS films over PBAT and PLA. Moreover, the self-degradable films obtained from the blends showed slow degradation, probably due to the higher content in PLA and PBAT. These observations pave the way for exploring enzymes capable of degrading all blend components or an enzymatic mixture for blend degradation.

How the Aliphatic Glycol Chain Length Determines the Pseudoeutectic Composition in Biodegradable Isodimorphic poly(alkylene succinate-ran-caprolactone) Random Copolyesters.

We synthesize four series of novel biodegradable poly(alkylene succinate-ran-caprolactone) random copolyesters using a two-step ring-opening/transesterification and polycondensation process with ε-caprolactone (PCL) as a common comonomer. The second comonomers are succinic acid derivatives, with variations in the number of methylene groups (nCH2) in the glycol segment, nCH2 = 2, 4, 8, and 12. The obtained copolyesters were poly(ethylene succinate-ran-PCL) (ESxCLy), poly(butylene succinate-ran-PCL) (BSxCLy), poly(octamethylene succinate-ran-PCL) (OSxCLy), and poly(dodecylene succinate-ran-PCL) (DSxCLy). We discovered a new mixed isodimorphic/comonomer exclusion crystallization in ESxCLy copolymers. The BSxCLy, OSxCLy, and DSxCLy copolymers display isodimorphic behavior. Our findings revealed a significant variation in the pseudoeutectic point position, from mixed isodimorphism/comonomer exclusion crystallization to isodimorphism with pseudoeutectic point variation from 54% to up to 90%. Moreover, we established a link between the melting temperature depression slope variation and the comonomer inclusion/exclusion balance, providing valuable insights into the complex topic of isodimorphic random copolymers.

Strong Hydrogen Bonds Sustain Even-Odd Effects in Poly(ester amide)s with Long Alkyl Chain Length in the Backbone.

The number of methylene groups between strongly interacting functional groups within polymer repeating units induces even-odd effects on thermal and mechanical properties. However, detailed studies correlating the even-odd effect with structural changes are still lacking. In this work, we establish correlations between the structure and thermal properties of poly(ester amide)s containing long alkyl chain lengths. The even-odd effect impacts the thermal properties, including the melting temperature and crystallinity degree. It influences the spherulitic morphology of poly(ester amide)s, controlling the appearance of banding. We demonstrate that even-odd effects in poly(ester amides)s persist even with 27 CH2 groups within the repeating unit, an effect due to strong hydrogen bonds caused by the amide groups. Our X-ray studies reveal that the even-odd effect originates from changes in the crystalline structure of the materials. This work helps elucidate the role of strong intermolecular interactions (i.e., hydrogen bonding) on the even-odd effect in long-chain poly(ester amides).

Origin of Melt Memory Effects in Poly(ethylene oxide): The Crucial Role of Entanglements.

The melt memory effect on crystallization is an intriguing phenomenon displayed by semicrystalline polymers, as opposed to low molar mass molecules. It concerns the effect of melt temperature on nucleation upon recrystallization. Typically, polymer crystals must be considerably superheated to erase the effect of previous morphology on the subsequent crystallization, avoiding an acceleration of the process. Despite being known for decades, its origin is still not fully understood. Investigating model poly(ethylene oxide) covering a wide range of molar mass, it is demonstrated that melt memory originates from topological constraints among the chains, i.e., entanglements, for PEO in which weak intermolecular interactions are present due to the ether groups. In fact, no memory is observed for samples below the critical molar mass for the formation of entanglements (about 1 kg mol-1). The increase in molar mass raises the number of entanglements and induces the formation of folded chains crystals, both factors leading to a topologically complex amorphous phase, enhancing the melt memory effect. The molecular origin of the melt memory effect in polymers with weak intermolecular interactions is thus ascribed to a slower isotropization in the melt of the chain segments originally contained in the crystals, due to the presence of entanglements among the chains. This study defines the distinction between small molecules and polymers from the point of view of melt memory.

Building Ultrastrong, Tough and Biodegradable Thermoplastic Elastomers from Multiblock Copolyesters via a "Reserve-Release" Crystallization Strategy.

Simultaneously attaining high strength and toughness has been a significant challenge in designing thermoplastic elastomers, especially biodegradable ones. In this context, we present a class of biodegradable elastomers based on multiblock copolyesters that afford extraordinary strength, toughness, and low-strain resilience despite expedient chemical synthesis and sample processing. With the incorporation of the semi-crystalline soft block and the judicious selection of block periodicity, the thermoplastic materials feature low quiescent crystallinity ("reserve") albeit with vast potential for strain-induced crystallization ("release"), resulting in their significantly enhanced ultimate strength and energy-dissipating capabilities. Moreover, a breadth of mechanical responses of the materials - from reinforced elastomers to shape-memory materials to toughened thermoplastics - can be achieved by orthogonal variation of segment lengths and ratios. This work and the "reserve-release" crystallization strategy herein highlight the double crystalline multiblock chain architecture as a potential avenue towards reconciling the strength-toughness trade-off in thermoplastic elastomers and can possibly be extended to other biodegradable building blocks to deliver functional materials with diverse mechanical performances.

Easy Synthetic Access to High-Melting Sulfurated Copolymers and their Self-Assembling Diblock Copolymers from Phenylisothiocyanate and Oxetane.

Although sulfurated polymers promise unique properties, their controlled synthesis, particularly when it comes to complex and functional architectures, remains challenging. Here, we show that the copolymerization of oxetane and phenyl isothiocyanate selectively yields polythioimidocarbonates as a new class of sulfur containing polymers, with narrow molecular weight distributions (Mn=5-80 kg/mol with D≤1.2; Mn,max=124 kg/mol) and high melting points of up to 181 °C. The method tolerates different substituent patterns on both the oxetane and the isothiocyanate. Self-nucleation experiments reveal that π-stacking of phenyl substituents, the presence of unsubstituted polymer backbones, and the kinetically controlled linkage selectivity are key factors in maximising melting points. The increased tolerance to macro-chain transfer agents and the controlled propagation allows the synthesis of double crystalline and amphiphilic diblock copolymers, which can be assembled into micellar- and worm-like structures with amorphous cores in water. In contrast, crystallization driven self-assembly in ethanol gives cylindrical micelles or platelets.

Installing Controlled Stereo-Defects Yields Semicrystalline and Biodegradable Poly(3-Hydroxybutyrate) with High Toughness and Optical Clarity.

Stereo-defects present in stereo-regular polymers often diminish thermal and mechanical properties, and hence suppressing or eliminating them is a major aspirational goal for achieving polymers with optimal or enhanced properties. Here, we accomplish the opposite by introducing controlled stereo-defects to semicrystalline biodegradable poly(3-hydroxybutyrate) (P3HB), which offers an attractive biodegradable alternative to semicrystalline isotactic polypropylene but is brittle and opaque. We enhance the specific properties and mechanical performance of P3HB by drastically toughening it and also rendering it with the desired optical clarity while maintaining its biodegradability and crystallinity. This toughening strategy of stereo-microstructural engineering without changing the chemical compositions also departs from the conventional approach of toughening P3HB through copolymerization that increases chemical complexity, suppresses crystallization in the resulting copolymers, and is thus undesirable in the context of polymer recycling and performance. More specifically, syndio-rich P3HB (sr-P3HB), readily synthesized from the eight-membered meso-dimethyl diolide, has a unique set of stereo-microstructures comprising enriched syndiotactic [rr] and no isotactic [mm] triads but abundant stereo-defects randomly distributed along the chain. This sr-P3HB material is characterized by high toughness (UT = 96 MJ/m3) as a result of its high elongation at break (>400%) and tensile strength (34 MPa), crystallinity (Tm = 114 °C), optical clarity (due to its submicron spherulites), and good barrier properties, while it still biodegrades in freshwater and soil.

Tailoring the Nucleation and Crystallization Rate of Polyhydroxybutyrate by Copolymerization.

In the polyester family, the biopolymer with the greatest industrial potential could be poly(3-hydroxybutyrate) (PHB), which can be produced nowadays biologically or chemically. The scarce commercial use of PHB derives from its poor mechanical properties, which can be improved by incorporating a flexible aliphatic polyester with good mechanical performance, such as poly(ε-caprolactone) (PCL), while retaining its biodegradability. This work studies the structural, thermal, and morphological properties of block and random copolymers of PHB and PCL. The presence of a comonomer influences the thermal parameters following nonisothermal crystallization and the kinetics of isothermal crystallization. Specifically, the copolymers exhibit lower melting and crystallization temperatures and present lower overall crystallization kinetics than neat homopolymers. The nucleation rates of the PHB components are greatly enhanced in the copolymers, reducing spherulitic sizes and promoting transparency with respect to neat PHB. However, their spherulitic growth rates are depressed so much that superstructural growth becomes the dominating factor that reduces the overall crystallization kinetics of the PHB component in the copolymers. The block and random copolymers analyzed here also display important differences in the structure, morphology, and crystallization that were examined in detail. Our results show that copolymerization can tailor the thermal properties, morphology (spherulitic size), and crystallization kinetics of PHB, potentially improving the processing, optical, and mechanical properties of PHB.

Synthesis, Morphology, and Crystallization Kinetics of Polyheptalactone (PHL).

Aliphatic polyesters are widely studied due to their excellent properties and low-cost production and also because, in many cases, they are biodegradable and/or recyclable. Therefore, expanding the range of available aliphatic polyesters is highly desirable. This paper reports the synthesis, morphology, and crystallization kinetics of a scarcely studied polyester, polyheptalactone (PHL). First, we synthesized the η-heptalactone monomer by the Baeyer-Villiger oxidation of cycloheptanone before several polyheptalactones of different molecular weights (in the range between 2 and 12 kDa), and low dispersities were prepared by ring-opening polymerization (ROP). The influence of molecular weight on primary nucleation rate, spherulitic growth rate, and overall crystallization rate was studied for the first time. All of these rates increased with PHL molecular weight, and they approached a plateau for the highest molecular weight samples employed here. Single crystals of PHLs were prepared for the first time, and hexagonal-shaped flat single crystals were obtained. The study of the crystallization and morphology of PHL revealed strong similarities with PCL, making PHLs very promising materials, considering their potential biodegradable character.

Tuning the crystallization and thermal properties of polyesters by introducing functional groups that induce intermolecular interactions.

The performance of sustainable polymers can be modified and enhanced by incorporating functional groups in the backbone of the polymer chain that increases intermolecular interactions, thus impacting the thermal properties of the material. However, in-depth studies on the role of intermolecular interactions on the crystallization of these polymers are still needed. This work aims to ascertain whether incorporating functional groups able to induce intermolecular interactions can be used as a suitable systematic strategy to modify the polymer thermal properties and crystallization kinetics. Thus, amide and additional ester groups have been incorporated into aliphatic polyesters (PEs). The impact of intermolecular interactions on the melting and crystallization behavior, crystallization kinetics, and crystalline structure has been determined. Functional groups that form strong intermolecular interactions increase both melting and crystallization temperatures but retard the crystallization kinetics. Selecting appropriate functional groups allows tuning the crystallinity degree, which can potentially improve the mechanical properties and degradability in semicrystalline materials. The results demonstrate that it is possible to tune the thermal transitions and the crystallization kinetics of PEs independently by varying their chemical structure.

Toughening Brittle Bio-P3HB with Synthetic P3HB of Engineered Stereomicrostructures.

Poly(3-hydroxybutyrate) (P3HB), a biologically produced, biodegradable natural polyester, exhibits excellent thermal and barrier properties but suffers from mechanical brittleness, largely limiting its applications. Here we report a mono-material product design strategy to toughen stereoperfect, brittle bio or synthetic P3HB by blending it with stereomicrostructurally engineered P3HB. Through tacticity ([mm] from 0 to 100 %) and molecular weight (Mn to 788 kDa) tuning, high-performance synthetic P3HB materials with tensile strength to ≈30 MPa, fracture strain to ≈800 %, and toughness to 126 MJ m-3 (>110× tougher than bio-P3HB) have been produced. Physical blending of the brittle P3HB with such P3HB in 10 to 90 wt % dramatically enhances its ductility from ≈5 % to 95-450 % and optical clarity from 19 % to 85 % visible light transmittance while maintaining desirably high elastic modulus (>1 GPa), tensile strength (>35 MPa), and melting temperature (160-170 °C). This P3HB-toughening-P3HB methodology departs from the traditional approach of incorporating chemically distinct components to toughen P3HB, which hinders chemical or mechanical recycling, highlighting the potential of the mono-material product design solely based on biodegradable P3HB to deliver P3HB materials with diverse performance properties.

Confined Crystallization of Polymers within Nanopores.

Crystallization of polymeric materials under nanoscopic confinement is highly relevant for nanotechnology applications. When a polymer is confined within rigid nanoporous anodic aluminum oxide (AAO) templates, the crystallization behavior experiences dramatic changes as the pore size is reduced, including nucleation mechanism, crystal orientation, crystallization kinetics, and polymorphic transition, etc. As an experimental prerequisite, exhaustive cleaning procedures after infiltrations of polymers in AAO pores must be performed to ensure producing an ensemble of isolated polymer-filled nanopores. Layers of residual polymers on the AAO surface percolate nanopores and lead to the so-called "fractionated crystallization", i.e., multiple crystallization peaks during cooling.Because the density of isolated nanopores in a typical AAO template exceeds the density of heterogeneities in bulk polymers, the majority of nanopores will be heterogeneity-free. This means that the nucleation will proceed by surface or homogeneous nucleation. As a consequence, a very large supercooling is necessary for crystallization, and its kinetics is reduced to a first-order process that is dominated by nucleation. Self-nucleation is a powerful method to exponentially increase nucleation density. However, when the diameter of the nanopores is lower than a critical value, confinement prevents the possibility to self-nucleate the material.Because of the anisotropic nature of AAO pores, polymer crystals inside AAO also exhibit anisotropy, which is determined by thermodynamic stability and kinetic selection rules. For low molecular weight poly(ethylene oxide) (PEO) with extended chain crystals, the orientation of polymer crystals changes from the "chain perpendicular to" to the "chain parallel to" the AAO pore axis, when the diameter of AAO decreases to the contour length of the PEO, indicating the effect of thermodynamic stability. When the thermodynamic requirement is satisfied, the orientation is determined by kinetics including crystal growth direction, nucleation, and crystal growth rate. An orientation diagram has been established for the PEO/AAO system, considering the cooling condition and pore size.The interfacial polymer layer has different physical properties as compared to the bulk. In poly(l-lactic acid), the relationship between the segmental mobility of the interfacial layer and crystallization rate is established. For the investigation of polymorphic transition of poly(butane-1), the results indicate that a 12 nm interfacial layer hinders the transition of Form II to Form I. Block and random copolymers have also been infiltrated into AAO nanopores, and their crystallization behavior is analogously affected as pore size is reduced.

Effect of Chain Stereoconfiguration on Poly(3-hydroxybutyrate) Crystallization Kinetics.

Poly(3-hydroxybutyrate) (PHB) is naturally accumulated by bacteria but can also be synthesized chemically. Its processability is limited, as it tends to degrade at temperatures above its melting temperature; hence, investigation into crystallization kinetics and morphology of PHB materials of both natural and synthetic origins is of great need and interest to get a better understanding of structure-property relationship. Accordingly, this contribution reports a first study of the crystallization and morphology of synthetic PHB materials of different molecular weights. These synthetic PHBs are racemic mixtures (50/50 mol %) of R and S chain configurations and are compared with an enantiopure bacterial R-PHB. Nonisothermal and isothermal crystallization studies show that R and S chains of PHB can cocrystallize in the same unit cell as the R-PHB. Most significantly, the results show that the presence of S chains decreases the overall crystallization rate, which could enhance the processability and industrialization of PHB-based materials.

The role of intermolecular interactions on melt memory and thermal fractionation of semicrystalline polymers.

The origin of melt memory effects associated with semicrystalline polymers and the physical parameters involved in this process have been widely studied in the literature. However, a comprehensive understanding of the role of intermolecular interactions on melt memory is still being developed. For this purpose, we have considered aliphatic polyesters and we have incorporated amide and additional ester groups. Inserting these additional functional groups, the strength of the intermolecular interactions increases widening the melt memory effect. Not only the presence of the functional groups but also the position of these groups in the repeating unit plays a role in the melt memory effect as it impacts the strength of the intermolecular interactions in the crystals. The study of the effect of intermolecular interactions has been extended to successive self-nucleation and annealing thermal fractionation experiments to explore for the first time the role of intermolecular forces on the fractionation capacity of linear polymers. We demonstrated that intermolecular interactions act as intrinsic defects interrupting the crystallizable chain length, thus facilitating thermal fractionation. Overall, this work sheds light on the role of intermolecular interactions on the crystallization behavior of a series of aliphatic polyesters.

Effect of the TrFE Content on the Crystallization and SSA Thermal Fractionation of P(VDF-co-TrFE) Copolymers.

In this contribution, we study the effect of trifluoro ethylene (TrFE) comonomer content (samples with 80/20, 75/25, and 70/30 VDF/TrFE molar ratios were used) on the crystallization in P(VDF-co-TrFE) in comparison with a PVDF (Poly(vinylidene fluoride)) homopolymer. Employing Polarized Light Optical Microscopy (PLOM), the growth rates of spherulites or axialites were determined. Differential Scanning Calorimetry (DSC) was used to determine overall crystallization rates, self-nucleation, and Successive Self-nucleation and Annealing (SSA) thermal fractionation. The ferroelectric character of the samples was explored by polarization measurements. The results indicate that TrFE inclusion can limit the overall crystallization of the copolymer samples, especially for the ones with 20 and 25% TrFE. Self-nucleation measurements in PVDF indicate that the homopolymer can be self-nucleated, exhibiting the classic three Domains. However, the increased nucleation capacity in the copolymers provokes the absence of the self-nucleation Domain II. The PVDF displays a monomodal distribution of thermal fractions after SSA, but the P(VDF-co-TrFE) copolymers do not experience thermal fractionation, apparently due to TrFE incorporation in the PVDF crystals. Finally, the maximum and remnant polarization increases with increasing TrFE content up to a maximum of 25% TrFE content, after which it starts to decrease due to the lower dipole moment of the TrFE defect inclusion within the PVDF crystals.

Effect of the Crystallization Conditions on the Exclusion/Inclusion Balance in Biodegradable Poly(butylene succinate-ran-butylene adipate) Copolymers.

Biomedical applications of polymers require precise control of the solid-state structure, which is of particular interest for biodegradable copolymers. In this work, we evaluated the influence of crystallization conditions on the comonomer exclusion/inclusion balance of biodegradable poly(butylene succinate-ran-butylene adipate) (PBSA) isodimorphic random copolymers. Regardless of the crystallization conditions, the copolymers retain their isodimorphic character, displaying a pseudo-eutectic behavior with crystallization in the entire composition range. This illustrates the thermodynamic nature of the isodimorphic behavior for PBSA random copolymers. However, depending on the composition, the crystallization conditions affect the exclusion/inclusion balance of the comonomers. Fast cooling favors butylene adipate (BA) inclusion inside the poly(butylene succinate) (PBS) crystals, whereas isothermal crystallization strongly limits it. PBA-rich compositions behave differently. Both fast and slow crystallization formed the ß-phase, whereas BS unit inclusion is favored independently of the cooling conditions. During successive self-nucleation and annealing, the BA inclusion is intermediate between non-isothermal and isothermal conditions, while the crystalline structure of the PBA phase changes from the ß-phase to the more stable α-phase. We propose a simple crystallographic model to explain the changes in the unit cell dimension of the copolymers.

Polymorphism and Multiple Melting Behavior of Bio-Based Poly(propylene 2,5-furandicarboxylate).

Furandicarboxylate-based polyesters are considered an interesting class of bio-based polymers due to their improved properties with respect to the petrol-based terephthalate homologs. An in-depth analysis of the crystal structure of poly(propylene 2,5-furandicarboxylate) (PPF), after maximum possible removal of the catalyst, was carried out. The study disclosed that purified PPF presents two different crystalline phases after crystallization from the melt. Crystallizations at temperatures lower than 120 °C lead to growth of a single crystal form (ß-form), whereas two different crystal forms (α and ß) were found to coexist at higher Tcs. This behavior is opposite to that previously observed for unpurified PPF. The possibility that the catalyst nucleates the α-phase, which therefore becomes the kinetically favored modification at low crystallization temperatures in the presence of a higher amount of catalyst residue, has been considered as a feasible explanation. Two concomitantly different spherulitic morphologies were observed and connected to the ß- and α-phase, respectively. The association between polymorphism and melting behavior was studied. The origin of the peaks that compose the multiple melting endotherm recorded at conventional heating rates was determined by combined wide-angle X-ray scattering, differential scanning calorimetry, fast scanning chip calorimetry, and polarized light optical microscopy measurements. The higher thermal stability of the α-crystals in comparison with the ß-form was thus demonstrated.

Interphase Design of Cellulose Nanocrystals/Poly(hydroxybutyrate-ran-valerate) Bionanocomposites for Mechanical and Thermal Properties Tuning.

Poly[(3-hydroxybutyrate)-ran-(3-hydroxyvalerate)] (PHBV) is a bacterial polyester with a strong potential as a substitute for oil-based thermoplastics due to its biodegradability and renewability. However, its inherent slow crystallization rate limits its thermomechanical properties and therefore its applications. In this work, surface-modified cellulose nanocrystals (CNCs) have been investigated as green and biosourced nucleating and reinforcing agent for PHBV matrix. Different ester moieties from the CNCs were thereby produced through a green one-pot hydrolysis/Fisher esterification. Beyond the improved dispersion, the CNCs surface esterification affected the thermal and thermomechanical properties of PHBV. The results demonstrate that butyrate-modified CNCs, mimicking the PHBV chemical structure, brought a considerable improvement toward the CNCs/matrix interface, leading to an enhancement of the PHBV thermomechanical properties via a more efficient stress transfer, especially above its glass transition.

Crystallization Kinetics of Poly(ethylene oxide) under Confinement in Nanoporous Alumina Studied by in Situ X-ray Scattering and Simulation.

While a relatively complete understanding of the nucleation and orientation of polymers under confinement in one-dimensional nanochannels has been achieved, crystallization kinetics investigation of confined polymers is still rare. In this work, we investigated the crystallization kinetics of poly(ethylene oxide) confined in anodic alumina oxide templates with different pore sizes using in situ wide-angle X-ray scattering (WAXS). The crystallization kinetics results were fitted with the Avrami equation. The Avrami index was determined by both "isothermal step crystallization" and in situ WAXS. The crystallization process of polymers under one-dimensional nanopore confinement was simulated by a "one-dimensional lattice model". Based on this model, it is shown that homogeneous nucleation with the simultaneous growth of multiple crystal planes with drastically different growth rates could result in Avrami indexes lower than 1.