The structure formation in amorphous-semicrystalline block copolymers is determined by the interplay of microphase separation in the melt and crystallization of the crystallizable block. The formed morphology strongly depends on the sequence of the two relevant physical events, i. e. if crystallization occurs from an already microphase-separated melt or from a homogeneous melt.
The kinetic nucleation theory of Hoffman and co-workers was initially developed for homopolymers. The extension of this theory to the crystallization of block copolymers was introduced by Richardson et al..55
In its original form, the Lauritzen-Hoffman theory provides expressions for the linear growth rate (Γ), i. e. the rate at which spherulites or axialites grow, as a function of the degree of supercooling (Tm0 – Tc), with the equilibrium melting temperature Tm0 and the crystallization temperature Tc.56 In this model it is assumed that the crystal lamellae at the growth front grow at the same rate as the macroscopic linear growth rate (Figure 1.5).
Secondary or tertiary nucleation controls the growth together with the short-range diffusion of the crystallizing units. There are also modification of this original theory in the literature, but these do not change the essential features.57-61
g
Γ
Figure 1.5: Growth of a lamellar crystal according to the Lauritzen-Hoffmann theory. The lateral growth rate is denoted g and the linear growth rate Γ.62
Three regimes of growth are predicted. In regime I, for small supercoolings, lateral growth of crystallites occurs with stems in a monolayer on the substrate, whereby the monolayers are added one by one according to the linear growth rate. The lateral growth rate (g) is significantly higher than the rate of formation of secondary nuclei. As a consequence,
and the crystal growth is determined by multiple nucleation. As the multiple nucleation is no longer restricted within a monolayer, the secondary nucleation rate is faster compared to regime I. In addition, because of the multiple nucleation on the already existing monolayers the crystallite surface exhibits an increasing roughness. Finally, in regime III, growth occurs by prolific multiple nucleation.
The growth rate in the three regimes, at a given crystallization temperature Tc, can be written as:56,63
Here U* is an activation energy, and T∞ reflects the temperature at which diffusion is stopped. The parameter j depends on the growing regime, and equals to 2 in regime I and III, whereas j = 1 in regime II. The monolayer thickness contributes as b, the specific free energy of the surface is denoted σ, and σL is the lateral surface free energy. ∆G corresponds to the specific change in free energy upon crystallization, and R and k are the universal gas constant and the Boltzmann constant, respectively. Γ0,i is a temperature dependent pre-factor, which is specific for the three regimes.
The approach of Hoffman and Lauritzen encountered in spite of its success also criticism, especially by Point64 and Sadler65. Sadler constructed an alternative model which works for rough growth faces, introducing a reversible detachment and attachment of short-chain sequences as elementary steps. Calculations revealed that the growth face exhibits many configurations, of which only a minority allows the face to progress. As a consequence, the rate of growth is controlled by high entropic activation barriers. However, the different models have one common feature, as they assume that the lamellar crystallites grow directly into the entangled melt.
More recently Strobl et al. introduced a new approach based on earlier works and on own investigations, proposing that crystallization proceeds via a transition of mesomorphic and granular crystalline layers to lamellar crystallites.66-68 A sketch of the proposed mechanism is given in Figure 1.6.
Figure 1.6: Sketch of the route proposed for the formation of polymer crystallites.68
The process starts with the attachment of straightened chain segments with a certain minimum length from the isotropic melt onto the lateral growth face of a layer with a mesomorphic inner structure. The stretching is not perfect, i. e. the chains, although basically helical, include many conformational defects. There exists a minimum thickness for the mesomorphic layer in order to be stable in the surrounding melt. Subsequently, each part of the mesomorphic layer thickens with time, implying a continuous rearrangement of the chain sequences in the zone composed of folds and loops near to the layer surface. When a critical thickness of the mesomorphic layer is reached, the layer solidifies by a structural transition.
The resulting structure can be described as a “granular crystal layer”, consisting of crystal blocks in a planar assembly. Finally, the crystal blocks merge together, which goes along with an improvement of their inner perfection. The resulting homogeneous lamellar crystallite exhibits the same thickness as the constituent blocks. The merging process provides a stabilization, however, the degree of stabilization might not be uniform through the sample.
As a result, some regions in the sample may even remain in the granular crystal state.
The orientation of crystalline stems with respect to the lamellar interface in block copolymers is a subject of ongoing interest and controversy. The two possible orientations of crystalline stems within a semicrystalline block copolymer are depicted schematically in Figure 1.7. The orientation of crystalline stems has been investigated intensively for polyethylene and poly(ethylene oxide) containing diblock copolymers and was found to depend in a very sensitive fashion on the sample preparation technique. In contrast to homopolymers, where the crystalline stems are arranged perpendicular with respect to the lamellar interphase, parallel chain orientation has been observed for block copolymers crystallizing from a microphase-separated melt. However, it is not clear if the parallel folding is the most stable one, or whether perpendicular orientation can also occur for crystallization
Figure 1.7: Schematic depiction of perpendicular and parallel chain folding of the crystalline chains with respect to the domain interphase in semicrystalline block copolymers.62
Investigations by Douzinas and Cohen on oriented polyethylene-block-poly(ethyl ethylene) (PE-b-PEE) diblock copolymers, exhibiting a microphase-separated melt, revealed that the PE chains are oriented parallel to the lamellar interphase.69 This is in agreement with results obtained by Séguéla and Prud’homme.70 There have been also investigations on lamellar polyethylene-block-poly(ethylene-alt-propylene) (PE-b-PEP) diblock copolymers which were oriented using a channel die.71 It turned out that the lamellae orient perpendicular to the plane of shear when the diblock copolymers were oriented above the melting temperature of PE, whereas a parallel orientation was found when compression occurred below the melting temperature. However, in both cases the crystalline PE chains were oriented parallel to the lamellar interphase. In contrast to these results, Rangarajan et al.
observed for PE-b-PEP diblock copolymers (12 – 56 wt-% PE) a perpendicular orientation of the crystalline PE stems.72 In this case the samples were not oriented and crystallization occurred from a homogeneous melt.
Investigations on oriented PE-b-PEE, PE-b-PEP, and polyethylene-block-poly(vinyl cyclohexane) (PE-b-PVCH) diblock copolymers have been performed by Hamley et al.73,74 In symmetric PE-b-PVCH diblock copolymers crystallization of PE is confined within a lamellar morphology with glassy PVCH lamellae, as the glass transition of PVCH is higher than the crystallization temperature of PE. A parallel orientation of the crystalline PE stems with regard to the lamellar interphase was observed both for diblock copolymers with a rubbery or a glassy amorphous block.
In contrast to the preferential parallel orientation of crystalline stems with respect to the domain interphase in PE containing diblock copolymers, investigations on poly(ethylene oxide) based diblock copolymers revealed a perpendicular folding of the crystalline PEO
chains. In this context, the reader is referred to representative works on poly(ethylene oxide)-block-poly(butylene oxide) (PEO-b-PBO)75,76 and polyisoprene-block-poly(ethylene oxide) (PI-b-PEO)77 diblock copolymers.
In semicrystalline-amorphous diblock copolymers basically two different situations can occur depending on the segregation strength between the chemically different blocks.
Crystallization can be either confined in lamellar, cylindrical or spherical microdomains for strongly segregated systems, or crystallization predominates the structure formation for weakly segregated or homogeneous systems. The final microphase and crystalline morphology is determined by three competing physical events: the microphase-separation in the melt (order-disorder transition temperature TODT), the crystallization temperature Tc of the crystallizable component, and the vitrification (glass transition temperature Tg) of the amorphous block. In general three different situations can be distinguished (a more detailed description including citations of various contributions can be found in chapter 3.2.1 and ref.78). In systems exhibiting a homogeneous melt (TODT < Tc > Tg), microphase-separation is driven by crystallization. This results in a lamellar morphology where crystalline lamellae are sandwiched by the amorphous block layers, regardless of the composition. In weakly segregated systems (TODT > Tc > Tg), often referred to as “soft confinement”, crystallization frequently occurs with little morphological constraint enabling a “breakout” from the ordered melt structure. Consequently, any preexisting morphology in the molten state is overwritten by crystallization, resulting in a lamellar structure. However, confined crystallization within spherical or cylindrical microdomains is possible in strongly segregated systems and/or for highly entangled amorphous blocks. A strictly confined crystallization within microdomains is observed for strongly segregated diblock copolymers with a glassy amorphous block (TODT > Tg > Tc, hard confinement). As a result, the initially formed melt structure is preserved upon crystallization.
Crystallization within block copolymer microdomains is not only affected by the strength of confinement. Furthermore, the structure of the microdomain, i. e. continuous (gyroid, lamellae) or dispersed (cylinders, spheres), and even the size of the microdomain exhibit a significant influence. For example, Chen et al. observed for blends of a polybutadiene-block-poly(ethylene oxide) (PB-b-PEO) diblock copolymer with PB a decrease in crystallization temperature for the PEO block with decreasing PEO domain size (PEO content).79 Similar results were obtained for other block copolymers, exhibiting confined crystallization within isolated spherical or cylindrical microdomains.80-84 In addition, confined
corresponding semicrystalline homopolymers due to spatial restrictions.82,84-91 Crystallization can even be suppressed if the crystallizable block is confined into spheres or cylinders.90-92 Studies on the crystallization kinetics revealed a strong dependence on the confinement active during crystallization. Unusual first-order crystallization kinetics with an Avrami exponent of n = 1 have been observed for strongly confined crystallization within spherical or cylindrical microdomains.93-95 This observation has been related to a homogeneous nucleation mechanism. However, in some special cases even lower Avrami exponents have been detected.80,90
The crystallization in polymers is usually induced by heterogeneous nucleation, homogeneous nucleation or self-nucleation. In crystallizable homopolymers crystallization in the bulk state commonly occurs on heterogeneous nuclei (catalyst debris, impurities, and other types of heterogeneities of unknown nature) at relatively low supercoolings (10 - 15 °C).96 Homogeneous nucleation includes the formation of a crystal-like embryo induced by density fluctuations in the melt, which occurs at comparatively high supercoolings (50 - 70 °C). The nucleation on remaining crystal fragments in the melt, which reflect crystallographically “ideal” nuclei, is referred to as self-nucleation. Within block copolymers the type of nucleation strongly depends on the type of microdomain. Crystallization in large or continuous domains is mostly induced by heterogeneous nucleation, since the probability that a heterogeneity is located within the crystallizable domain is sufficiently high. However, if the crystallizable block is confined into small isolated microdomains (spheres, cylinders) crystallization proceeds in a fractionated manner, i. e. several crystallization exotherms are observed, or crystallization can only be induced by homogeneous nucleation.79-84,90,97-101
Microdomains that contain the heterogeneities usually active at low supercoolings in the bulk homopolymer will crystallize at an identical temperature compared to that of the bulk polymer. However, if less efficient heterogeneities are present in the microdomain, a larger supercooling is necessary in order to induce crystallization. Those microdomains that do not contain any heterogeneity will only be able to nucleate homogeneously, in the case that the interphase does not affect the nucleation process. Especially, in block copolymers where the crystallizable component is confined into small isolated microdomains the number density of isolated microdomains is significantly higher than the average number of available heterogeneities.83 At least 1015 isolated microdomains/cm3 could be present, while for instance a bulk PEO homopolymer contains less than 106 heterogeneities/cm3. As a result, the probability of a heterogeneity to be situated in an isolated microdomain is vanishing small, thus favoring homogeneous nucleation.
Besides the vast number of publications concerning the crystallization within semicrystalline-amorphous diblock copolymers, there have been only few contributions on ABC triblock copolymers with crystallizable components. Among them are reports by Stadler et al. and other groups on polystyrene-block-polybutadiene-block-poly(ε-caprolactone) (PS-b-PB-b-PCL) triblock copolymers and their hydrogenated analogues (PS-b-PE-b-PCL) in which a complex interplay between microphase-separation and crystallization has been found.100-108 In addition, there are also reports on PS-b-PI-b-PEO109-112, PS-b-PEP-b-PE113, poly(α-methyl styrene)-block-polyisobutylene-block-polypivalolactone (PmS-b-PIB-b-PVL)114 and PS-b-PEO-b-PCL82 triblock copolymers.