Cross-nucleation of polybutene-1 Form II on Form I seeds with different morphology

2.1 Material

The polymer studied in the present work is a butene-1 homopolymer (PB-1) with commercial-grade name of PB0110M, kindly provided by LyondellBasell. It has a weight-average molecular weight of 850 kg/mol and a polydispersity index of 6.8.

2.2 Sample preparation

Granules of PB-1 were used without any further treatment to make thin films, 30 to 50 μm thick, by compression-molding at a temperature of 180°C. PB-1 fibers used in this work were lab-spun using a capillary rheometer (RH7, Bohlin) at the Institute of Chemistry of the Chinese Academy of Science in Beijing, by the group of Prof Dujin Wang. The temperature of the barrel was 180°C and the rotation speed of the collector was set to 200 rpm.

To prepare the substrates of interest characterized by different morphologies, the thin film samples were heated up to 180°C in a Mettler FP90 hot-stage, kept at this temperature for 5 minutes to erase the previous processing history, and further cooled to the crystallization temperature. Temperatures of 90°C and 108°C were selected, in order to obtain a spherulitic and a hedritic morphology, respectively.39 After an appropriate crystallization time of approximately 4 and 270 minutes at low and high temperature, respectively, morphologies of similar size were reached in the two cases. Then the samples were quickly cooled down to room temperature and aged for more than 1 month in order to completely transform the original Form II crystals into Form I. It should be noted that, according to previously adopted procedures for cross-nucleation studies in PB-1, a dual morphology is produced.17, 38, 40 Indeed, low melting temperature crystals of Form I, formed during quenching to room temperature, are essential for having molten PB-1 in contact with crystalline Form I seeds (with higher melting temperature).17, 19

2.3 Polarized light optical microscopy

The morphology and the nucleation behavior were observed in situ by a Leica DMLP optical microscope under crossed polarizers, equipped with a computer-controlled digital camera (Optika B5). The thermal treatments were applied by a calibrated Mettler Toledo FP82HT hot-stage. To investigate the nucleation on the substrates of spherulite and hedrite, the Form I films were heated to different melting temperatures (T_h) at 20°C/min, and kept for 5 minutes to melt completely Form II crystals or Form I crystals with lower thermal stability, and subsequently quenched to T_c for performing the isothermal crystallization (Figure 1A).

For the experiments with the fiber substrate, these thin PB-1 films were first heated to 180°C and kept at this temperature for 5 minutes to erase the previous processing history, then they were cooled down to different melting temperatures (T_h). The PB-1 fibers, containing Form I crystals, were then manually introduced in the film at this temperature. After a second annealing step at T_h, to relax the induced stresses, the samples were cooled down to the selected crystallization temperature (T_c) (Figure 1B). The described thermal protocols are presented in Figure 1.

3.1 Determination of nucleation induction time via light intensity measurements during crystallization

Figure 2 shows an example of the time-resolved images obtained during isothermal crystallization, and explains the method used for induction time determination. Nucleation of Form II crystals occurs at every place on the side of the original Form I spherulite, forming a sort of crystalline “corona” around it (Figure 2A). In order to accurately detect the induction time, that is, the time at which the Form II cross-nuclei have reached a critical size and the transcrystalline growth proceeds, the increase of the light intensity in the sample due to the formation of birefringent Form II crystals is exploited. A circular “Region of Interest,” centered in the middle of the nucleating spherulite, is selected on the image analysis software, and the mean light intensity in the selected area is then calculated for each acquired frame. By plotting this intensity as a function of time (Figure 2B), it is possible to unambiguously determine the time at which it starts to increase from its initial value, that is, the induction time. Further details on the analysis method can be found in our recent work.41 The exact value of the induction time is determined by the intersection point between two fitting lines: one in the time region of the initial plateau value and the second in the first growth step part. An example of the analyzed data is reported in Figure 2B.

3.2 Cross-nucleation of PB-1 Form II on Form I seeds with different morphology

Figure 3 shows some representative optical micrographs of PB-1 crystallized on the surface of Form I substrates with different morphologies: spherulite, hedrite, and fiber. All the samples were crystallized isothermally at 105°C, after melting the original Form II/Form I crystals at 124°C. The thermal treatment at relatively high temperature ensures that the remaining seeds are composed of Form I only, while any crystalline memory of possible residual Form II crystals (ie, self-nucleation) is erased.40 In all the three morphologies, a clear transcrystalline layer (TCL), indicative of a very high “linear density” of nucleation sites, develops with time. The TCL13, 14, 42, 43 is a consequence of lack of lateral separation between the individual growing spherulites on the nucleating surface, causing the crystals to grow exclusively perpendicularly to it. It is apparent that the nucleating efficiency of the three substrates is particularly high; however, some subtle difference among the three can be captured. In fact, while individual splaying spherulites can be somehow recognized in Figure 3A,B (with spherulitic or hedritic Form I seeds), this is not the case for the crystals nucleating on the fiber surface, due to the extremely high nucleation density.

However, the different cross-nucleating ability of the various substrates can be more clearly deduced by comparing the time evolution of the morphology, at the same crystallization temperature. The second column of Figure 3 reports for each case the time at which the first cross-nucleation event could be observed (highlighted by the red circles). It can be seen that a substantially shorter time is required for cross-nucleation to occur on the fiber substrate, with respect to the spherulitic or hedritic ones. In the last images of Figure 3A-C, the TCL has grown to a similar thickness in all the three morphologies, being the growth rate the same in the three experiments, the earlier onset of growth, that is, shorter induction time, for the fiber sample is confirmed.

During primary nucleation, a particular molecular arrangement must be fulfilled to allow the formation of the new phase. In the case of polymer crystallization from the melt, the chain segments must approach themselves to distances commensurate to those characteristics of the crystalline unit cell and must possess the right conformation, as the crystal symmetry imposes. The chain segments with those attributes form a crystalline aggregate which varies the system free energy ΔG. Considering for the sake of simplicity a spherical nucleus of radius r, a maximum in ΔG(r) exists which corresponds to the critical size (r*) that the new crystal must attain in order to be able to spontaneously grow into a crystal. Clusters smaller than r* are called subcritical nuclei or embryos, they are unstable and tend to disappear from the system. Aggregates that exceed r* are called supercritical nuclei and can continue to grow because their growth is thermodynamically favored.44

As the magnitude of the energy barrier for nucleation depends inversely on the undercooling, that is, on the distance between the crystallization and melting temperature, experiments were performed at different crystallization temperatures. Figure 4A reports the example of evolution of light intensity, extracted from the optical micrographs, as a function of time during crystallization at different temperatures for the fibrous Form I substrate. The time of formation of the critical nuclei, represented by the light intensity induction time, gets shorter and shorter with decreasing T_c for any of the considered substrates. In particular, while the differences between spherulitic and hedritic Form I seeds are relatively small (data are reported in Figure S1), the high cross-nucleation efficiency of the Form I fiber is apparent by comparing the time scale of the x-axis (Figure 4A). A clearer comparison between the three seeds is offered in Figure 4B, which considers the increase in transmitted light at the same crystallization temperature for the three different systems. The chosen condition is the same reported in the micrographs of Figure 3. A difference of about a factor 0.8 in the induction time can be already appreciated between the spherulitic or hedritic seeds, while Form I fibers substrate can nucleate Form II about two to three times faster than Form I spherulite.

In order to apply a model-based comparison of the cross-nucleation ability associated to different Form I morphologies, the values of the determined induction times as a function of temperature are reported in Figure 5. The order of efficiency deduced from Figures 3, 4, and S1, that is, fiber > hedrite > spherulite, is confirmed in the whole range of explored undercooling. As expected, a strong dependence of nucleation kinetics on the crystallization temperature is observed, with induction times increasing exponentially approaching the melting point of Form II.

It should be pointed out that both spherulitic and hedritic Form I substrates were prepared in situ in the sample, by melt crystallization, while fibrous Form I seed was introduced into the matrix melt manually. The insertion process necessarily involved shear stresses applied to the PB-1 melt. Given the fact that flow-induced nucleation in fiber-pulling experiments is well documented, and is known to have long-lasting effects,45 the evaluation of its importance in the present case is mandatory, in order to understand whether a fiber-like Form I really possesses the highest cross-nucleation efficiency.

The annealing times were varied in a wide range, according to the known long lifetime of PB-1 flow-induced precursors.45 Figure S2 reveals that the change of the induction time, with melt annealing time, if any, is safely negligible and cannot account for the large difference observed for the case between the nucleation time of Form II at the interface with the fiber and with the hedrite of Form I (around 140 seconds).

To further confirm that nucleation of Form II on top of Form I fibers is not dominated by shear-induced effects, the same experiment, including the fiber introduction step, using a completely different fiber, made of iPP, was performed. Since the elastic moduli and size of the two fibers are not largely different, similar shear stresses are expected to be generated by the fiber introduction procedure in the two cases. The induction times observed for nucleation on iPP and Form I PB-1 fibers are compared in Figure S3. Very different nucleation kinetics of Form II are observed on the two fibers. In particular, nucleation on iPP fiber occurs more slowly than cross-nucleation on Form I PB-1 fiber. This observation further supports our previous conclusion: the effect of shear-induced nucleation due to the sample preparation procedure is not meaningful. In the opposite case, a similar kinetic of nucleation would be observed for the two fibers. Thus, the observed faster nucleation promoted by the Form I PB-1 fiber, with respect to the other PB-1 substrates made of the same crystalline polymorph but possessing different morphologies, is confirmed.

3.3 Crystal growth of PB-1 Form II on Form I seeds with different morphology

In order to exclude any possible difference between the growth rates of Form II crystals in the different samples, and in view of obtaining surface energy data for the subsequent estimation of the nucleation barrier, the growth kinetics in the different samples was determined by following the time dependence of the TCL thickness.

Figure S4 shows the thickness of the TCLs of Form II growing at the interface of the Form I seeds with different morphologies, measured via polarized optical microscropy (POM), as a function of crystallization time for various crystallization temperatures. The increase in size is linear with time, which allows an easy calculation of the growth rate from the slope of the fitting lines. As expected, the crystal growth rate of PB-1 Form II increases with decreasing the isothermal crystallization temperature. This change is more marked in the temperature range 103°C to 110°C. The derived crystal growth rates are thus analyzed according to the classical Lauritzen-Hoffman theory. The growth rate (G) can be expressed by a function of the undercooling ΔT in a linearized form, according to:

(1)

The constants that appear in Equation (1) are: G₀ is a temperature-independent parameter, U* is the activation energy related to the transport of chain segments across the phase boundary, R is the gas constant, T _∞ is the temperature below which all motions associated with viscous flow cease, β is a constant characterizing the regime of growth, b₀ is the thickness of each newly formed layer, σ and σ_e are the lateral and fold surface energies, respectively; T_m is the equilibrium melting temperature, k is the Boltzmann constant, Δh₀ is the melting enthalpy, and f is a correction factor which takes into account the change of melting enthalpy with crystallization temperature.

Figure S5 shows the trend of log G + U*/R(T−T _∞) as a function of 1/(TΔTf). The linear fit of the growth rate data with the L-H model with a single slope in the whole undercooling range implies that only one regime is active between 100°C and 110°C. This corresponds to regime I, in agreement with the results of Monasse and Haudin.46 On the other hand, it is apparent that the TCL of PB-1 Form II grows in the melt with the same rate, independently from the exact substrate on which it nucleates. Therefore, it can be concluded that the observed differences in the kinetics of light intensity evolution among the different Form I seeds are not related to the growth stage, but can correctly be attributed to the cross-nucleation kinetics only.

Muchova et al.47 have developed a microscopic method to monitor the early stages of the spherulite growth of polypropylene. They found that there are two relations between the derivative of the light intensity (φ) with respect to the time:

(2)

(3)

where ν is the linear growth rate, which is constant at a given crystallization temperature, Z is the number of growing spherulites, K is a constant which involves the dependence of the transmitted light intensity on the difference in the refractive indices of the ordinary and extraordinary beams, t is the time, and t _i is the induction time. The first equation describes the derivative of the light intensity when the spherulites growth can be considered three-dimensional (3D), while the second relation refers to the case of two-dimensional (2D) growth. Representative examples of the evolution of the time derivative of light intensity with respect to time for the different Form I substrates are shown in Figure S6. In all the cases, after the initial transient, a clear linear region of the data can be identified, confirming the adequacy of Equation (3), that is, the growth of PB-1 Form II on the different substrates can be considered 2D. Similar conclusions on this method have been recently drawn by analyzing the light intensity arising from the development of PP transcrystalline layers at the interface with solid NAs.41

The relationship between the growth rate values of the TCL, calculated through the thickness vs time measurements and the light intensity method, has been further explored. Figure 6 shows the growth rate values calculated at different T_c from TCL thickness analysis (Figure S4), as a function of the parameter Aν, defined as the square root of the fitting slope of the linear part in the plot of the light intensity method (Figure S6). From Equation (3), we can derive that A is a constant equal to (KZ)^1/2. If the applied model is correct, a linear relationship between these two independently derived quantities should be obtained. As can be seen in Figure 6, the growth rate data for all the different substrates fall on the same line. Therefore, we can conclude that this model for the data analysis is validated, analogously to our previous work on heterogeneous nucleation of polypropylene,41 and that the parameters K and Z are independent from the morphology of the Form I seeds.

3.4 Model analysis for cross-nucleation of PB-1 Form II on Form I seeds

In the presence of heterogeneous substrates in contact with the polymer melt, there is the availability of solid surfaces on which the embryos can form. Several different types of heterogeneity (extraneous solids, cavities, already formed crystal surfaces, etc) can enhance the formation of stable embryos and have important implications for polymer crystallization. One classical approach assumes the formation of prismatic embryos with a rectangular cross-section of size a and b, and height (l) in the direction of the chain axis on a flat surface. In this case, the change in the Gibbs energy has the form:

(4)

where σ is the free energy of the lateral surfaces in contact with the undercooled melt, σ_e is the free energy of the surfaces perpendicular to the chain direction (the same as in Equation 1), and Δσ is the interfacial free energy difference, given by:

(5)

in which σ_s/c is the crystal-substrate interfacial energy and σ_s/m is the melt-substrate interfacial energy. Therefore, Δσ can be brought down to the surface tension properties of the substrate, polymer crystal, and polymer melt. Thus, Δσ is a convenient way to define the nucleating ability of the substrate toward the polymer melt. The lower its value, the lower the nucleation energy barrier, resulting in a faster nucleation.

Ishida et al.48 have proposed a model according to which the formation of the first layer of crystalline segments on the foreign substance is responsible of the attainment of the nucleus critical size, within the induction time t _i. Thus, Δσ can be obtained from the variation of the nucleation rate I with crystallization temperature by determining the product σσ_eΔσ:

(6)

where I₀ is a temperature-independent frequency term, and the other symbols have been previously defined.

By plotting ln I + U*/R(T−T _∞) vs 1/T(ΔTf)², a linear fitting can be obtained and the slope (K _i) of the line is proportional to σσ_eΔσ. In order to determine Δσ, one also needs to measure the growth rate at different crystallization temperatures and determine the value of the σσ_e product from its temperature variation. In fact, according to L-H growth model (Equation 1), a plot of ln G + U*/R(T−T _∞) vs 1/TΔTf yields a straight line with a slope K _g, proportional to σσ_e. From these two separate sets of experiments, Δσ is obtained. Assuming from the literature an activation energy U* of 6.28 kJ/mol, a bulk enthalpy of fusion Δh₀ of the Form II of 56 J/cm³ and a molecular stem width b₀ of 7.45 × 10⁻⁸ cm,49 three very close values of the term σσ_e has been calculated for cross-nucleation on spherulitic, hedritic, and fibrous Form I seeds: 56.07 erg² cm⁻⁴, 56.63 erg² cm⁻⁴, and 53.41 erg² cm⁻⁴, respectively.

However, as mentioned earlier, the nucleation density could not be easily counted when transcrystallization was formed at the substrate boundary in composites with very high nucleating efficiency, as in the case of polyethylene/polyethylene (PE/PE) composites.48 Thus, nucleation induction time data were used, under the assumption that the product between nucleation rate and induction time at a given temperature is constant:

(7)

Therefore, by relating the nucleation rate and the induction time an efficient way to obtain Δσ is provided.

In Figure 7 Ishida's model is applied to the measured cross-nucleation induction times for PB-1 nucleated onto different Form I seeds. A good linearity of the data is observed, allowing us to perform a linear fitting and derive the slope K _i, that is, calculate the quantity σσ_eΔσ. Combining it with the σσ_e calculated from K _g obtained from the Lauritzen-Hoffman plot (Figure S5), an estimate of Δσ for the spherulite, the hedrite, and the fiber substrate can be derived: 0.294 erg cm⁻², 0.301 erg cm⁻², and 0.291 erg cm⁻², respectively.

As judging from the obtained values, the model of Ishida is not capable of capturing significant differences between the nucleating efficiency of the different substrates. In fact, the lines of Figure 7 are practically parallel to each other, indicating that the same cross-nucleation barrier would be obtained for the different Form I seeds. Clearly this conclusion cannot account for the differences experimentally observed in the induction time values of each system, given the negligible difference in the growth rate.

On the other hand, a more detailed model for the heterogeneous nucleation was proposed by Muchova et al. It consisted in the sum of two qualitatively different steps:47, 50 the formation of the first layer of segments on the foreign substance, that occurs within a time t_h, and the formation of further layers until the growth of a nucleus of critical size is completed, within a time t_s. Thus, the overall induction time of the process is given by the sum of these two individual steps, that is, t _i = t_h + t_s. The two components of the induction time can be expressed by these relations:

(8)

(9)

where A₁ and A₂ are proportionality constants. It should be noted that t_h describes exactly Ishida's model.

It is known that the size of the critical nuclei increases with crystallization temperature. At high temperatures of crystallization, the number of the folding segment layers is considerable and the time of the formation of the first layer (t_h) becomes negligible in comparison with the time in which further layers are formed. In this case, equation t _i = t_h + t_s for the induction time can be simplified to t _i ≈ t_s, and the equation of the induction time can be rewritten into a logarithmic form:

(10)

where the influence of the transport term is included in the constant C. According to Equation (10), the dependence of ln(t _iΔT) − U*/R(T−T _∞) on 1/TfΔT is a straight line with intercept Q on the y-axis, equals to:

As can be noticed, Q includes the interfacial free energy difference (Δσ).

Figure 8 shows the evolution of ln(t _iΔT) − U*/R(T−T _∞) as a function of 1/TfΔT for PB-1 matrix crystallized in contact with Form I seeds with different morphologies. The analysis of the cross-nucleation induction time data with a model which expresses the nucleation barrier taking into account the formation of several crystalline layers, up to the attainment of critical dimensions, can correctly capture the different nucleating ability of the various substrates. In fact, the lines display a different intercept with the y-axis, given by different Δσ. However, its absolute value cannot be obtained due to the unknown constant C.

Therefore, in order to correctly quantify the nucleating activity of each substrate, a new approach, consisting in the use of the sum of Equations (8) and (9) to fit the experimental induction time data, is required. In this way, a better identification of the crystallization temperature window in which each one of Muchova's models (t_h and t_s) is valid, can be obtained. The model describing the total induction time as the sum of the individual steps is referred as “detailed model” in the following.

Indeed, the description of the total induction time by the detailed model allows us to estimate in which range of temperature each step is dominant and what is its exact contribution to the overall induction time at a given crystallization temperature. In Figure 9A and Figure S7, the contributions of first and further layers models to the detailed model are shown for each system with different PB-1 Form I seeds. It is clear that the contribution of the further layer model (t_s) is much larger than that of the first layer model (t_h) at higher temperatures (>100°C). This means that the data in the test temperature range follow very closely the trend described by the t_s model alone, that is, the rate determining step in the attainment of the nucleus critical size is the addition of several crystalline layers. On the contrary, for lower crystallization temperatures (<87°C), the formation of the first crystalline layer is enough for the nucleus to attain the critical size.

Figure 9B shows the curves obtained by fitting the experimental induction time data with the detailed model equation for the three PB-1 Form I substrates. The parameter A₁ from Equation (8) was obtained using crystallization induction time data of bulk PB-1, given that nucleation is likely controlled by the formation of the first layer onto substrates of low nucleation efficiency and at high undercooling.41 A value of 0.005 second could be determined and used in the subsequent fit of the data of interest for all the substrates. The resulting values of the unknown parameters from the sum of Equations (8) and (9) (A₂, Δσ_spherulite, Δσ_hedrite, and Δσ_fiber) are 0.002 second, 0.295 erg cm⁻², 0.225 erg cm⁻², and 0.105 erg cm⁻², respectively. Therefore, the Δσ values obtained for the three substrates agree with the experimental trend of nucleation kinetics.

Given the results discussed above, it can be concluded that the kinetic of nucleation cannot be estimated by modeling a single step only, but rather by considering the two steps simultaneously. Figure S8 shows the plot of the curves relative to the first layer model (t_h) and the further layer model (t_s) obtained during the fitting of the detailed model for the different Form I seeds with varying morphologies. Within the range of experimental temperature, the differences between t_h and t_s curves at the same crystallization temperature increases in the order: fiber > hedrite > spherulite. This order mirrors the influence of the formation of the first crystalline layer on the nucleation barrier, that is, the lower the Δσ, the less important becomes the first step in determining the overall induction time. In view of interpreting the observed effect of seed's morphology on cross-nucleation, it is worth to briefly consider the absolute values of the obtained free energy difference parameters. For all the considered substrates, extremely low values of Δσ were found, in comparison to the systems for which most of the literature data are available, that is, polymer/fiber composites, with values ranging from 4 to 20 erg cm⁻².42, 51 On the other hand, such low values are comparable to those obtained in particular cases, such as those of ultrahigh molecular weight polyethylene fibers in polyethylene or polycaprolactone matrices,48, 52 for which epitaxial nucleation is obvious or well known.53 Thus, particularly favorable interactions between crystallizing Form II and Form I seeds must be in place. It is conceivable that cross-nucleation in PB-1 is governed by either “true” crystallographic epitaxy between the two structures, or at least by a “soft epitaxy” mechanism related to a matching between the topographical details of parent and daughter crystals at the nanoscale.