Crystallization Kinetics for the Split Dual Phase Model of the Amorphous State of Polymers

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1 This article was downloaded by: [Professor J. P. Ibar] On: 09 May 2015, At: 03:04 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Journal of Macromolecular Science, Part B: Physics Publication details, including instructions for authors and subscription information: Crystallization Kinetics for the Split Dual Phase Model of the Amorphous State of Polymers J. P. Ibar a a Institute for Polymer Materials (POLYMAT), Joxe Mari Korta Center, University of the Basque Country (UPV-EHU), Donostia-San Sebastian, Spain Accepted author version posted online: 08 Nov 2012.Published online: 29 Mar To cite this article: J. P. Ibar (2013) Crystallization Kinetics for the Split Dual Phase Model of the Amorphous State of Polymers, Journal of Macromolecular Science, Part B: Physics, 52:7, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 Journal of Macromolecular Science R, Part B: Physics, 52: , 2013 Copyright Taylor & Francis Group, LLC ISSN: print / X online DOI: / Crystallization Kinetics for the Split Dual Phase Model of the Amorphous State of Polymers J. P. IBAR Institute for Polymer Materials (POLYMAT), Joxe Mari Korta Center, University of the Basque Country (UPV-EHU), Donostia-San Sebastian, Spain Introduction We analyze constant rate cooling and heating crystallization kinetics of PET samples by DSC. The samples have various degrees of disentanglement, obtained by Rheo- Fluidification. According to the interactive Split Dual Phase model, the amorphous state is made up of two coupled and interactive amorphous phases. These two phases have distinct viscoelastic and thermodynamic characteristics (T g, free volume, G and G, etc.), which are determined by the potential energy of the conformers and by the state of entanglement of the macromolecular coils. Semi-crystalline polymers, such as polyethylene terephthalate (PET), are amorphous in the molten state and should have Dual Phase behavior. The phase duality should manifest itself during crystallization from the melt during cooling, or during cold crystallization while heating quenched samples. The purpose of this communication is to quantitatively describe the kinetics of crystallization of PET samples with a dual phase kinetics formulation, and determine the respective influence of molecular weight and degree of entanglement on the kinetics parameters, rate of crystallization and percentage of crystallinity. Keywords crystallization kinetics, entanglement state, PET, Rheo-Fluidification, splitdual-phase model, thermal-history effect Split Dual Phase As described in more detail in previous publications, [1,2] entanglement can be viewed as a two dual-phase system in polymeric material. In the Split Dual Phase model, the viscoelastic properties of the two phases are notably different, as well as interactive and coupled. Figure 1 provides a computer designed sketch of the interactive split dual phases. [2] Upon deformation in the melt, the dual phases do not respond with the same relaxation times, and, as a result, one phase usually re-structures with respect to the other, essentially providing the known entropic response of the melt to deformation: the two phases re-arrange, but do not separate. [1] There are ways, however, to manipulate the two phases in order to influence the overall behavior, for instance it is possible to partially or fully disentangle the phases. [3] To produce phase-disentanglement, [3 6] extensional shear vibration is exercised on the melt as it is continuously extruded to pass through treatment stations at a determined Received 12 September 2012; accepted 24 October Address correspondence to J. P. Ibar, Institute for Polymer Materials (POLYMAT), Joxe Mari Korta Center, University of the Basque Country (UPV-EHU), Avenue de Tolosa, 72, Donostia- San Sebastian, Spain. jpibar@alum.mit.edu 950

3 Split Dual Phase Model Crystallization Kinetics 951 Figure 1. Sketch of the Split-Dual-Phase model of entanglements. This model is described in Ref. [1]. It is the corner stone of a new interpretation of viscoelasticity and of the strain dependent instability of the entanglement network, which we call disentanglement in this paper. temperature, frequency, and amplitude of vibration, under specific shear rate and extensional rate conditions, to obtain a controlled progressive pulling of one phase out of the other. This re-organization and/or mutual transfer of the number of bonds from one dual phase to the other results in the modification of the entanglement network and is what we call phasedisentanglement. When disentanglement and its opposite, re-entanglement, are properly controlled, the viscosity and the elasticity of polymer melts can be varied significantly, [3,6] with consequences expected on the kinetics of crystallization for semi-crystalline polymers such as PET. The treated melt can be immediately processed (e.g., injection molded) or it can be cooled at the end of the Rheo-Fluidizer to be pelletized and preserve cold some of the benefits for future melting, The efficiency of the disentanglement process depends on both processing variables (pressure on the melt, vibration parameters, and shear and extensional rates) and time; the longer the treatment, the more disentanglement. This new technology of disentanglement is called Rheo-Fluidification Processing. [3] The Split Dual Phase model, which describes the interactive coupling kinetics governing the conformational properties of isolated and entangled macro-coils [1,2] can be applied to the qualitative and quantitative understanding of the results obtained by Rheo-Fluidification Processing. For amorphous polymers, because they do not crystallize, the challenge is to compare the properties of the disentangled melt or glass with those of a normal melt or glass, and see whether the results are consistent with the picture provided by the Split Dual Phase model. For crystallizable polymers, such as PET, the process of crystallization might be largely influenced by the presence, in the molten state, of the two interactive amorphous phases, and the challenge is to determine what new degree of freedom is offered by the new disentanglement technology to manipulate crystallization (rate and level). In particular, the

4 952 J. P. Ibar Split Dual Phase model stipulates the existence of two crystallization peaks kinetics, one within each phase. This assumption is tested in this paper. Experimental Non-Isothermal Crystallization Determination of degree of crystallinity was accomplished by DSC analysis at constant heating or cooling rate. Heat flow was normalized by the sample weight and plotted against time or temperature. Tests were automatically performed on a DSC 82a from Mettler Toledo International Inc (USA), in N 2 flow of 60 ml/min using sealed 40 μl Alpan crucibles and lids. Heating and cooling rates were 20 C/min and 10 C/min, respectively. Two successive runs were performed on each sample: Heat Hold 2 min-cool-hold 2 min- Heat-Hold 2 min-cool (Fig. 2). The PET samples exhibited cold crystallization during the first heating segment, followed by melting, and a second crystallization, from the melt, occurred on subsequent cooling at 10 C/min. The virgin PET used in this study had an intrinsic viscosity IV of This corresponds toam n of 12,600 and M w of 39,000, as measured by gel permeation chromatography, GPC, with respect to PS standards (uncorrected with the Mark Houwink constants). Disentangled samples were obtained using the Rheo-Fluidification apparatus and method described elsewhere [3] By varying the rheological parameters in the two treatment stations (temperature, shear rate, vibration frequency, and amplitude), we obtained melts with various degrees of disentanglement and molecular weight. The disentangled pellets were characterized by both their melt flow index (MFI) and by gel permeation chromatography (GPC) in order Figure 2. DSC traces heat flow vs. temperature for PET 1st and 2nd runs showing T g,coldcrystallization (1st heating), melting peak, post melting baseline behavior. The cooling trace shows the crystallization peak on cooling. In the 2nd heating, no cold-crystallization is shown and a very small C p at T g is observed (Color figure available online).

5 Split Dual Phase Model Crystallization Kinetics 953 to determine their molecular weight distribution (MWD), in particular Mw, which permits to quantify their degree of disentanglement. What we call the percentage of disentanglement is the ratio of the measured MFI of the treated sample to that of the virgin sample, after correction of the influence of the decrease of M w for the treated sample on viscosity. This parameter, we are aware, is a gross simplification of the state of the melt that ignores the possible change of molecular topology, such as the formation of long or short chain branching, which also affects the viscosity. Molecular weight measurements were performed using a Waters 150CV+ automated GPC apparatus (Waters HPLC, USA). A 2% solution of a freshly made mixture of hexafluoroisopropanol/methyl chloride (in proportion 1:9) was used to dissolve the samples and for the eluting fluid. A 0.2% w/v solution was prepared from the 2% solution and 20 μl injected at 30 C (column and pump were also set at 30 C) at a flow rate of 0.5 ml/min with a pressure of bars. A UV detector operating at 254 nm was used. The upper curve in Fig. 2 shows the typical aspect of the crystallization peak on cooling of a PET sample as measured by DSC. After the baseline is zeroed-in, the degree of conversion from amorphous to crystal form, is calculated at each time t from the area under the curve up to that time. Heat flow [d( H/m)/dt] vs. time is further normalized by the total area S under the peak to obtain the degree of conversion α: α = S t 1 1 S = 0 d( H/dt) dt, (1) m where S 1 is the cumulative area under the peak up to t 1. From Eq. (1), it is clear that: dα dt = d( H/dt)/m. (2) S In order to analyze the thermal effect due to crystallization only, without interference from the C p baseline, which is influenced somewhat by a phase transition, the baseline must be subtracted out. The baseline is defined on both sides of the crystallization peak, each baseline segment being fitted with a best function, F 1 and F 2, obtained by regression, and one assumes that the analytical function of the baseline is given by (3): Baseline = χ F 2 + (1 χ) F 1. (3) [ ( )] t χ = tanh(70 ln, (4) t m where t m corresponds to the peak maximum. The constant 70 in Eq. (4) is arbitrary; it is chosen to simulate a sharp transition of the baseline from F 1 to F 2 right at T m, i.e., to make the respective baseline equations apply, from both sides, up to the peak maximum: Baseline = F 2 for t > t m = F 1 for t < t m Dual Split Kinetics Many prior studies have been devoted to the description of either isothermal or nonisothermal crystallization of PET. A good review of previous work can be found in Hieber s own contribution to the subject. [7] None of the existing models addresses the issue of crystallization kinetics from dual phases.

6 954 J. P. Ibar Since the Split Dual Phase model predicts the existence of two crystallization peaks, one within each phase, the total rate of crystallization, α, can be deconvoluted into two rates: α = α 1 + α 2 (5) In the following, we assume that the degree of crystallization for each phase, α i,varies with time like an S curve, which can be fitted by a tangent hyperbolic function varying between 0 and 1 [such as in Eq. (7)]. One can easily show mathematically that for such functions the derivative, i.e., the rate of crystallization in each phase, dα i /dt, is proportional to both α i and (1 α i ), which yields: with α = β α 1 + (1 β) α 2 (6) β = p 1 /0.5 α 1 = 0.5 (1 + tanh(p 2t + p 3 )), α 2 = 0.5 (1 + tanh(p 4t + p 5 )) (7) where p 1,p 2,p 3,p 4,p 5 are curve fitting constants characteristic of the crystallization kinetics at the corresponding heating or cooling constant rate. β is the proportion of phase 1, (1 β) the proportion of phase 2. From Eqs (5) to (7), one can derive the equation for the total crystallization rate, dα/dt: dα dt [ ] exp(2p 2 t + 2p 3 ) = 4p 1 p 2 (1 + exp((2p 2 t + 2p 3 )) 2 [ ] exp(2p 4 t + 2p 5 ) + (0.5 p 1 ) p 4 (1 + exp((2p 4 t + 2p 5 )) 2 Parameters p 2 and p 4 represent the maximum rate of crystallization for each phase, which occurs, respectively, at times t m1 and t m2 : t m1 = p 3 p 2 (8) t m2 = p 5 p 4 (9) From Eqs (6) (8), one can write: dα 1 dt = p 2 2 (1 tanh2 (p 2.(t t m1 )) dα 2 dt dα dt = p 4 2 (1 tanh2 (p 4.(t t m2 )), = β dα 1 dt + (1 β) dα 2 dt which shows that the individual dual peaks can be characterized by only two parameters, their position and their height, i.e., the maximum crystallization rate in that phase. β, the (10)

7 Split Dual Phase Model Crystallization Kinetics 955 dual phase split ratio, varies between 0 and 1, characterizing the partition between the two phases. Results and Discussion We distinguish the two situations, which can occur: crystallization from the melt and cold crystallization, the latter of which occurs on heating the glass after quenching (or cooling at a known rate). The two behaviors are shown in Fig. 2, and, more specifically, in Figs 3 and 4, respectively. 1. Crystallization from the Melt on Cooling (Figs 3, 5 10) Figure 3 is a plot of C p against temperature, normalized and converted against time in Fig. 5. It is clear in Fig. 3 that there is a very little change of the baseline at the maximum crystallization on cooling [ C p (T c ) = 0.024], and that the baseline subtraction, shown in Fig. 5 was smooth and reliable. The crystallization peak can, therefore, be unequivocally extracted from the C p - t DSC trace (Figs 5 7). It is the green (lower) curve in Fig. 5, magnified in Fig. 6, and deconvoluted by regression with Eq. (8) into two peaks visible in Fig. 7 (one red, the small peak, and the other green, the larger peak). The split between the two phase crystallization is shown in Fig. 8. The regression is almost perfect (r 2 = , κ 2 /DoF = ): p 1 = ; p 2 = ; p 3 = ; p 4 = ; p 5 = , from which we calculate β = t m1 = 513 s. t m2 = s. Figure 3. C p vs. T (normalized by the weight) for the cooling trace showing the baseline extrapolation procedure to determine the surface area under the peak, proportional to the amount of crystallization occurring during cooling (10 C/min). C p (@T c ) is the difference between the two extrapolated baselines at the point of maximum, T c (Color figure available online).

8 956 J. P. Ibar Figure 4. C p vs. T for the 1st heating trace showing the T g, the cold crystallization peak at T cc,as well as the melting peak at T m. Since the cooling rate is known, it was 10 C/min, one can calculate the temperature of the two peaks at the maximum, i.e., C and C. In this particular example, p 2, the rate of crystallization in phase 1, was approximately three times what it was for phase 2, p 4. Note that this dual-phase behavior only corresponds to certain melt history, that of melts Figure 5. Kinetics of crystallization during cooling. C p vs. time and determination of the baseline (Color figure available online).

9 Split Dual Phase Model Crystallization Kinetics 957 Figure 6. PET crystallization during cooling. C p -baseline (lower curve). This is the peak to quantify to establish the crystallization kinetics. showing a high disentanglement ratio for the resin melted. For other thermal mechanical histories, with smaller disentanglement ratio, the second peak was larger than the first one, and the overall crystallization peak seemed to be occurring at a lower temperature. In general, various disentanglement conditions produced different β, but the same value of t m1 and t m2. This seemed to also hold true for the crystallization kinetics from the glass, as Figure 7. Result of the deconvolution of the 1st cooling crystallization peak into two peaks according to Eq. (8) (Color figure available online).

10 958 J. P. Ibar Figure 8. Deconvolution of the global rate of crystallization, α, into two crystallization rates α 1 and α 2 for the peak of Fig. 6 (Color figure available online). shown later. Figure 9 demonstrates that, for each phase, the rate of crystallization dα i/dt, was almost perfectly proportional to the product of α i and (1 α i), which verifies the initial assumption (Fig. 9 only shows the fit for phase 1). Figure 10 displays a rare case, where two peaks were actually visible during crystallization from the melt, yet this is not necessarily providing the evidence of a dual phase behavior, without the recourse to mathematical sophistication to demonstrate it. Two peaks could also be produced by other Figure 9. Test of the crystallization kinetics for phase 1 according to Eq. (8).

11 Split Dual Phase Model Crystallization Kinetics 959 Figure 10. Normalized heat flow vs. temperature for the 1st cooling trace of a disentangled PET showing two peaks of crystallization. The disentanglement processor is discussed in Ref. [3]. The question of the origin of the two peaks remains unresolved (see text). sources, such as a modification of the molecular weight distribution. This question will be elucidated in another paper. 2. Cold Crystallization on Heating Figure 2 also displays a cold crystallization behavior on 1st heating with two peaks present. The second peak fuses somewhat with a falling baseline, giving the peak the aspect of a shoulder. Figure 4, for which Heat flow data have been converted to heat capacity (C p ), clearly illustrates the large baseline drop [ C p (T cc ) = 0.25 J/g/ C] at the maximum of the crystallization process, and it is not known how sigmoidally the baseline should drop from the segment before the peak to the segment after the peak. The shape of the baseline does, indeed, influence the contour of the extracted crystallization peak, and, consequently, the kinetics. However, the magnitude difference (shown in Fig. 4) between the baseline C p drop at T cc, and the crystallization peak is so big that any error on baseline definition would only slightly impact our findings. The same Eqs (5) (10) apply to the deconvolution of the cold crystallization peak, and with the same success. Varying M w and the disentanglement ratio plays a role on the crystallization results, but all cold crystallization peaks can successfully be described by a dual phase crystallization equation, Eq. (8). The curve fitting parameters, p i, all vary with the state of the initial resin, whether it was air cooled or quenched, disentangled or not, and with the molecular weight. However, Figs 11 and 12 reveal some interesting correlations between these parameters and between the physical variables. Figure 11 is a plot of p 2 vs. p 3, where p 2 and p 3 are defined in Eq. (7) describing the kinetics of crystallization in phase 1. Likewise, Fig. 12 is a plot of p 5 vs. p 4, also defined in Eq. (7), applicable to phase 2. The different points in these figures refer to results obtained with several samples, all processed differently, all with a known M w and a known percentage of disentanglement,

12 960 J. P. Ibar Figure 11. Plot of the crystallization kinetics parameters found for phase 1 for a series of samples submitted to a Rheo-Fluidification disentanglement treatment (of variable thermo-mechanical history) prior to pelletizing. p 3 and p 2 are defined by Eq. (8). A single straight line has been drawn through the data, defining a single T ml value. Perhaps a second straight line could have been added to go through a series of lower points (Color figure available online). Figure 12. Same plot as Fig. 11 but for phase 2 of the crystallization deconvolution. p 5 and p 4 characterize the kinetics of crystallization for this deconvoluted peak according to Eq. (8). Several straight lines are clearly visible for phase 2, corresponding to several families of T m2 values (Color figure available online).

13 Split Dual Phase Model Crystallization Kinetics 961 characterized separately. All the points of Fig. 11 collect on a single straight line passing through the origin, with slope equal to ( t m1 ) = (r 2 = ), which corresponds to having, for the first peak maximum temperature, regardless of the processing conditions, a constant crystallization temperature of T m1 = C (at 20 C/min heating rate, heating from 30 C), The rate of cold crystallization in that phase 1, p2, varies between 0.03 and 0.19, depending on the processing conditions, with most values between 0.05 and 0.13, a three-fold span. However, the temperature at which cold crystallization occurs in phase 1 is independent of the value of M w and of the percent disentanglement, two parameters determined by the processing conditions in the Rheo-Fluidizer stations. Figure 12 describes the kinetic in phase 2, which is slightly more complex. A plot of p 5 vs. p 4 shows not one but several straight lines, all passing through the origin, defining several T m2, 4 in Fig. 12 to be precise (corresponding to the four colors); the four temperatures defined by the slope are, from the top line to the bottom one: C; C; C; and C. A careful examination of the characteristics of the points belonging to each individual straight line of Fig. 12 reveals that the M w for the samples on each line were the same, the steeper the slope the higher M w. The maximum crystallization rate in phase 2, p 4, varied between and 0.06, a shorter span than for phase 1. The coefficient of correlation r 2 for the regression was close to 1 (0.9999) for all deconvolutions of the cold crystallization peak done with PET, and for a given M w (same IV), the position of the elementary peaks was constant, regardless of the processing conditions; only the rate of crystallization and the disentanglement split ratio, β, varied. For the results presented in Figs 11 and 12, β takes a value between 0.2 and 0.7, depending on the initial disentanglement ratio and the amount of crystallinity before heating. Influence of M w and the Disentanglement State on the Kinetics Figure 13 is a plot of T c, the onset of the 1st cooling crystallization, against the total amount of crystallization, X c %, acquired on cooling during the crystallization step. The Figure 13. Temperature of crystallization (1st cooling) vs. percent crystallinity acquired on cooling for a series of samples obtained under a variety of Rheo-Fluidification treatments. The treatment rarely occurred without the secondary effect of M w degradation due to the sensitivity of PET to moisture (Color figure available online).

14 962 J. P. Ibar points relate to different conditions of disentanglement processing (from 0% to 180% disentanglement) on samples having various M w (from 19,000 to 39,000). Remember that percent disentanglement is defined from the MFI improvement [the ratio of the treated pellet MFI to the reference (virgin) pellet MFI after the treated MFI value is corrected (decreased) for the change of M w that occurred during the Rheo-Fluidification treatment]. For certain polymer melts, such as PMMA, very little degradation occurs during the treatment, but for others, such as for PET, there is a change of M w collateral to a modification of the entanglement network stability produced by the Rheo-Fluidizer. Under certain conditions, long chain branches (LCB) are formed; a situation that complicates the task to quantify which part of the fluidity increase is due to disentanglement (recoverable deformation of the elastic network). In such a case, the percent disentanglement, defined as the increase of MFI after correction for the change of viscosity due to degradation, is a simplification, which needs further correction for the effect of branching on the melt viscosity. In Fig. 13, the sample with the highest M w and 0% disentanglement is located at the bottom left of the chart. Samples located horizontally to its right have the same M w and a higher disentanglement level. All points located on the (red) line have 0% disentanglement and a lower M w. One sees that lowering M w, by approximately 2, results in an increase of crystallinity by 10% and triggers crystallization 20 C sooner. By contrast, it seems that disentanglement played a role in increasing the total amount of crystallinity (by increasing the rate of crystallization), but not by triggering it sooner. The amount of crystallinity increased because the phenomenon happened faster during the same amount of time. This is in agreement with the results found for the individual crystallizations in Figs 11 and 12, which occur at the same place, but perhaps with three times the rate. Notice in Fig. 13 the numbers 1, 2, 3, and 4 near some data points; they reflect the order of the level of disentanglement, 1 being the highest, 160%, and 2 is 82%. It is clear that one requires a higher degree of disentanglement, at constant M w, to obtain a larger crystallinity on cooling. Figure 14. Cross-plot of the rate of crystallization in phase 1 and 2 for the 1st heating cold crystallization peak (see text).

15 Split Dual Phase Model Crystallization Kinetics 963 Figure 14 is a cross-plot of the two rates of crystallization in the dual phases, p 4 vs. p 2. There seems to be a set of converging straight lines passing through the scattered data. Most of the data are located in the south-east quadrant, with respect to the compensation point, which means that most of the (low level) disentanglement treatments increased the crystallization rate in phase 1, but decreased it in phase 2. Very few treatments, yet well characterized, correspond to an increase of crystallinity in both phases (in the north west quadrant). This might be desirable. Other conditions result in a decrease of the crystallinity in both dual phases (south west quadrant). Generally speaking, disentanglement manipulation during processing (Rheo-Fluidification) provides a new way to control crystallinity, not just during 1st heating, but also upon 1st or 2nd cooling. The deconvolution of crystallization kinetics allows us to quantify the effect of thermal history on the crystallization behavior. Conclusion Crystallization kinetics from the melt on cooling and from the glass on heating can be described successfully by equations derived from the assumption of the existence of two amorphous phases, from both of which the germination and growth of crystals can take place. For PET crystallization kinetics, the equations used to fit the normalized rate of crystallization during non-isothermal experiments provide excellent fits, and the possibility to quantify the effect of processing variables on crystallization behavior, in particular the effect of M w and disentanglement. We have simplified the solution in this paper by considering the individual crystallizations separately and independently. This should be revised in future work to account for the interactive character of the dual phases. Acknowledgments Part of this work was accomplished while the author was at Eknet Research c/o the Industrial Materials Institute (IMI), Boucherville, Quebec, Canada. The author also acknowledges the financial support from a Marie-Curie grant and from a Fellowship Award by the Ikerbasque Foundation. References 1. Ibar, J.P. The great myths of polymer rheology, Part III: Elasticity of the network of entanglements. J. Macrom. Sci. Part B, Phys. 2013, 52, Ibar, J.P. Do we need a new theory in polymer physics? J. Macromol. Sci.-Rev. Macromol. Chem. Phys. 1997, C37, Ibar, J.P. Processing polymer melts under Rheo-Fluidification flow conditions: Part 1, Boosting shear-thinning by adding low frequency non-linear vibration to induce strain softening. J. Macromol. Sci., Part B, Phys. 2013, 52, Ibar, J.P. Method and apparatus to control viscosity of molten plastics prior to a molding operation. US Patent 6,210,030, Ibar, J.P. Viscosity control for molten plastics prior to molding. U.S. Patent 5,885,496, Ibar, J.P. Control of viscosity of polymer melts prior to molding by disentanglement methods. In SPE ANTEC Proceedings; Taylor and Francis: New York, NY, 1999, paper Hieber, C.A. Correlations for the quiescent crystallization kinetics of isotactic polypropylene and polyethylene terephthalate. Polymer 1995, 36, 1455.