Understanding Self-poisoning Phenomenon in Crystal Growth of Short

Sep 22, 2009 - As a result, minima in crystal growth rates of strictly monodisperse ... from secondary crystallization lagging behind the crystal grow...
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J. Phys. Chem. B 2009, 113, 13485–13490

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Understanding Self-poisoning Phenomenon in Crystal Growth of Short-Chain Polymers Yu Ma,† Bo Qi,† Yijin Ren,† Goran Ungar,‡,§ Jamie K. Hobbs,| and Wenbing Hu*,† Department of Polymer Science and Engineering, State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing UniVersity, 210093, Nanjing, China, Department of Engineering Materials, UniVersity of Sheffield, Sheffield, S1 3JD, United Kingdom, World Class UniVersity Program “Chemical ConVergence for Energy and EnVironment”, Seoul National UniVersity, Bldg. 302, San 56-1, Gwanak-gu, Seoul 151-744, Korea, and Department of Chemistry and Department of Physics and Astronomy, UniVersity of Sheffield, Sheffield, S3 7HF, United Kingdom ReceiVed: NoVember 6, 2008; ReVised Manuscript ReceiVed: July 27, 2009

Flexible polymers crystallize with chain folding, which shows a unique phenomenon called self-poisoning. As a result, minima in crystal growth rates of strictly monodisperse short-chain polymers are observed near the temperatures of transitions from extended-chain to once-folded-chain growth, from once-folded to twicefolded growth, etc. We employed dynamic Monte Carlo simulation of lattice polymers to visualize such transitions in molecular details. We observed a rate crossover between chain extension and lateral growth of polymer lamellar crystals at the wedge-shaped growth front, resulting in a rate minimum around the melting point of the metastable once-folded lamellar crystal. The rate minimum can be interpreted as due to the dependence of crystal growth rates on the excess crystal thickness beyond the minimum stable thickness. Furthermore, during crystal thickening, numerous molten chains are shown to be sucked into the lamellar crystals through the basal planes, demonstrating an important source of crystallinity from secondary crystallization lagging behind the crystal growth front. I. Introduction Most thermoplastics are semicrystalline polymers, and crystallization is at the heart of their processing, be it by extrusion, injection molding, fiber spinning, etc.1 We now know a fair amount about the morphology of semicrystalline polymers, which is based on thin chain-folded lamellar crystals whose existence was discovered 50 years ago.2-4 However, although the kinetics of polymer crystallization has been studied extensively, the basic mechanism remains as controversial as ever.5,6 Crystallization of long-chain polymers is arguably the most intractable of all crystallization processes since crystallizing units are linked together, and thus, crystal growth is coupled with complex conformational rearrangements. The inability to handle such complexity analytically is the main reason for insufficient progress in understanding polymer crystallization. The early workers recognized this problem and devised rather crude “coarse-grain” analytical theories,7,8 which prevail to this day, albeit with many subsequent modifications.9,10 Because the resulting theoretical expressions involve several adjustable parameters, a number of them can fit many experimental data,11 even though they may be based on fundamentally different concepts.11,12 In such situations, help may come from observations that stand out as qualitatively unique and “anomalous”; only theories capable of explaining such anomalies in a self-consistent manner can claim to be fundamentally sound. One such anomaly is the behavior of monodisperse n-alkanes with a chain length between * To whom correspondence should be addressed. E-mail: wbhu@ nju.edu.cn. † Nanjing University. ‡ Department of Engineering Materials, University of Sheffield. § Seoul National University. | Department of Chemistry and Department of Physics and Astronomy, University of Sheffield.

ca. 120 and 390 carbons, which exhibit deep minima in the temperature dependence of crystal growth rate, both from melt and from solution.13,14 Moreover, crystal growth rates of these oligomers of polyethylene also exhibit deep minima as a function of increasing solution concentration, the growth becoming completely arrested at a critical supersaturation and setting off again if the concentration is either increased or decreased.15 These intriguing and counterintuitive observations have been attributed, tentatively, to “self-poisoning”. It should be noted that the fold length of short-chain polymers is always an integer fraction of chain lengths; that is, chains are either fully extended or folded exactly in two, three, etc.16-18 The minima of crystal growth rates occur at the growth transitions between successive integer folded forms.19 Thus, for example, just above the extended to once-folded growth transition temperature, the suppressed growth of extended-chain crystals is attributed to nearly stable but unproductive chain-folding at the crystal growth front.20 Accordingly, the surface is “poisoned” not by impurities but by the “wrongly” folded host polymers. However, the model employed in ref 20 to describe the above process was still “coarse-grained”, without detailed information at the molecular level. Yet the reason that it could handle the problem at all was due to the extended chain having been broken into two segments. One might argue, with some justification, that the half-chain (“folded-chain”) depositions were imposed artificially. The attempt to explain the growth rate minima using the classic rigid stem model21 had to resort to highly unrealistic assumptions and was seriously flawed, as explained in ref 22. With the rapid development of computational techniques, molecular simulation has become a powerful tool in the investigation of polymer crystallization. Langevin dynamics simulations of 200 united atoms at the crystal growth front in solution have demonstrated sequential free energy minima at numbers of folded stems from six to four.23 Moreover, dynamic

10.1021/jp809785r CCC: $40.75  2009 American Chemical Society Published on Web 09/22/2009

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E ) [aEC + pEP +

∑ f(i)ER]/(kT) ) [a + pEP/EC + i

∑ f(i)ER/EC]EC/(kT)

(1)

i

Figure 1. Snapshots of the bulk 16-mers (a) in the initial melt state with a crystalline template layer at X ) 128 (all bonds are drawn as thin cylinders), (b) as crystal growing with extended chains after 320 000 MC cycles, and (c) as crystal growing with once-folded chains after 70 000 MC cycles. The lattice box has the size of 128 × 32 × 32 (XYZ). In both (b) and (c), EP/EC ) 1, ER/EC ) 0.02, and values for kT/EC are denoted in the figures; only the bonds containing more than 15 parallel neighbors are drawn as tiny cylinders.

Monte Carlo simulations of lattice polymers have reproduced the metastable once-folding of 16-mer short chains upon crystal growth in the melt, provided with a frictional barrier for c-slip chain diffusion in the crystal.24 Here, using the same approach as dynamic Monte Carlo simulations, we reproduce the minimum growth rates of lamellar crystals in the range of the growth transition from once-folded to extended-chain. Such molecular simulations of the self-poisoning phenomenon will allow us to identify its microscopic mechanism. The paper is organized as follows: after the introduction, we briefly describe the simulation techniques, followed by simulation results and discussion. The paper ends with conclusions. II. Simulation Techniques In our approach, polymer chains (16 monomers in length) were performing microrelaxation25 on a cubic lattice of size 128 × 32 × 32 (XYZ) with periodic boundary conditions. The occupation density is as high as 0.9375 to mimic the bulk polymer phase. In an efficient sampling algorithm, we let void sites seek for their neighboring monomers in the bulk phase. Such a chain length is sufficient to depict qualitative features of chain folding, whereas for quantitative comparisons with real chain-folding, more sophisticate molecular dynamic simulations for alkane chains of at least 120 monomer units are required.13,14 The melt state is prepared by a thermal relaxation of preset ordered chains over 104 Monte Carlo (MC) cycles, each MC cycle corresponding to 128 × 32 × 32 trial moves on the lattice sites. At different temperatures, crystal growth from the melt was induced on both sides by a solid template layer formed by extended 16-mers at X ) 128, as shown in Figure 1. A conventional Metropolis sampling algorithm has been employed with the potential energy change at each step of microrelaxation

where EC is the potential energy for each noncollinear connection of consecutive bonds along the chain, EP is the excess energy of each pair of nonparallel neighboring bonds, ER is the frictional barrier for sliding diffusion of the ith bond imposed by each parallel neighbor, a and p are the net numbers of corresponding changes, and f(i) is the number of parallel neighbors around the ith bond along the sliding diffusion path. The summation integrates all the parallel neighbors along the path of sliding diffusion. In practice, we set EP/EC ) 1 to maintain high flexibility of chains in the temperature range of crystallization driven by EP and set relatively low values of ER/ EC ) 0.02 and 0.04 to make the crystal thickening rate sufficiently high to allow the observations of both once-folded and extended-chain crystal growth within a reasonable simulation time. Because ER played a role mainly in the crystalline phase and f(i) was estimated only at the initial state in each step of microrelaxation, the detailed balance between forward and backward jumps in microrelaxation at the crystal boundary was broken. Therefore, the validity of our simulations was limited to the nonequilibrium crystallization process. The crystal gains additional stability through such a restriction in the crystal, which gives rise to a slightly higher melting point compared with the case without the frictional barrier for sliding diffusion. A similar effect has been observed in our previous simulations of crystallization and melting of statistical copolymers, where comonomers moving into the crystalline region along the sliding diffusion trajectory were prevented by their sizes relatively larger than monomers. Such a situation occurs, for example, in the case of linear low-density polyethylene with many short branches along the chain.26 kT/EC represents the variable system temperature. III. Results and Discussion One can see from Figure 1b,c that, at high temperatures, the lamellar crystal grows directly with the chains extended. However, at low temperatures, once-folded chains dominate the growth front, while chain extension, marked by a sharp boundary between two different crystal thicknesses, lags behind the growth front. A wedge-shaped growth front can be observed either for extended-chain crystals or for folded-chain crystals. The wedge shape might be an intrinsic feature of the polymer crystal growth front in the melt because of the situation that, in the melt, a new layer may immediately add onto the old one before the thickening of the old one has been saturated. At very high temperatures or in dilute solutions, a new layer becomes a rare event and such a situation may degenerate toward a sharp interface.23 The transition between extended and once-folded-chain crystal growth is also reflected in the temperature dependence of linear crystal growth rates, as summarized for ER/EC ) 0.02 and 0.04 in Figure 2. For ER/EC ) 0.02, only the expected break in slope occurs, in agreement with the experimental observation on the crystal growth of short-chain poly(ethylene oxide).27 However, for ER/EC ) 0.04, a clear minimum appears, although it does not reach down to zero growth rate as observed for both solution and melt crystallization of n-alkanes.19,28 One can see that, at high temperatures, the chain-extending rate overlaps with the extended-chain crystal growth rate, but at low temperatures,

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Figure 2. Linear crystal growth rates of bulk 16-mers as a function of temperature with EP/EC ) 1, for ER/EC ) 0.02 (black circles) and 0.04 (red triangles). The data for linear crystal growth rates were averaged by calculating the X distance of the growth front from the template as a function of time at 16 Y positions (eight equally spaced on each growth side). The X distance of the growth front is defined by the largest X distance of 4 (filled symbols, to capture the crystal growth front) or 10 (hollow symbols, to capture the chain extension front) vertically (Z) oriented successive crystalline bonds in a chain, each crystalline bond surrounded with more than 15 parallel neighbors, with 3 noncrystalline layers beyond this distance. The line segments are drawn to guide the eye.

chain extension advances much more slowly than the foldedchain crystal growth. The two rates meet near the break in the slopes of the growth rate. The fact that, for ER/EC ) 0.02, there is no obvious rate minimum but that there is one for ER/EC ) 0.04 implies that the observed self-poisoning is dependent on chain extension being retarded. At the minimum of crystal growth rates, chain extension makes a crossover there. There is evidence from realtime synchrotron SAXS experiments13 that, in some alkanes, crystallization just below the rate minimum produces folded chains first, closely followed by chain extension. Indeed, the lifetime of chain-folded deposition can be expressed in terms of the rate of chain extension at the wedge-shaped growth front. For low ER values, thickening of the wedge-shaped growth front always occurs at the growth front of extended-chain crystals, as observed experimentally in the extended-chain crystal growth of polyethylene under high pressure.29 Thus, if monodisperse chains were crystallizing in a mobile hexagonal columnar mesophase, such as that in polyethylene at high pressure, we would expect only a shallow minimum, if any, at the extended to folded chain growth transition. Although polyethylene oligomers do not display the hexagonal phase at high pressure, such experiments might be feasible at atmospheric pressure in the mobile phase of polymers, such as poly(dialkyl siloxanes), poly(dialkyl silanes), etc.,30 if sufficiently long monodisperse oligomers could be prepared. Next, we turn to the state shown in Figure 1c in the upper range of temperatures in order to observe isothermal refolding and melting behavior. Figure 3a shows that, if the temperature is not too high, melting of the folded chain crystal takes place, followed by crystal growth with chain extension. At higher temperatures, the melting curves themselves show two segments. The first and the second segments represent melting of foldedchain and extended-chain crystal, respectively. In Figure 3b, the linear melting and growth rates are plotted together. One can see that the growth and melting rates for a crystal of a given thickness fall on the same curve. This result implies that the

Figure 3. Isothermal melting curves (a) and linear crystal growth/ melting rates (b) as a function of temperature in the high temperature range for the crystal prepared in Figure 1c. The crystallinity is defined as the fraction of bonds containing more than 15 parallel neighbors. The linear growth/melting rates in (b) were obtained from the same procedures as in Figure 2 with the criterion of four vertical crystalline bonds and from the same time periods shown for different melting/ growth behaviors in (a).

zero-growth-rate temperatures for the folded chains and the extended chains coincide separately with two melting points of the corresponding crystals. As observed in Figure 1c, when the temperature decreases below the melting point of once-folded-chain crystals, the location of thickening changes from the growth front of the extended-chain crystal to a position lagging behind the foldedchain growth front. The folded chains are metastable when their free energy is lower than that of the melt but higher than that of the extended chains. Because, in the present simulations, the frictional barrier is not high, the folded-chain crystal will eventually transform into the extended-chain crystal after the growth fronts developed from both sides had impinged. In reality, in n-alkanes, the frictional barrier is very much higher; hence, the metastable folded-chain crystals survive during the time window of the experiments, which may be several orders of magnitude longer than the time window of our present simulations. According to the present results, it is because of the high actual frictional barrier in alkanes that the experimentally observed minimum reaches very close to zero growth rate at the melting point of folded-chain crystals.19,28 We also observe the rate of advance of the chain-extension front during melting of folded-chain crystals at T ) 4.7, as

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Figure 4. Time dependence of the positions of the chain-extending front (triangles) and the folded-chain crystal melting front (circles) at T ) 4.7 for the crystal on the right in Figure 1c. The positions of the growth fronts are calculated as the distances from the template layer.

shown in Figure 4. Here, we see an interesting situation where, at the same time as the growth front of the folded-chain crystal retreats, the extension front behind it advances. The two fronts meet, followed by lateral growth of the extended-chain crystal. Similar behavior has actually been observed in the wellcontrolled annealing experiments on poly(ethylene oxide) folded-chain crystals.27 The rate of advancing chain extension is larger than the rate of direct lateral growth of the extendedchain crystal from the melt. This behavior implies that crystallization of each chain incurs a free energy barrier higher than chain extension. This is reasonable if we consider that the lateral growth of the extended-chain crystal passes over a free energy barrier for deposition of a folded chain, as well as a subsequent barrier for chain extension on a wedge-shaped growth front. The folded-chain conformation is thus trapped between two barriers. Therefore, if the temperature is above the melting point of folded-chain crystals, it lingers for a while before melting again or extending further; if the temperature drops below that melting point, the folded-chain crystal continues to grow, while further chain extension may follow as the thickening front arrives from behind. The thickening process at the crystal growth front is apparent from the wedge-shaped growth profile. We calculated averages over the stem lengths as a function of their distance from the growth front for the samples with ER/EC ) 0.04 at different temperatures, as shown in Figure 5. At T ) 4.9, the growth front profile of extended-chain crystals is quite steep. However, at T ) 4.76, just above the temperature of the growth rate minimum, a ledge develops at around half the extended-chain length. This indicates that the half-length stem at the wedgeshaped growth front tends to have a longer than average lifetime before it undergoes further increase, or sometimes decrease, in length. The delay is the result of the entrapment of folded chains between the free energy barriers for extension and removal, respectively. The total free energy barrier to crystal growth is thus increased at this temperature by the chain-folded diversions, resulting in the growth rate minimum. The half-chain length becomes dominant at T ) 4.6, where folded-chain crystal growth takes over. There are diverse views on the important question of the nature of the free energy barrier to crystal growth of polymers.10,11 The original Lauritzen-Hoffman theory was based on an enthalpic barrier for secondary layer nucleation at the smooth growth front.7,9 Following this approach, a two-dimensional

Figure 5. Growth tip profiles with the average stem length as a function of the distance from the crystal growth front for the bulk 16-mers with EP/EC ) 1 and ER/EC ) 0.04: (a) at T ) 4.9, time 5 × 105 MC cycles; (b) T ) 4.76, time 5 × 105 MC cycles; and (c) T ) 4.6, time 6 × 104 MC cycles.

model for lateral extended-chain crystal growth was proposed by Hikosaka.31 Focusing attention on each single chain, the intramolecular crystal nucleation model was proposed more recently.32,33 Alternatively, a possible entropic nature of the barrier was suggested by Sadler and Gilmer for the growth front pinned by ill-fitting chains.34-36 Strobl suggested that a mesophase may preexist at the wedge-shaped growth front,37 and Muthukumar considered the entropy penalty from the amorphous chains linking different nuclei.38 According to the Sadler’s derivation,36 the advancing rate of the crystal growth front of polymers can be expressed as

G ∝ (l - lmin)∆f/(kT)exp(-b)

(2)

Self-poisoning Phenomenon in Crystal Growth

Figure 6. Logarithmic crystal growth rate of short chains versus temperature (schematic). As the melting point of the once-folded-chain crystals is approached from below, chain extension at the growth front is trapped at half the chain length. The curvature of the dashed curve mimics the experimental data reported by Kovacs et al.,27 representing the conventional crystal growth rate with chain folding independent of chain lengths.

where l is the saturated stem length at the crystal growth front, lmin is the minimum stem length stable at the crystallization temperature, b the barrier with various arguments described in the above paragraph, and ∆f/(kT) the reduced free energy change per unit of stem lengths. The excess crystal thickness l - lmin represents the thermodynamic driving force for crystal growth. The arguments in the above paragraph are mainly focused on the exponential barrier term. However, excess crystal thickness in the Sadler’s derivation shows how exceptional kinetic anomalies may arise when the growing thickness is arrested by integer chain folding. As shown by the dashed curve in Figure 6, for crystal growth with chain folding independent of chain lengths, both l and lmin smoothly increase with the crystallization temperature, giving rise to a smooth change of excess thickness and thus a continuous downward curvature of crystal growth rate versus temperature. Temperature dependence of crystallization is usually discussed in terms of changes with increasing supercooling. It is, however, instructive to discuss polymer crystallization as a function of increasing temperature and thus increasing crystalline stem length, that is, from the perspective of an extending chain. With increasing temperatures, if a short chain’s l is trapped at half the chain length, the excess thickness will approach zero due to the increase in lmin, giving rise to the rate approaching zero, as depicted by the deViation curve (solid) in Figure 6. Zero-growth rate is reached when the crystallization temperature arrives at the melting point of the once-folded-chain lamellae and the excess thickness approaches zero. Above that melting point, the crystal growth rate should immediately return back to the conventional crystal growth rate (the normal dashed curve), with enough excess crystal thickness. However, such a large excess thickness may not be immediately available because of the retardation of the once-folded state on chain extending at the crystal growth front (see Figure 5b). The once-folded state, although unstable in its dominant crystal above the melting point, incurs still a free energy barrier for further chain extension, as described also by Higgs et al.20 The capability of sliding diffusion will facilitate chain extension leaving away from the integer-folding trap, intercepting a more severe retardation of crystal growth, as demonstrated in Figure 2. Far above the melting point of once-folded-chain crystals, fully extended short chains will make another trap for the crystal growth rates to deviate from the conventional curvature but to stop at the melting point of extended-chain crystals. On the opposite direction in Figure 6, with decreasing temperatures, chain extension at the growth front of extended-

J. Phys. Chem. B, Vol. 113, No. 41, 2009 13489 chain crystals will be gradually retarded by the slowness in the further extending of integer-folded chains as the melting point of folded-chain crystals is approached, leading to the so-called self-poisoning phenomenon. Below that melting point, the folded chains can survive and even dominate the lateral crystal growth. In polymer solutions, because the excess thickness represents a thermodynamic driving force, such as either supercooling or supersaturation, depending upon which dimension we look at in the phase diagram, the local rate minimum of integer chain folding occurs not only in the temperature scale but also in the concentration scale, producing the phenomenon of the dilution wave.15 The self-diffusion of short chains in the melt can be neglected in its effect on the self-poisoning phenomenon because the Rouse relaxation time of 16-mers in the melt is about 50 MC cycles (see Figure 21 in ref 25), corresponding to the scale of growth rates 0.02 lattice sites/MC cycle and thus much beyond the time window of our observations reported in Figure 2. The small Rouse time reflects a high efficiency of microrelaxation of monomers, including sliding diffusion along the chain. In other words, the diffusion of molecules appears much faster than crystal growth, so the kinetics of crystal growth is dominated by an interfacial process causing linear time dependence of crystal growth. Concerning crystal thickening, there are two basic mechanisms, that is, sliding diffusion and melting-recrystallization.39 Numerous studies have shown that the former mechanism occurs generally if the temperature is raised slowly, whereas the latter takes place on faster heating.40 To see which mechanism of crystal thickening is dominant under the conditions of our simulation, we recorded snapshots of the chain-extension process behind the growth front. Two such snapshots, after 80 000 and 102 000 MC cycles are shown in Figure 7. Figure 7a highlights in blue those extended chains that originate from once-folded chains. They are abundant in the area of crystal thickening, demonstrating that chain extension is the dominant process of crystal thickening. Figure 7b highlights those chains that are being incorporated into the crystal from the melt. These chains fill the voids inside the crystal created by the extension of folded chains. Their presence draws attention to an important source of crystallinity commonly neglected in the analysis of overall crystallization kinetics and relegated to the secondary crystallization process. For polymers with high c-slip mobility, this source of crystallinity also contributes to primary crystallization. However, in a stack of lamellar crystals, thickening may also occur with two neighboring lamellae merging,41,42 which does not increase crystallinity significantly. Finally, Figure 7c highlights those crystalline chains that diffuse out into the melt. Those are few because thickening occurs predominantly by sliding diffusion rather than melting-recrystallization. IV. Conclusion By means of molecular simulations, we visualized the transition of crystal growth from once-folded to extended states of shortchain polymers. The minimum in the crystal growth rate reveals a retardation effect of integer-folded chains for chain extension at the crystal growth front. The self-poisoning phenomenon can thus be interpreted on the basis of crystal metastability provided by the reduced c-slip diffusion in the crystalline phase. In addition, crystal thickening succeeding the growth makes a significant contribution to overall crystallinity, highlighting the importance of secondary crystallization in the analysis of crystallization kinetics based on time evolution of crystallinity. The present work supports the notion that self-poisoning, that is, crystal growth blocked by incomplete metastable stems upon

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Ma et al. of China (NNSFC Grant Nos. 20674036 and 20825415) and the Ministry of Education of China (Contract No. NCET-040448). The joint funding from NNSFC and the Royal Society of the United Kingdom and the funding from the State Key Laboratory for Modification of Chemical Fibers and Polymer Materials at Donghua University of China are appreciated too. References and Notes

Figure 7. Snapshots of crystal thickening at the beginning and the end of the time period of 80 000 to 102 000 MC cycles, under the same conditions as in Figure 1c. Only those 16-mer chains having more than four consecutive crystalline bonds along the chain are drawn with their bonds as thin cylinders, each crystalline bond containing more than 15 parallel neighbors. (a) 421 blue chains are changing from oncefolded to extended conformation. (b) 447 blue chains are absorbed into the crystal from the melt. (c) 85 blue chains are released from within the crystal into the melt.

chain extension at the crystal growth front, prevails in all polymer crystallization; the anomalous growth minima in monodisperse oligomers only make this phenomenon patently apparent. Additional experiments on the microscopic observations of folded-chain crystal growth, followed by chain extension, may provide further tests for our simulation results. A polymer with a mobile phase at atmospheric pressure, such as poly(1,4-t-butadiene), might provide an interesting example. For crystal growth in oligomers of such polymers, the mobile phase allows a high c-slip diffusion rate and thus fast thickening, which is expected to reduce or eliminate the anomalous growth minima. Acknowledgment. We thank Dr. Xiangbing Zeng of Sheffield University for helpful discussions. W.H. is grateful for the support provided by the National Natural Science Foundation

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