Understanding the growth rates of polymer cocrystallization in the binary mixtures of different chain lengths

Polymer materials often contain a polydispersity of molecular lengths. We studied the linear growth rates of polymer lamellar crystals in the binary mixtures of different chain lengths by means of dynamic Monte Carlo simulations. Both chain lengths were chosen large enough to perform chain folding upon crystal growth but not very large to avoid the effect of chain entanglement in the bulk phase. We found that the crystal growth rates exhibit a linear dependence upon the compositions of mixtures. This linear relation implies that the overall crystal growth rates are integrated by the separate contributions of variable-length single polymers, supporting the model of intramolecular crystal nucleation. In each event of crystal growth of single polymers, long chains yield more crystallinity than short chains. This high efficiency explains higher crystal growth rates of long chains than that of short chains, and the explanation is quite different from the traditional view on the basis of their different melting points. In addition, with a partial release of sliding diffusion for crystal thickening, a new dependence of crystal growth rates occurs near the dilute end of long-chain compositions at high temperatures, which can be attributed to the preference of integer-number chain folding at the crystal growth front. The preferred fold lengths may vary with chain lengths and thus influence the crystal growth rates.     

Random Re-entry Theory of Polymer Melt Crystallization

Consideration of crystallization kinetics in high molecular weight polymers shows that adjacent re-entry is unlikely in melt crystallization and that sections of individual chains will crystallize concurrently at several sites. Surface nucleation controlled growth models can be set up which do not require adjacent re-entry but are in agreement with observations on growth rates and crystal thicknesses. The predominant process in crystallization with random re-entry is the incorporation into the crystal of a loop of chain which has both ends attached to the crystal surface. This leads to predictions of the crystallinity of quenched, spherulitic polymers. Radii of gyration of chains in the crystalline state can be calculated and are in agreement with neutron scattering results.     

Polymer crystallization from the melt at large undercoolings

Consideration of crystallization kinetics in high-molecular-weight polymers shows that adjacent reentry is unlikely in melt crystallization and that sections of individual chains will crystallize concurrently at several sites. Hence the characteristic crystallization process will be that of a loop of chain with both ends attached to different sites on the crystal surface. Analysis of this process leads to predictions of crystallinity values for various conditions of chain mobility in the crystal and of entanglements in the amorphous regions. Observations on polymers crystallized at high undercoolings where a crystallinity of about 30% is usually observed suggest that the common case is that of a highly entangled amorphous layer and rapid, local annealing of the chains but with no long-range motion in the crystal. This model of loop crystallization is shown to agree with available small-angle neutron scattering data. The overall crystallization kinetics are in accord with surface nucleation controlled growth which also arises out of the Lauritzen-Hoffman adjacent reentry model and has been shown to fit experimental results on growth rates.     

Secondary nucleation and growth of ZnO

Recently we discovered that under certain conditions new crystal growth (branch) can be induced on specific crystalline planes of the same material. This is a new phenomenon and is in sharp contrast to typical nucleation and growth in which a crystal will simply grow larger in preferred directions depending on the surface energy of the specific crystalline planes. Based on our observation, we developed a sequential nucleation and growth technique offering the power to assemble complex hierarchical crystals step-by-step. However, the key questions of when and how the secondary nucleation takes place have not been answered. Here we systematically study secondary ZnO crystal growth using organic diamine additives with a range of chain lengths and concentration. We found that ZnO branches form for a narrow diamine concentration range with a critical lower and upper critical nucleation concentration limit, which increases by about a factor of 5 for each additional carbon in the diaminoalkane chain. Our results suggest that the narrow window for secondary growth is dictated by the solubility of the ZnO crystals, where the low critical nucleation concentration is determined by slight etching of the surface to produce new nucleation sites, and the upper critical concentration is determined by the supersaturation concentration. Kinetic measurements show that the induction time and growth rate increase with increasing diamine concentration and follow classical nucleation and growth theory. Observations of branch morphological evolution reveal the mechanisms guiding the tunable crystal size and morphology.     

刚性侧链型液晶高分子与含二维液晶基元的液晶高分子

提出了“刚性侧链型液晶高分子”与“含二维液晶基元的液晶高分子”两个新概念。     

Effect of the coil-globule transition on the free-energy barrier for intrachain crystal nucleation

The rate of crystal nucleation of colloids and globular proteins can be enhanced by critical density fluctuations. It has been argued that a closely related phenomenon influences the rate of intramolecular "crystallization" of single-chain polymers. We report Monte Carlo simulations of the free-energy barrier that separates the crystalline state of a homopolymer chain from the disordered state. The simulations show that the barrier for nucleation of the ordered state is drastically lowered as the disordered state changes from a coil to a globule. We discuss the relation of the present findings to intramolecular nucleation of heteropolymers, such as proteins.     

Light scattering from a nematic monodomain in an electric field Twist elastic constant and viscosity coefficient of nematic polymer-solvent mixtures

The light scattering technique was used to investigate the viscoelastic parameters characterizing director twist distortions in miscible nematic mixtures of 5CB (pentacyanobiphenyl) with two side chain liquid crystal polymers and a main chain liquid crystal polymer. By applying an AC electric field to homeotropically-aligned nematic monodomains of the mixtures, the field-dependent scattering intensities and director orientation fluctuation relaxation rates yield, respectively, the twist elastic constant K₂₂ and viscosity coefficient γ₁. The results directly demonstrate that the addition of liquid crystal polymers causes substantial decreases of the relaxation rates for dynamic light scattering from the twist mode and these changes are due to small decreases in K₂₂ coupled with large increases in γ₁. The decrements in K₂₂ are comparable for both side chain and main chain liquid crystal polymers. The relative increase in the twist viscosity for the side chain liquid crystal polymers is much smaller than those of main chain polymers. A theoretical model is used to qualitatively interpret the difference between the viscous behaviour of the twist mode for both side chain and main chain liquid crystal polymers in a nematic solvent.     

Light scattering from a nematic monodomain in an electric field Twist elastic constant and viscosity coefficient of nematic polymer–solvent mixtures

Abstract

The light scattering technique was used to investigate the viscoelastic parameters characterizing director twist distortions in miscible nematic mixtures of 5CB (pentacyanobiphenyl) with two side chain liquid crystal polymers and a main chain liquid crystal polymer. By applying an AC electric field to homeotropically-aligned nematic monodomains of the mixtures, the field-dependent scattering intensities and director orientation fluctuation relaxation rates yield, respectively, the twist elastic constant K ₂₂ and viscosity coefficient γ₁. The results directly demonstrate that the addition of liquid crystal polymers causes substantial decreases of the relaxation rates for dynamic light scattering from the twist mode and these changes are due to small decreases in K ₂₂ coupled with large increases in γ₁. The decrements in K ₂₂ are comparable for both side chain and main chain liquid crystal polymers. The relative increase in the twist viscosity for the side chain liquid crystal polymers is much smaller than those of main chain polymers. A theoretical model is used to qualitatively interpret the difference between the viscous behaviour of the twist mode for both side chain and main chain liquid crystal polymers in a nematic solvent.     

Dislocation approach to the plastic deformation of semicrystalline polymers: Kinetic aspects for polyethylene and polypropylene*

The plasticity of semicrystalline polymers is analyzed in the framework of Young's dislocation model under the assumption of nucleation of screw dislocations from the lateral surface of the crystalline lamellae. It is proposed that the driving force for the nucleation and propagation across the crystal width of these screw dislocations relies on chain twist defects that migrate along the chains stems and allow a step‐by‐step translation of the stems through the crystal thickness. Such defects are identified as thermally activated conformational defects responsible for the so‐called crystalline relaxation. Dislocation kinetic equations are derived. Plastic flow rates attainable by dislocation motion in polyethylene and polypropylene are assessed with frequency–temperature data of the crystalline relaxation. Comparisons are made with experimental strain rates that enable homogeneous plastic deformation. In addition to temperature, the crystal lamellar thickness, which is a basic factor of the plastic flow stress in Young's dislocation model, is a major factor in dislocation kinetics through its influence on chain twist activation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 593–601, 2002; DOI 10.1002/polb.10118     

刚性链侧链型液晶高分子合成与研究

以自由基聚合方法，合成了一系列含有３个苯环通过酯键相联的液晶性单体及其聚合物，这类刚性液晶基元不通过柔性间隔基而直接竖挂在聚丙烯酸酯大分子主链上，具有很高的Ｔｇ·ＤＳＣ及偏光显微镜结果表明，所有的单体和聚合物均为向列型热致性液晶。     

Polymer crystallization: Simulation with entropic barrier model and application to specific polymers

The growth of polymer single crystals has been simulated on the basis of a simple two-dimensional ‘entropic barrier’ model. The chain is described by a sequence of growth units. Their additions and removals are determined by rate constants obeying detailed balance. The crystallization is then simulated by a kinetic Monte Carlo algorithm. An application of the model to specific crystallizable polymers (polyethylene, isotactic polystyrene, isotactic polypropylene, polyhydroxybuterate and polypivalolactone) is presented. Input parameter values for the model are derived from the respective surface free energies, bulk enthalpies, melting points and crystallographic repeat lengths. The only free parameter is the length of a polymer growth unit. This is set to half the lamellar crystal thickness at large undercooling. The lamellar thicknesses calculated on this basis are in good agreement with experimental data. An analysis of the growth unit lengths of the different polymers indicates a scaling with the chain persistence length in the melt.     

Limited Fraction of Crystallized Side Chains in Bottlebrush Poly(n-alkyl methacrylate)s

Crystallinity of bottlebrush polymers due to side chain crystallization has been considered to be related to the length of the side chains only under the assumption of complete participation of crystallization by all side chains.Recent experimental results revealed that in poly(n-alkyl methacrylate)s a fraction of side chains could not crystallize due to constraints imposed by the trapped main chain entanglements and required expansion of main chain-main chain distance.This result renders the original simplified consideration of the origin of crystallinity in bottlebrush polymers questionable.In this work,we introduce a new parameter fc,the fraction of crystallizable side chains,to better describe the crystallinity of bottlebrush polymers.A linear relationship between the melting enthalpy and the number of alkyl groups in side chains for bottlebrush polymers reported repeatedly indicates that fc remains essentially unchanged when bottlebrush polymers had the same main chain structure and grafting degree but different side chain lengths.The slope of the above-mentioned linear relationship is thus AHCH2×fc,where AHCH2 stands for the melting enthalpy of one mole alkyl group packed into the crystal.With a known value of fc,it is possible to estimate the value of AHCH2.In case of poly(n-alkyl methacrylate)s,we estimated AHCH2 of hexagonal crystal being at most 5.74 kJ/mol with the knowledge of possibly smallest fc of 0.67 obtained from small angle X-ray scattering data.Therefore,the crystallinity of bottlebrush polymer would be calculated based on the equation Xc = fc×Nc/N with N and Nc being the number of alkyl groups in a side chain and those packed in the crystalline structure,respectively.Both chemical structure and grafting degree of bottlebrush polymers affect fc.     

Mesogen-jacketed Liquid Crystal Polymers With Mesogens of Aromatic Amide Structure

The synthesis and property of a new series of "mesogen-jacketed liquid crystal polymers" are reported. These polymers have aromatic amide structures as the mesogenic groups and are represented by poly-2,5-bis(4-methoxy- benzamido)styrene. The preliminary study on properties shows that the polymers have very high glass transition temperatures as well as very low critical concentrations for the formation of the lyotropic liquid crystal phase. The results indicate a high degree of chain rigidity. However, the liquid crystalline order of molecular organization in bulk samples disappears upon heating to the glass transition temperature as revealed by polarizing microscopy and by X-ray diffractometer. Therefore, the liquid crystalline order of these polymers forms only through solution but not through heating. This behavior is different from that of the previously studied poly-2,5-bis[(4-methoxybenzoyl)oxy]styrene and its homologs. The latter polymers are liquid crystals both lyotropically and thermotropically. © 1997 John Wiley & Sons, Ltd.     

Structure—Property relationships for exciton transfer in conjugated polymers

The ability of conjugated polymers to function as electronic materials is dependent on the efficient transport of excitons along the polymer chain. Generally, the photophysics of the chromophore monomer dictate the excited state behavior of the corresponding conjugated polymers. Different molecular structures are examined to study the role of excited state lifetimes and molecular conformations on energy transfer. The incorporation of rigid, three‐dimensional scaffolds, such as iptycenes and cyclophanes, can encourage an oblique packing of the chromophore units of a conjugated polymer, thus allowing the formation of electronically‐coupled aggregates that retain high quantum yields of emission. Rigid iptycene scaffolds also act as excellent structural directors that encourage complete solvation of PPEs in a liquid crystal (LC) solvent. LC‐PPE mixtures display both an enhanced conformational alignment of polymer chains and extended effective conjugation lengths relative to isotropic solutions, which leads to enhanced energy transfer. Facile exciton migration in poly(p‐phenylene ethynylene)s (PPEs) allows energy absorbed over large areas to be funneled into traps created by the binding of analytes, resulting in signal amplification in sensory devices. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Monitoring the formation of self-assembled monolayers of alkanedithiols using a micromechanical cantilever sensor

Using a micromechanical cantilever device, the surface stress induced during the growth of alkanedithiol (HS(CH2)nSH) monolayers on gold in solution is continuously monitored and reported. Adsorption of alkanedithiols of varying chain lengths is observed and compared to each other, as well as to the adsorption of hydroxyalkanethiols (HS(CH2)nOH) and alkanethiols (HS(CH2)nCH3). The results have revealed a significant change in surface stress on the basis of the chain length of the alkanedithiol. The long-chain (n > 10) alkanedithiol adsorption imposes a tensile stress on the gold-coated surface of the cantilever rather than the compressive stress exhibited by both alkanethiols and short-chain dithiols. Our results suggest a phenomenon in which the two thiols of the alkanedithiol adsorb onto the gold surface forming a loop inducing a tensile stress on the cantilever for long chain lengths. This study shows that micromechanical cantilever sensors can be very valuable tools in the exploration and characterization of self-assembled monolayers.     

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.     

Effect of molecular weight on the radial growth rates of polymer spherulites

Data existing in the literature for the spherulitic growth rate of molecular weight fractions of linear polyethylene, poly-(tetramethyl-p-silphenylene)siloxane, and trans-1,4-polyisoprene have been analyzed according to nucleation theory on taking into account the influence of chain length on the free energy of fusion. All three polymers display very similar behavior in that the interfacial free energy reaches an asymptotic value at high molecular weights, decreases as the molecular weight is lowered, and appears to also reach an asymptotic value at low molecular weights. Although the changes in the interfacial energy with molecular weight are quite distinct, the relative change is much less than has been previously reported when a molecular crystal analysis is used. The same general behavior observed points out the dominating influence of the chain-like character of the molecules in governing the growth rate.     

Synthesis and properties of mesogen‐jacketed liquid crystalline polymers containing biphenyl mesogen with asymmetric substitutions

This work focuses on the design, synthesis, and characterization of a series of mesogen‐jacketed liquid crystalline polymers (MJLCPs), poly(alkyl 4′‐(octyloxy)‐2‐vinylbiphenyl‐4‐carboxylate) (pVBP(m,8), m = 1, 2, 4, 6, 8, 10, 12). For the first time, we realized asymmetric substitutions in the mesogens of MJLCPs. The polymers obtained by conventional free radical polymerization were investigated in detail by a combination of various techniques, such as differential scanning calorimetry, wide‐angle X‐ray diffraction, and polarized light microscopy. Our results showed that all the polymers were thermally stable, and their glass transition temperatures decreased when m increased. The liquid crystalline (LC) phases that developed at high temperatures and disappeared at low temperatures were strongly dependent on the difference in lengths of alkyl groups on the 4 and 4′ substitution positions of the side‐chain biphenyl. While polymer pVBP(1,8) was not liquid crystalline, columnar liquid crystalline phases were observed for all other pVBP(m,8) (m = 2, 4, 6, 8, 10, 12) polymers. Polymer pVBP(8,8) showed a tetragonal columnar nematic liquid crystalline phase, and the other LC polymers exhibited columnar nematic phases. In additions, the smaller the difference in the lengths of the terminal alkyls, the easier the development of the liquid crystalline phase. Birefringence measurements showed that solution‐cast polymer films exhibited moderately high positive birefringence values, indicating potential applications as optical compensation films for liquid crystal displays. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Crystallization and melting of narrow composition distribution polyethylenes: Investigation and implications of crystal thickening

The crystal structure produced during the isothermal crystallization of polyethylene (PE) copolymers with a broad range of comonomer concentrations was determined by the measurement of the melting endotherms directly after crystallization. PE copolymers with higher concentrations of short‐chain branches (≥10 branches per 1000 total carbon atoms) exhibited strong resistance to crystal thickening during isothermal crystallization. Negligible thickening, estimated to be only about 0.1 nm in 10 min of isothermal crystallization, was observed. The side‐chain branches apparently acted as limiting points of chain incorporation into the crystals, which exhibited great resistance to the modification of their position, that is, crystal thickening. Even with long periods (up to 8 h) of isothermal storage, crystal thickening was very small or negligible, about 0.3 nm. The crystal thickness was calculated from differential scanning calorimetry data. The behavior of copolymers with lower branching concentrations and the unbranched PE homopolymer was quite different from that of the copolymers with higher branching. Polymers with low or no branching exhibited the initial crystallization of a thinner crystal population, which thickened substantially with increasing time. The thickening observed for these lower or unbranched polymers was an order of magnitude larger, that is, 1.6–2.0 nm in 10 min of isothermal crystallization. Copolymers with higher concentrations of branching had relatively short sequence lengths of ethylene units between branch points, and this resulted in strong control over the crystal thickness by the branch points and great resistance to crystal thickening, even with long times of isothermal crystallization. Copolymers with low concentrations of branching had relatively long sequence lengths of ethylene units between branch points, and this resulted in little control over the crystal thickness by the branch points and rapid crystal thickening upon isothermal crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 235–246, 2003