NMR approach to the kinetics of polymer crystallization. 1. Cis-1,4-polybutadiene

The isothermal crystallization kinetics of cis-1,4-polybutadiene (PB) in bulk, was studied over the temperature range 193 to 235 K, using ¹H pulsed high-resolution FT-NMR. Analysis of the spectral line area and width, corresponding to the resonance of protons bonded to noncrystalline chain segments, yields two major results:

• (i) The line area variations are associated with the overall progression of crystallization in the sample, which is shown to obey on Avrami law. The time exponent n and rate constant k were determined for each isotherm; their temperature dependence reflects the nucleation and crystal growth mechanisms and provides an estimate of relevant thermodynamic parameters.
• (ii) The line-width is assumed to be closely related to a statistical network with the average mesh size determined by a random distribution of crystallites. Finally, concomitant spin-lattice relaxation time (T₁) measurements show an increase of this parameter which parallels the development of the crystalline fraction.

     

NMR studies of polymer solutions. II. Polyethylene

The intramolecular structure of polyethylene in solution was studied by a high-resolution nuclear magnetic resonance technique. Highly purified n-alkanes (99.5%) from C₅H₁₂ to C₃₆H₇₄ were used as its oligomers. The NMR spectra of the polyethylenes (oligomers) are very sensitive to the solvents used. The internal methylene protons of all polyethylenes of various chain length resonance at an identical frequency in carbon tetrachloride. A sharp transition in the NMR spectrum of polyethylene in α-chloronaphthalene at 35°C. was observed at n-C₁₇H₃₆, above which there exist two distinguishable NMR peaks for internal methylene protons, and below which (fewer carbons) only a single peak was seen. The NMR spectra of the internal methylene protons of the polyethylenes (oligomers) taken in benzene are very similar to those taken in pyridine. They are not as easily resolved as those NMR spectra taken in α-chloronaphthalene solutions. The effect of the size of the aromatic solvent molecule on the NMR spectra of the internal methylene protons of the polyethylenes (oligomers) in solutions was demonstrated by using aromatic solvents of various sizes, such as chlorobenzene, α-chloronaphthalene, and 9-chloronathracene. The results indicate that the formation of polymeric structure of the internal methylene groups in the polyethylene chain is very sensitive to the size of the solvent used. The interaction of the solvent with the methylene groups of the polyethylenes varies as a function of chain length; it is stronger for those low member n-alkanes and decreases gradually to an asymptotic value.     

Polymeric nature of selenium crystallization. II. Crystallization kinetics and secondary crystallization

The crystallization of elemental selenium has been studied in light of present concepts of crystallization in organic polymers. Bulk-crystallization kinetic data as measured by a dynamic density technique and spherulite growth-rate data as measured by optical microscopy are presented for the temperature range 70°C to 160°C. Plots of extent of isothermal crystallization versus time were sigmoidal in shape. Spherulite growth rates were constant for a given temperature and reached a maximum at approximately 130°C. Evidence is presented for secondary crystallization in selenium, and a model is proposed for destruction of chain folds with interlamellar crystallization during the spherulitic-to-“metallic” transformation above 100°C.     

Influence of the order of polymer melt on the crystallization behavior: II. Crystallization kinetics of isotactic polypropylene

The crystallization behavior of isotactic polypropylene (iPP) melts with a high order has been carefully examined by differential scanning calorimetry (DSC) and polarized light microscopy (PLM). The experimental results show that the helically ordered iPP melt crystallizes by heterogeneous nucleation with two-dimensional diffusion controlled growth and the Avrami exponent is about 2. The data available both from our DSC and PLM experiments and from the literature indicate that the order of a polymer melt can speed up the crystallization process. When some unmelted materials exist in the ordered melt, the crystallization will become more rapid. Received: 16 June 2000 Accepted: 16 October 2000     

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.     

Temperature effects for isothermal polymer crystallization kinetics

We adopt the cluster size distribution model to investigate the effect of temperature on homogeneous nucleation and crystal growth for isothermal polymer crystallization. The model includes the temperature effects of interfacial energy, nucleation rate, growth and dissociation rate coefficients, and equilibrium solubility. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different temperatures. The denucleation (Ostwald ripening effect) is also investigated by comparing moment and numerical solutions of the population balance equations. Agreement between the model results and temperature-sensitive experimental measurements for different polymer systems required strong temperature dependence for the crystal-melt interfacial energy.     

NMR approach to kinetics of polymer ordering in polyacrylonitrile solutions and acrylonitrile-sodium methallylsulfonate copolymer solutions: Solution-concentration and polymer-tacticity effect

Partial crystallinity of polyacrylonitrile and acrylonitrile-sodium methallylsulfonate copolymer is detected by X-ray diffraction in dimethyl formamide and glycerol-dimethyl formamide solutions in the range of polymer concentration (0.14, 0.325 mol/mol). Kinetics of isothermal ordering are followed by NMR for various temperatures, polymer concentration of the solutions and polymer tacticities. The rate of polymer ordering increases upon either a decrease of the temperature, an increase of the polymer concentration or an increase of the percentage of isotactic triads. Mandelkern's model of isothermal polymer crystallisation is applied to estimate the size of critical crystalline nuclei. Assuming that crystallites growth is negligible along polymer chain axis, one can deduce the maximal size of crystallites along this axis. The size of the crystallites perpendicularly to polymer chain axis is evaluated by X-ray diffraction. It is found to be of the order of 100 Å.     

NMR study of polyethylene crystallization kinetics under high pressure

Crystallization of polyethylene under hydrostatic pressures of 1–4.5 kbar is directly observed using pulsed proton NMR. The rate of growth of extended-chain polyethylene crystals is measured over this pressure range and to a maximum temperature of 227°C. The observed crystallization isotherms are superimposable on a log time scale; this implies a consistent mechanism for extended-chain growth over this pressure range. Avrami coefficients for high-pressure extended-chain crystallization are determined to be 1.3–1.7. A decrease of crystal nucleus surface free energies with increasing pressure is indicated. Findings are consistent with Wunderlich's model of initial folded-chain crystallization followed immediately by chain extension. Future applications of this NMR technique are briefly considered.     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

磁场影响聚合物本体结晶动力学的机理分析

在经典的热力学理论基础上,探讨了磁场对聚合物本体结晶过程的成核与生长的影响,建立了相关结晶动力学理论方程.初步认为,磁场产生的＂磁结晶效应＂可能是由于晶相与非晶相之间磁化率差异导致了两相之间磁化能的差异,也可能由于聚合物体系在结晶前会形成一种有序相,减小了体系的熵值,进而改变了结晶过程中的体系自由能,影响其成核与晶体生长,乃至整个结晶动力学方程.利用Matlab软件结合PLLA的各结晶参数值,绘制了结晶自由能与各成核临界参数之间的函数图像.结果表明,在低过冷度下,较小的自由能扰动可能导致较大的晶核临界参数变化.     

Overall crystallization kinetics of thin polymer films. General theoretical approach. I. Volume nucleation

A general theoretical approach of the overall crystallization kinetics of thin polymer films is developed. This new model makes it possible to calculate the evolution of the transformed volume fraction anywhere in the film, whatever the cooling conditions are. In its isothermal limit this model is equivalent to previous approaches which have been well verified by a computer simulation. In conclusion, it is pointed out that both isothermal and anisothermal determinations of crystallization kinetic parameters are greatly dependent on the sample thickness.     

Shear flow effects on polymer melts crystallization: kinetics features

In this work the kinetics of the isothermal crystallization from the melt of isotactic polyolefins in quiescent conditions as well as after the application of a step-shear flow is investigated by means of rheological measurements. It is shown that the kinetics of the crystallization, as measured by the increase of the storage modulus, is not affected by the strain amplitude and the frequency of the oscillation, once they are properly chosen. A strong enhancement of the crystallization kinetics has been obtained when the step-shear flow was applied at the crystallization temperature T_C=92°C for two different molecular weight poly(1-butene) samples (i-PB400 and i-PB200) and at T_C=137°C for a polypropylene (i-PP). In particular, the overall-crystallization rate constants of the i-PB400 increased with increasing the applied shear rate at a constant total strain of 60. At higher shear flow temperatures slower kinetics occurred in all the cases until the effect of the applied shear flow was lost. Moreover, the effect of the molecular weight on the flow induced crystallization phenomenon is investigated on the two i-PB samples and the results have clearly shown that the higher molecular weight i-PB200 polymer is much more sensitive than the i-PB400 to the flow history.     

Use of differential scanning calorimetry to study polymer crystallization kinetics with longer half times

A method has been developed to determine polymer crystallization parameters with longer half times using differential scanning calorimetry. This method can be used irrespective of the crystallization temperature, sample weight, nature of the polymer and the sensitivity of the instrument. The results obtained from this method for polyethylene samples are compared with those obtained from dilatometry. Similar values for the kinetic parameters are obtained using both techniques. The calorimetric method has been used for other polymers such as polypropylene and poly(4-methyl-1-pentene).     

Investigation of polymer crystallization kinetics with time dependent light attenuation measurements

Results obtained for samples of syndiotactic polypropylene and poly(ethylene-co-octene) demonstrated the usefulness of light attenuation measurements in investigations of polymer crystallization. The earlier stages with separated growing spherulites fall in the range of Rayleigh–Debye–Gans scattering. Known relationships describing the dependence of the linear attenuation coefficient on the radius and the index of refraction of a spherulite can be applied in evaluations. The sensitivity of attenuation measurements is much higher than that of conventional tools.     

Polysiloxanes having aromatic heterocyclic units. I. Polydimethylsiloxane benzimidazole polymer

A polymer containing dimethylsiloxane units (35) and benzimidazole units (1) has been prepared by the condensation of 3,3′-diaminobenzidine and an α,ω-bis-(γ-carboxy-n-propyl) polydimethylsiloxane. The new polymer has some rubbery properties, but it decomposes catastrophically at 400°C.     

Approach to generalization of concentration dependence of zero-shear viscosity in polymer solutions

The possibility of constructing zero-shear viscosity master curves valid for the entire range of concentration for a large number of polymer solutions in different solvents independent of molecular weight and the nature of the solvent is considered. The results obtained show that the parameters characterizing the individual macromolecular chain., viz., the dimensions of the polymer coil and the rheological effectiveness of segmental interactions, are significant in determining the viscosity of polymer solutions from very dilute to highly concentrated ones. The relation between the parameter of rheological interaction and characteristics of polymer solutions such as the flexibility of the polymer chain and the Flory-Huggins parameter is discussed. This permits one to separate the influence of the energy and entropy factors on the concentration dependence of zero-shear viscosity.     

A simple method of evaluating non-isothermal crystallization kinetics in multicomponent polymer systems

A new simple method of evaluating non-isothermal crystallization kinetics is proposed. The procedure based on mathematical treatment of DSC cumulative crystallization curves at their inflection point provides three kinetic parameters: temperature of start of crystallization (T_s), temperature of maximum crystallization rate (T_i) and numerical value of the maximum crystallization rate (s_i), and also final crystallinity after cooling (CR_c). The method is demonstrated on the system poly(ɛ-caprolactone)/poly(lactic acid)/clay C15 and related microfibrillar composite. The method provides the values of T_s and T_i with standard deviation σ = 0.3 and 0.4 °C, respectively. The coefficient of variation v of s_i and CR_c is 5.8 and 1.5%, respectively. The proposed method does not refer to any crystallization model and does not require exact determination of the starting time. It is particularly useful for characterizing a series of samples derived by modification of the neat polymer.     

Corresponding state relations for the Newtonian viscosity of polymer solutions. II. Further systems and concentrated solutions

In earlier work we have indicated a superposition principle for moderately concentrated mixtures (c ? 2/[η]) in good and poor solvents. By an examination of data on a number of vinyl polymers and cellulose derivatives in good as well as poor solvents, the validity of this principle is extended to concentrated solutions (c ? 50%). The characteristic concentration factor γ is proportional to M over the whole concentration range, with 0.47 ≤ a₁ ≤ 1.10 being larger for good than for poor solvents, the result obtained earlier. Significant deviations from this relationship are noted in good solvents for those low molecular weights at which deviations from the usual intrinsic viscosity relationship occur. This may be related to the expansion factor of the polymer coil. On the basis of these results, the concentration and molecular weight dependence of the viscosity in the concentrated solution can be related to each other in terms of the parameter a₁ and thus to thermodynamic characteristics. In this manner a bridge between the relatively dilute and concentrated regions is established. Currently used semiempirical expressions are analyzed in terms of these results. For the polystyrene–cyclohexane systems and θ ? 9 ≦ T ≦ θ + 3, γ can be identified with the critical concentration for phase separation. Provided an “entanglement” concentration c_e exists, in the neighbourhood of which the concentration dependence of the viscosity changes reapidly, γ can alternatively be shown to be proportional to c_e, or c_e ∝ M. The temperature reduction scheme suggested earlier remains to be investigated.     

Adiabatic compressibility of polymer solutions—II. Polystyrene in toluene

Adiabatic compressibility data for polystyrene, using samples of various molecular weights dissolved in toluene, are reported as a function of concentration. These data are compared with calculations of the incremental compressibility obtained from viscoelastic and longitudinal acoustic relaxation studies. The differences between the observed and calculated increments are attributed to polymer-solvent interactions.     

Solvent-induced crystallization. I. Crystallization kinetics

The kinetics of crystallization of quenched poly(ethylene terephthalate) (PET) films during the imbibition of methylene chloride (MeCl₂) vapor is studied by density measurements. The effects of film thickness (0.0025–0.086 cm) and temperature (0–38°C) were examined. The data suggest that MeCl₂ transport controls the crystallization in thick films and at elevated temperatures, but that spherulite growth controls in thin films and at reduced temperatures. The application of a mathematical model developed previously supports this mechanistic interpretation of the data.