Chain dynamics in polymer melts near tg studied by depolarized rayleigh scattering and viscoelastic measurements

In terms of the freely jointed chain model, the depolarized Rayleigh scattering time-correlation function has been analysed. The reorientation motion of a Kuhn segment represents the process in a polymer melt as often observed by depolarized photon-correlation spectroscopy at temperatures close to the glass transition point. With respect to the coordinate frame associated with the Kuhn segment, it is shown that the local segmental motions (corresponding to the so-called (ß process) should be reflected in the short time region of the photon-correlation spectroscopy as implied by a previous experimental observation. The a process as probed by the depolarized light scattering and that as extracted from the viscoelastic data in terms of a previously developed molecular theory are in good agreement in both the magnitude and the temperature dependence of the relaxation time (from 110 to 130°C).     

In situ investigation by quasi-elastic light scattering of an irreversible sol-gel transition

We report a dynamic light scattering study of semi-dilute solutions of polydisperse branched polymers. The autocorrelation function of the intensity of scattered light exhibits two decay modes. Experiments performed in situ on the sol phase of a system undergoing irreversible gelation show that the slow relaxation time diverges at the sol-gel transition.     

Scaling laws and polystyrene networks: a quasi-elastic light scattering study

Randomly crosslinked networks with a range of crosslink densities were prepared by γ-irradiation. Quasielastic light scattering measurements were made on the gels swollen to equilibrium in cyclohexane at 308, 318 and 333 K. The longitudinal osmotic modulus M_os was obtained from the intensity of the dynamically scattered light, and the cooperative diffusion coefficient D_c calculated from the relaxation rate of the autocorrelation function. The concentration dependence of these parameters at the theta temperature was found to be consistent with the scaling predictions, but at higher temperatures where excluded volume conditions prevail, deviations from scaling behaviour were observed. These discrepancies are probably caused by defects in the network structure.     

Melt memory effects on recrystallization of polyamide 6 revealed by depolarized light scattering and small‐angle X‐ray scattering

Melt memory effects on recrystallization of polyamide 6 were studied in a length scale from nm to μm using small‐angle X‐ray scattering (SAXS) and depolarized light scattering (DPLS). The memory effects on recrystallization rate were discussed in terms of the incubation period before nucleation and the half time of the crystallization, which were measures of the nucleation rate and the growth rate, respectively. Both rates are almost independent of the annealing temperature of the melt in the remelting process for the short term annealing below ～ 3 min while they are slowed as the annealing temperature increases for the long term annealing, showing that the relaxation of melt memory takes very long even above the equilibrium melting temperature T. Extrapolating the incubation period to infinite annealing, time we found that it was very hard to attain the fully relaxed state in polyamide 6 even above the equilibrium melting temperature. This must be due to the strong hydrogen bonding in polyamide 6. We also discuss the memory effects on the final structure after recrystallization based on the SAXS and DPLS profiles. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Dynamics of polymer molecules using neutron spin—echo

The dynamics of single polymer chains have been investigated in dilute solution and in the melt using the neutron spin—echo technique. In dilute solution the intramolecular motion is described to a first approximation by that for a Rouse chain incorporating hydrodynamic interactions (Zimm). It is characterised by an inverse correlation time which may be normalised by temperature, solvent viscosity and segment size, and which for long chains varies as Q³ at small scattering angles (Q is the change in wavevector on scattering). At very low Q vectors the predicted ‘universal’ regime is observed, but over most of the accessible range chemical structure also becomes important. For short chains, deviations from this Q³ behaviour are associated with overall molecular diffusion. In the melt, chain entanglements come into play and modify the simple Rouse-type motion. The correlation functions are described by a combination of Rouse motion over short distances and times and a long-time slow-motion predicted by the reptation model of melt dynamics.     

Molecular dynamics study on the effect of molecular orientation on polymer welding

Coarse-grained molecular dynamics simulation of a bead-spring polymer model was conducted for interdiffusion of two polymer flow fronts flowing parallel to one another as would be found in a weld-line. The effect of molecular orientation of the flow fronts on the interfacial structure was simulated. It was observed that the time evolution of the interfacial thickness was suppressed by shear flow for a chain whose length was longer than entanglement length. According to the analysis of autocorrelation function of end-to-end vector, it was revealed that anisotropic motion of chain was responsible for the growth of interfacial thickness and relaxation of the chain orientation was an important mechanism to explain the effect of shear flow on the growth of interfacial thickness. From the analysis of the segment motion at the interface with taking the density profile of end beads and center beads during the diffusion, it was found that interdiffusion of the end segment was always faster than that of center segments and significantly suppressed in oriented long chain.     

First international symposium on polymer electrolytes

We review the effects of temperature on conductance and viscosity in the liquid state of vitreous ionic conductors and show how differences may be best understood by comparison of relaxation times for electrical and mechanical stresses acting on liquid or glassy states of the material. This leads to the definition of a conductivity/viscosity mode decoupling index, useful as a figure of merit for the solid electrolyte. In applying the same approach to polymer electrolyte systems a problem is encountered due to the molecular weight dependence of the viscosity. This is resolved by deriving a ‘monomer’ shear relaxation time for the polymer electrolyte solution and showing that this quantity corresponds closely with the ‘local’ mechanical relaxation time obtained from light scattering studies (which is a molecular weight independent quantity for pure polypropylene oxide and other polymers of low T_g). Comparison of the electrical relaxation times of the polymer solution with the ‘local’ (or ‘matrix’) relaxation times then shows that the relationship found for superionic glass-forming systems is inverted in the case of polymer electrolytes. The latter have fractional decoupling indexes which may be interpreted in terms of serial coupling phenomena; i.e. ions must first decouple from their partner ions (in ion pairs), or from their intramolecular solvation states, before they can contribute to conductivity relaxation which is itself coupled to the local polymer matrix relaxation. An extreme case is illustrated using the weak electrolyte, lithium acetate, for which the decoupling index is ～6 × 10^?5.     

Dynamic light scattering of dilute PVA-borax aqueous solutions

Poly(vinyl alcohol)-borate (PVA-borate) complexes in dilute aqueous solutions were investigated by dynamic light scattering (DLS). Two relaxation modes obtained, were scattering vector-q² dependent and diffusive. The amplitude of slow mode was independent of borax concentration. In the very dilute PVA concentration regime ( [PVA] < 5 g/L), the PVA di-diol-borate complexation was dominated by intra-molecular reaction, and the fast mode correlation length ς_f which corresponds to the polymer chain dimension increased rapidly with borax concentrations lower than 0.06 M, and reached an asymptote in the higher borax concentration regime. However, for a dilute PVA aqueous solution with higher PVA content (i.e., [PVA] = 9 g/L), both intra-and inter-molecular PVA di-diol-borate complexations might happen. The chain expansion and shrinkage of PVA-borate complex with increasing borax concentration was observed due to the balance between the electrostatic repulsion of the charged diol-borate complexes and the intra-molecular crosslink induced by the intra-molecular di-diol-borate complexation.     

Insight into dynamics of polyelectrolyte chains in salt-free solutions by laser light scattering and analytical ultracentrifugation

We have investigated the dynamics of xanthan aqueous solutions with and without added salt (NaCl) by using laser light scattering (LLS) and analytical ultracentrifugation (AUC) via sedimentation velocity (SV). The fast and slow modes are observed in salt-free and low-salt xanthan solutions by dynamic light scattering (DLS). The scattering ratio (KC/R_s(q)) and apparent diffusion coefficient (D_s,app(q)) of the slow mode is linearly related to scattering vector (q²), indicating that it is related to the diffusion of scattering objects. The intensity contribution (α_s) of the slow mode is independent of scattering angles, indicating that the slow mode is not related to some scattering objects larger than the LLS observation length. However, the slow mode disappears in SV experiments, indicating that it arises from the temporal aggregates due to long range electrostatic interactions between chains, which can be destroyed in centrifugal field. The diffusion coefficient measured by SV is close to that of the fast mode in DLS measurements, indicating that it is the coupling diffusion of macroions and counterions. The present studies also demonstrate that the chain stiffness does not change the characteristics of the dynamics of polyelectrolyte in solutions.     

Correlation of dielectric and visco-elastic relaxation in polymer solutions

The interpretation of studies of dielectric relaxation in polymers is often restricted by ignorance of the mode of motion responsible for dipole orientation in an applied field. Relevant information can be drawn from studies of visco-elastic relaxation, since the visco-elastic relaxation time is comparable with the dielectric relaxation time when the latter requires some ‘whole molecule’ mode of motion involving simultaneous movement of many chain segments. The dielectric and visco-elastic relaxation times are expected to differ when the former involves a localised segmental motion. The dielectric relaxation process is shown to involve a localised segmental motion in acrylic polymers, but involves a ‘whole molecule’ rotation in low molecular weight poly(N-vinylcarbazole). Poly(p-substituted phenyl acetylenes) exhibit two dielectric relaxation processes. A low frequency relaxation comparable with the visco-elastic relaxation is ascribed to the backbone double bonds being polarised unidirectionally along the chain, and a high frequency process is ascribed to a localised segmental motion of the substituted phenyl moiety.     

Real-time dynamic light scattering on gelation and vitrification

The time-resolved dynamic light scattering has been employed to investigate gelation of divinylbenzene (DVB; branched chains) and vitrification of styrene (St; linear chains) during radical polymerization in bulk. The intensity correlation function (ICF) was obtained every 30 s during polymerization process. The DVB system exhibited a power law behavior in ICF characteristic of gelation threshold, which was followed by vitrification. In the case of St, two relaxation modes appeared before vitrification, which were assigned to be the cooperative and the slow relaxation modes.     

Coupling of mutual diffusion to viscoelasticity in moderately concentrated polyisobutylene solutions

The normalized intensity autocorrelation function g⁽²⁾(t) were obtained by dynamic light scattering for moderately concentrated entangled solutions of polyisobutylene in n-heptane at 25.0 °C and in isoamyl isovalerate (IAIV) at 25.0 °C (Θ). The obtained data have been successfully analyzed by the ‘procedure X’ familiar for determination of mechanical relaxation spectra on the basis of the recent theory for g⁽²⁾(t). The results have shown that while the mutual diffusion coefficient D increases in the n-heptane solutions and decreases in the IAIV solutions with increasing polymer mass concentration c, the friction coefficient ζ for both solutions increases with c showing the same power-law behavior irrespective of the weight-average molecular weight M_w and solvent quality. It has been found that the instantaneous longitudinal modulus L₀ for n-heptane solutions increases in proportion to c², obeying the familiar relation for the plateau value (4/3)G_N of the longitudinal stress relaxation modulus, but L₀ for the IAIV solutions becomes progressively smaller than the values predicted from the relation with decreasing c. The terminal relaxation time τ_m has been found to follow the power-law τ_m∝M_w^3.4 established by rheological measurements.     

Dynamics of ESIPT fluorescent methylmethacrylate-benzazole dye copolymers

The dynamics of fluorescent methylmethacrylate-benzazole dye copolymers were investigated in different concentration regimes by dynamic light scattering. In the dilute regime the polymer behaves as typical polydisperse linear chains in good solvent with a dynamics dominated by a single fast mode. In the semidilute regime, the cooperative diffusion coefficient, D_coop and the correlation length, ξ could be obtained. Above the semidilute regime the intensity autocorrelation functions show two-step decays, indicating the existence of low range correlations. The dye incorporation, even though small, affects the copolymer dynamics behavior in concentrated solutions if compared to PMMA, which is probably ascribed to a polymer-solvent interaction.     

Dynamic light scattering studies on random cross-linking of polystyrene in semi-dilute solution

The random cross-linking of appropriately functionalized polystyrene in semi-dilute toluene solution (c = 0.01–0.05 g/mL) was studied by time-dependent measurements of dynamic light scattering. Macroscopic gelation occurred from concentrations as low as 0.02 g/mL. The gelation time, determined from the first appearance of fluctuations of the scattering intensity and the initial amplitude of the intensity correlation function (ICF), decreases markedly from about 100 min to 10 min with an increase of polymer concentration or cross-linker content. After the gel point, the ICFs display a characteristic power-law decay. The power-law exponent, n = 0.75 ± 0.06, does not change with (i) extent of reaction, (ii) polymer concentration, and (iii) cross-linker concentration, within the inspected ranges. This universal behavior is traced back to the fact that gelation took place as a result of random cross-linking of existent macromolecules, whose state of solution does not change markedly during conversion.     

Static,dynamic and electric light scattering by aqueous colloids of diamond

The study of light scattering of aqueous colloids of diamond with particle size 10–400 nm was conducted. Particle concentration in colloids was low, and light scattering could be considered single. Methods of static, dynamic, and electric light scattering were employed. During the static light scattering experiments we took into account particle distribution on size that was determined from electron microscope measurements. It was shown that the experimentally obtained indicatrix of light scattering of polydisperse non-spherical diamond particle solution is in good agreement with the theoretical one for spherical particles. Autocorrelation function of depolarized light scattering intensity coincides with the time dependence of relaxation of scattered light intensity alteration after the electric field which induced particle orientation is switched off. This allows to use dynamic light scattering technique during the study of electro-optical properties of polydisperse colloids of diamond.     

汽-液流动沸腾蒸发系统的混沌分析及预测

应用功率谱、自相关系数、吸引子相图、关联维数等分析工具,对汽-液两相流动沸腾蒸发系统的传热系数时间序列进行了定性和定量混沌研究.研究结果为:时间序列的功率谱在半对数坐标下呈指数下降趋势;自相关系数随时间的推移而减小;吸引子相图呈现精细结构;关联维数随嵌入维数的增大而趋于一个稳定的分数值.这说明汽-液两相流动沸腾蒸发系统呈现混沌特性.在此基础上,应用临近点相似混沌预测法对不同加热蒸汽压力(0.11 MPa、0.13 MPa、0.15 MPa)下的传热系数时间序列进行了混沌预测.结果表明:预测值和实验值在有限时间长度内吻合程度较好;预测的平均相对误差随加热蒸汽压力的增加而增大;高精度预测时间长度随加热蒸汽压力增加而减小.这表明该系统具有短期可预测性.     

Dynamics of amylopectin in semidilute aqueous solution

The dynamic behaviors of potato amylopectin and waxy corn amylopectin in semidilute solution were investigated by laser light scattering and viscometer. For potato amylopectin with relatively smaller molecular weight, only pure diffusion motion of amylopectin was found by LLS in dilute regime. When the concentration was above the critical overlapping concentration (C^∗), three relaxation modes were found. The line-width of fast mode (Γ_f) had a q² dependence, where q is the scattering vector, and the correlative length (〈ξ_h〉) could be scaled to concentration (C) as 〈ξ_h〉 ∼ C^−0.79±0.1 when C > 2%. This mode was attributed to the cooperative relaxation motion of the “blobs” in the transient network. The line-width of slow relaxation mode (Γ_s) could be scaled with q as Γs∼qαs, α_s varying from 2.0 to 2.66 as the concentration increased. The relaxation time of slow relaxation mode (τ_s) had a C^1.8±0.1 dependence. This mode was originated from the association of the amylopectin. The medium mode was found when C > 4%. The line-width of medium relaxation mode (Γ_m) could be scaled to q as Γm∼qαm, α_m varying from 2.7 to 2.5 with the increasing concentration. The relaxation time of medium relaxation mode (τ_m) had C^0.7±0.1 dependence. The relative intensity contribution of the medium relaxation mode decreased with a rise in the concentration. This mode was attributed to the thermally agitated density fluctuation in semidilute solution induced by heterogeneities of the transient network. For waxy corn amylopectin with relatively huge molecular weight (∼10⁸ g/mol), only the internal motion of the single amylopectin molecule was found in dilute regime when qR_g ≥ 2, where R_g is the gyration radius of amylopectin. It was also found that there were three relaxation modes in semidilute solution of waxy corn amylopectin. The fast relaxation mode was found to be caused first by the internal motion of the single amylopectin molecule, and then, with the increasing concentration, by the cooperative motion of the transient network. The medium and slow relaxations for waxy corn amylopectin have the same physical origin as those for potato amylopectin. However, the C dependence and the q dependence of the medium and slow relaxation times for waxy corn amylopectin were different from those for potato amylopectin. This was attributed to the strong dynamic coupling effect in semidilute solution of the waxy corn amylopectin. The concentration dependence of the viscosity of amylopectin in semidilute solution indicated that the topological entanglement of amylopectin was weak due to the highly branching.     

Scattering functions of poly(amino acid) in helix-coil transition

Scattering functions of poly(amino acid) in the helix-coil transition region have been calculated on the basis of the Zimm-Bragg theory, to examine the effects of the helical content on the scattering function and on the cross-section factor, from which the radius of gyration of the cross section and the mass per unit length of the helical sequence can be obtained. The molecule is assumed to contain only one α-helical sequence of any length, leaving unfolded coils at the chain ends. The statistical mechanical averages of the interference among scattering units, apart from the interference within the helical sequence, are approximated by the expansion in terms of the even moments up to the eighth moment, which are calculated by the generator matrix method based on the conformation energies computed for poly (l-alanine). The scattering function at intermediate angles varies systematically according to the variation of the helical content, demonstrating the sensitivity of intermediate-angle scattering to the conformational changes in the helix-coil transition. The comparison of the Guinier plots of the cross-section factors, calculated from the scattering functions at various helical contents, has indicated that the radius of gyration of the cross section of the helical sequence can be determined accurately from the plots even when the coil content is as much as 30%, and that the mass per unit length is determinable to within an error of 6% unless the coil content exceeds 10%.     

Dynamic light scattering and small-angle neutron scattering studies on phenolic resin solutions

Solution properties of unfractionated phenolic resins prepared by polycondensation of phenol and formaldehyde using oxalic acid as a catalyst were investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The hydrodynamic radius, obtained by DLS experiments with 1 vol % solution in acetone, and the correlation length, ξ, of the Ornstein-Zernike equation, obtained by SANS experiments with 10 vol % solution in tetrahydrofuran, obey a power-law relation as a function of z-average molecular weight estimated by gel permeation chromatography, with scaling exponents of 0.57 and 0.27, respectively. These behaviors are unaffected by polymerization conditions, such as initial phenol-to-formaldehyde molar ratio in the range from 0.9 to 1.5, catalyst concentration with oxalic acid-to-phenol molar ratio from 0.01 to 0.1, and reaction time within the period in which the polymer remains soluble. SANS curves for polymers prepared under different conditions are sufficiently superimposed onto a single curve with the reduced variables, ξ⁻²I(q) and ξq. These results indicate that unfractionated phenolic resins have a self-similar structure with respect to the molecular weight.