The influence of shear rate, temperature and chain conformation on the critical concentration c

 When viscometry is used, a crossover phenomenon is observed separating the dilute solutions into extremely dilute solutions and dilute solutions. The critical concentration c ^**, determined from this crossover phenomenon, strongly depends on the shear rate in the solution. At very high values of shear rate the critical concentration c ^** becomes very low and depends only on the contour length of the elongated chains of different polymers. An increase of the temperature induces an increase of c ^** because the relaxation time of the chains decreases. If a polymer adopts a rodlike conformation (in a given solvent at a given temperature) the excluded volume of its chains increases and its critical concentration c ^** decreases. Received: 14 October 1996 Accepted: 3 March 1997     

EFFECT OF OVERLAP CONCENTRATION AND PERSISTENCE LENGTH ON DNA SEPARATION IN POLYMER SOLUTIONS BY ELECTROPHORESIS

The persistence length and the overlap concentration(c~*) of poly(ethylene oxide)(PEO) and hydroxyethylcellulose(HEC) with similar molecular weight in 1×TBE buffer were studied by laser light scattering and viscometry.Their effect on DNA separation was investigated by capillary electrophoresis.It was determined that the persistence length of HEC was at least 5 times higher than that of PEO.Therefore,the c~* of HEC was smaller than that of PEO by a factor of ca.2.5.It was also found that the c~* values de...     

On the resistance to the interpenetration between macromolecular coils of different segment densities

Using viscometry techniques on polymer fractions, we determine the critical concentrationc ^* (separating the dilute and semi dilute solutions). The same measurements have been conducted with mixtures of these fractions (mixtures 1:1 by weight of fractions differing in molecular mass and chemical nature, or fractions differing only in molecular mass). The determined values of critical concentrationc ^* of the mixtures are higher than the values calculated based on the critical concentrations of the corresponding fractions. This deviation from the additivity rule is attributed to the resistance in the interpenetration (delay to the attainment of the homogeneous state) between macromolecular coils of different chemical nature or of the same chemical nature but of different molecular mass. Higher values of the reduced viscosities of the mixture of the fractions, compared to the values calculated using the reduced viscosities of the corresponding fractions, are observed above the critical concentrationc ^*. In this concentration region the interaction parameter between two different polymers is calculated.     

Molecular geometry and chain entanglement: parameters for the tube model

The tube diameter in the reptation model is the distance between a given chain segment and its nearest segment in adjacent chains. This dimention is thus related to the cross-sectional area of polymer chains and the nearest approach among chains, without effects of thermal fluctuation and steric repulsion. Prior calculated tube diameters are much larger, about 5 times, than the actual chain cross-sectional areas. This is ascribed to the local freedom required for mutual rearrangement among neighboring chain segments. This tube diameter concept seems to us to infer a relationship to the corresponding entanglement spacing. Indeed, we report here that the critical molecular weight, M_c, for the onset of entanglements is found to be M_c = 28 A/(〈R²〉₀/M), where A is the chain cross-sectional area and 〈R²〉₀ the mean-square end-to-end distance of a freely jointed chain of molecular weight M. The new, computed relationship between the critical number of backbone atoms for entanglement and the chain cross-sectional area of polymers, N_c = A^0,44, is concordant with the cross-sectional area of polymer chains being the parameter controlling the critical entanglement number of backbone atoms of flexible polymers.     

Model for the fracture energy of glassy polymer–polymer interfaces

The increase in the interfacial fracture energy (G_c) with increasing interfacial width (a_i) goes through a transition at a critical value of a_i that is unique to each polymer–polymer system. This transition point does not scale with the bulk entanglement spacing (d_t) for different systems, implying that the role of chain friction in reinforcing these interfaces is more important than previously thought. A theoretical model has been developed to calculate G_c as a function of the interfacial stress transfer due to individual polymer chains. When including the effects of chain friction only, the model reproduces the nonuniversal behavior of G_c with respect to a_i/d_t but yields poor fits for a_i/d_t > 1. The effects of entanglements are then added by calculating the fraction of entangled chains as a function of a_i/d_t. This contribution, although not material specific, matches the qualitative behavior of G_c for large values of a_i/d_t. When both contributions are included in the model, excellent fits are obtained for all data sets. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2377–2386, 2002     

二维红外相关光谱研究缠结对冷冻升华无规聚苯乙烯分子运动的影响

用冷冻升华法制备了浓度为1×10^－4 和2×10^－5 g/mL的单链无规聚苯乙烯(a-PS). 利用FTIR测试方法, 测定a-PS在等温处理时红外吸收峰的时间依赖性与温度依赖性, 研究样品中链缠结和链结构单元的堆积等因素对红外吸收峰的影响, 进而探讨链缠结对a-PS分子运动的影响. 同时, 也通过二维相关分析来研究a-PS等温实验过程中, 链缠结的变化情况以及官能团之间的变化顺序, 推断在a-PS等温时, 与链结构单元的堆积相联系的苯环振动首先发生, 其次才是与链缠结相关联的CH₂振动发生变化, 并由此确定缠结对冷冻升华a-PS分子运动的影响.     

Study of polymer complexes by size exclusion chromatography coupled with light scattering in combination with fluorescence spectroscopy

Poly(methyl methacrylate) stereocomplexes prepared at different concentration in dilute tetrahydrofuran solutions were studied by size exclusion chromatography coupled with refractive and light scattering detectors in combination with fluorescence spectroscopy. A considerable increase in segment density due to complexation compared with free poly(methyl methacrylate) chain was only slightly affected by the polymer concentration in solution where stereocomplexes were formed. At polymer concentrations up to 3×10⁻³ g cm⁻³, an increase in non‐uniformity of polymer complex molecular weight and size and a shift to higher values of both were observed. In semidilute solutions (at c > 3×10⁻³ g cm⁻³) stereocomplexes virtually did not become heavier and larger.     

The dynamics of polymer melts as seen by neutron spin echo spectroscopy

Using the neutron spin echo spectroscopy, the internal segmental diffusion of chain molecules in polymer melts and concentrated solutions was studied. These investigations show that beyond a characteristic length d_t and after a cross over time τ_e(d_t) the segmental diffusion of the single chains is strongly impeded and deviates from the Rouse dynamics. d_t is polymer specific and depends on the temperature as well as on the polymer concentration. Within the framework of the reptation concept, where d_t is identified with the mean distance between intermolecular entanglements or with the tube diameter, the microscopically determined d_t-values agree quite well with those derived from related macroscopic measurements of the plateau modulus. A similar good agreement is also found with respect to the segmental friction coefficients obtained either from the Rouse regime of the NSE spectra or from Theological data of corresponding short chain systems, where entanglements are not yet effective.     

Dependence of Polymer Chain Entanglements on the Solution Concentration

For the viscometric determination of molecular weights of polymers, sufficiently dilute solutions have to be used so that entanglements of the polymer chain are absent. The concentration of the polymer should be such that the relative viscosity (η_r) lies in the range 1.1–1.5 [1]. Similarly, for molecular weight determination by light scattering, the suggested concentration for polymer with weight-average molecular weight ( M _w ) > 10⁵ is 0.5 wt%; for those with M _w < 10⁵, up to 1% may be used [2].

The limits of polymer concentration for such measurements are not clearly known. On dissolution, the polymer molecules adopt a more or less extended configuration whose shape depends on the structure and molecular weight of the polymer, the properties of the solvent, and the temperature

[3]. The molecules of flexible linear polymers acquire a coiled configuration due to free rotation about the C-C bonds. When a dilute solution satisfies theta conditions, the polymer molecules are free from all kinds of interaction and move freely. Then their solution properties could possibly be related to their end-to-end distance. Based on this concept, our attempt to establish the permissible limits of polymer concentration for dilute solutions of several polymers of different molecular weights is reported here.     

CRITICAL CONCENTRATIONS OF α(1→3)-D-GLUCAN FROM LENTINUS EDODES IN NaOH AQUEOUS SOLUTION

Critical concentrations of α-(1→3)-D-glucan L-FV-Ⅱ from Lentinus edodes were studied by viscometry andfluorescence probe techniques. The dependence of the reduced viscosity on concentration of the glucan in 0.5 mol/L NaOHaqueous solutions with or without urea showed two turning points corresponding to the dynamic contact concentration c_s andthe overlap concentration c~* of the polymer. The values of c_s and c~* were found to be 1×10~(-3) g cm~(-3) and 1.1×10~(-2) g cm~(-3),respectively, for L-FV-Ⅱ in 0.5 mol/L NaOH aqueous solutions. The two critical concentrations of L-FV-Ⅱ in 0.5 mol/LNaOH aqueous solutions were also found to be 1.2×10~(-3) g cm~(-3) fbr c_s and 9.2×10~(-3) g cm~(-3) for c~* from the concentrationdependence of phenanthrene fluorescence intensities. The overlap concentration c~* of L-FV-Ⅱ in 0.5 mol/L NaOH aqueoussolutions was lower than that of polystyrene with same molecular weight in benzene, owing to the fact that polysaccharidetends to undergo aggregation caused by intermolecular hydrogen bonding. A normal viscosity behavior of L-FV-Ⅱ in 0.5 mol/L urea/0.5 mol/L NaOH aqueous solutions can still be observed in an extremely low concentration range at 25℃.     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

Rheology of polymers that are initially in the disentangled state

An attempt was made to measure the effects of molecular entanglements on the rheological properties of polymer melts. Two classes of polymers were studied; glassy atactic polystyrene polymers covering a 60-fold range in molecular weight, and semicrystalline high-density polyethylene from two sources covering about a twofold range in molecular weight. The entanglements initially present were removed or greatly reduced in number by freeze drying the polystyrene polymers from dilute solutions below and above C*, the critical overlap concentration, and by slowly crystallizing the polyethylene from very dilute solutions. Since only minor rheological changes were observed with polystyrene, it would appear that the initially isolated coils interpenetrate more rapidly than is indicated by the results of Liu and Morawetz, or that the rheological behavior is rather insensitive to whether the flow obstacles are intermolecular or intramolecular. The enhancement of the viscosity and elasticity observed with polyethylene polymers indicate the importance of the crystallization step on the local melt topology of the polymer chains.     

Crystallization behavior of single or pauci chain aggregates of isotactic polystyrene

Single and pauci chain aggregates of isotactic polystyrene (i-PS) were prepared by the freeze-drying process from dilute solutions with the concentration from 1×10⁻³ to 2×10⁻⁵ g/mL. It was found by DSC measurements that the melting point of samples gradually shifted to lower temperatures with the decrease of the solution concentration used for sample preparation. As a result, the lamella thickness of bulk samples and the samples prepared by the freeze-drying process from a solution of 2×10⁻⁵ g/mL was 19.3 and 12.6 nm, respectively. At 468.3 K the half crystallization time (t _1/2) of samples freeze-dried from a solution of 1×10⁻⁴ g/mL was about 36 s, which was merely one tenth of that of the bulk sample. In addition, the growth rate of spherulite (dr/dt) of samples prepared from a solution of 2×10⁻⁵ g/mL was faster than that of the bulk sample annealed at 478.3 K. All these results should be attributed to the fewer entanglements in samples prepared by freeze-drying process from dilute solutions, and presented clear evidence for the influence of chain entanglements on the crystallization behavior of polymers. __________ Translated from Chemical Journal of Chinese Universities, 2005, 26(10) (in Chinese)     

Nuclear magnetic resonance relaxation studies of polyacrylamide solution

 The cohesive interaction among polymer chains in a polyacrylamide (PAAm)–D₂O solution has been studied by NMR relaxation. The NMR relaxation times of PAAm in the good solvent D₂O were measured at different temperatures. The results show that the solution system has a high local viscosity and that its relaxation characteristic is soft-solid-like. The temperature dependence of the relaxation behavior of the solution is obviously different from that of ordinary polymer solutions. The difference lies in the relaxation behavior of the methylene protons in the main chain of PAAm, as shown by analyzing the relaxation process with single exponential and biexponential decays. As the temperature increases, the solvation is weakened, leading polymer chains to form curling coils, thus hindering the movement of the methylene protons among the main chains. It can be expected from the existence of 80% fast-relaxing protons that there are a zhigh number of entanglements among the polymer chains in PAAm solution. The information about entanglements among the polymer chains can be deduced from the biexponential dependence of the spin–spin relaxation on the concentration of the polymer solutions. Received: 14 April 1999/Accepted in revised form: 12 October 1999     

Polystyrene degradation induced by stresses resulting from the freezing of its solutions

Solutions of polystyrene in p-xylene were frozen in liquid nitrogen. No changes in molecular weight and distribution were caused by freezing solutions for a series of narrow distribution polystyrenes with molecular weights of near 2 × 10⁶ and lower. Likewise a commercial polystyrene of M?_w = 234,000 showed no change, even after 45 cycles of freezing and thawing. However, an ultrahigh molecular weight polystyrene (M?_w = 7.3 × 10⁶) showed appreciable degradation even after a few freezing cycles of its solutions. The changes in molecular weight and distribution were analyzed by gel-permeation chromatography. The results depended very much on the choice of solvent, cooling rate, and concentration. The extent of degradation was found to depend on polymer concentration in two distinct ways. Indeed, two different degradation mechanisms have been distinguished at low and at high concentrations. The change between mechanisms took place between 1.0 and 2.5 g/l. for polystyrene in p-xylene. This appears to provide a rare measure of polymer-polymer interactions (entanglements) in dilute solutions. Degradation in the entanglement region proceeded via a random chain-scission mechanism as tested by the Scott method. In contrast, at low concentrations degradation was characterized by the formation of appreciable amounts of low molecular weight polystyrene. The presence of an antioxidant (Ionol) during freezing did not change the extent of degradation significantly.     

Kinetics of fluid spreading on viscoelastic substrates

The spontaneous spreading of non‐film‐forming fluids on the surfaces of aqueous solutions of poly(2‐acrylamido‐2‐methyl‐propanesulfonic acid) and its chemically crosslinked gels was studied. The experiments were performed in the same concentration range for the solutions and gels, far above the overlap concentration of the polymer solutions. The leading edge (R) of the spreading liquid showed a power‐law behavior with time t: R = K(t + c)^α, where α is the spreading exponent and K is the spreading prefactor. α and K were significantly different for the polymer solutions and gels. Here c was a constant that depended on the initial conditions of the spreading liquids. Depending on the polymer concentration, α of the polymer solutions varied between the upper (3/4) and lower (1/10) theoretical limits for viscose liquids and solids, respectively. This indicates that no universal scaling law exists for the spreading process on viscoelastic surfaces. On the polymer gels, which were elastic substrates, universal values of α could be observed and could be expressed as R ∝ (t + c)^0.45 and R ∝ (t + c)^0.3 for miscible and nonmiscible spreading liquids, respectively; they showed no dependence on the polymer concentration or network mesh size. This shows that on an elastic gel surface, spreading is more or less similar to that on a solid surface. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 562–572, 2005     

A steered molecular dynamics simulation on the elastic behavior of adsorbed star polymer chains

<正>Elastic behavior of 4-branched star polymer chain with different chain length N adsorbed on attractive surface is investigated using steered molecular dynamics(SMD) simulation method based on the united-atom(UA) model for branched alkanes.The simulation is realized by pulling up the chain via a linear spring with a constant velocity v = 0.005 nm/ps.At the beginning,the chain lies extensionally on adsorbed surface and suffers continuous deformations during the tensile process.Statistical parameters as mean-square radii of gyration S~2_(xy),S~2_z,shape factor δ,describing the conformational changes,sectional density den which gives the states of the chain,and average surface attractive energy U_a,average total energy U,average force f probed by the spring,which characterize the thermodynamic properties, are calculated in the stimulant process.Remarkably,distinguishing from the case in linear chains that there only exists one long plateau in the curve of f,the force plateau in our study for star chains is multiple,denoting different steps of desorption,and this agrees well with the experimental results in essence.We find during the tensile process,there are three characteristic distances Z_c,Z_t and Z_0 from the attractive surface,and these values vary with N.When Z=Z_c,the chain is stripped from the surface,but due to the form of wall-monomer interaction,the surface retains weak influence on the chain till Z = Z_c.From Z=Z_t,parameters U_a,U and f respectively reach a stable value,while the shape and the size of the chain still need adjustments after Z_t till Z_0 to reach their equilibrium states.Specifically,for short chain of N= 41,Z_t and Z_0 are incorporated.These results may help us to deepen the knowledge about the elastic behavior of adsorbed star polymer chains.     

Degradation on freezing dilute polystyrene solutions in p-xylene

Chain scission was observed during the crystallization of p-xylene in dilute polystyrene solutions. Degradation yields were determined by gel permeation chromatography, as a function of the number of freeze-and-thaw cycles, polymer concentration, and initial polymer molecular weight (M). The rate constant for chain scission K_c increases with the polymer chain length, from 0.021%/cycle at M = 110·10³ to 4.7%/cycle at M = 8.5·10⁶. Over the two decades range of investigated molecular weights, K_c follows an empirical scaling law of the form K_c ～ (M ? M_lim)^1.17578, where M_lim is a limiting molecular weight ? 29,000 g. mol^?1 below which no degradation could be induced. Some propensity for midchain scission was detected, although this tendency was much weaker in comparison to flow-induced degradation. A chain scission model based on crack propagation failed to reproduce the experimental results. To explain the observed dependence of K_c with the square of the radius of gyration, an interfacial stress transmission mechanism between the crystallization fronts and the polymer coil has been proposed. © 1994 John Wiley & Sons, Inc.     

Interaction between Na+ and polymer in aqueous solution of sodium salts of poly(2-hydroxyethyl methacrylate-co-methacrylic acid) studied by 23Na-NMR

The interaction between Na⁺ and polymer was studied by ²³Na-NMR for the aqueous solution of P(HEMA-co-MAANa), sodium salt of poly(2-hydroxyethyl methacrylate-co-methacrylic acid), as a function of the polymer concentration, charge density of the polymer chain, and temperature. The NMR line width of ²³Na-NMR in 1% (w/v) aqueous solution of the P(HEMA-co-MAANa) narrowed with increasing temperature due to the rapid exchange of Na⁺ between free and polymer-bound states with a rate of exchange exceeding the quadrupolar relaxation rate in the latter state. At high concentrations of the polymer above 1.0% (w/v) at 298 K, the ²³Na-NMR relaxation fits for a single Lorentzian due to the rapid exchange between two Na⁺ states. However, it follows a biexponential decay of magnetization in dilute solutions of polymer. The biexponential decay character of relaxation increased with the increase of the fraction of the MAANa monomer unit on the polymer chain. This feature of ²³Na-NMR relaxation was used to deduce the correlation time (τ_c), the degree of binding (p_B), and the quadrupole coupling constants (X) of the polymer-bound counterion. The χ and τ_c values show that the mobilities of the polymer chain are correlated with the motion of Na⁺ in aqueous solution of the polymer and there is a small degree of the specific binding between COO^? and Na⁺. No evidence in support of the intramolecular conformational change by the charge density variation in P(HEMA-co-MAANa) was obtained. © 1993 John Wiley & Sons, Inc.     

Steady-state properties and dynamic behavior of polymer chains in dilute solution under elongational flow

The behavior of polymer chains in dilute solution under a steady, homogeneous elongational flow has been studied employing Brownian dynamics simulation. We first consider the dependence of polymer properties in steady state on the elongational rate, ϵ. When this rate exceeds some critical value, ϵ_c, the properties show a dramatic change from the values typical of the coil state to those of a stretched conformation. We describe the dependence of ϵ_c on chain length for different polymer/solvent conditions. Following the trajectories of individual molecules, we have characterized dynamic aspects of the coil-stretch transition. Each chain suffer the transition after some time, t_trans, has elapsed after the flow start-up. The values of t_trans vary remarkably from one molecule to another, and we have characterized the statistical distribution of this quantity. We also determine the kinetics of the coil-to-stretch process, which seems to follow a first-order kinetics after some induction time. The dependence of the statistical and kinetic parameters on chain length and elongational rate has been determined.