Elastic behavior of concentrated solutions of acrylonitrile copolymers

The elastic behavior of concentrated solution of acrylonitrile copolymer was investigated by the capillary end correction method. The results were as follows. (1) The shear stress is proportional to recoverable shear strain in accordance with Hooke's law below critical concentration; above a critical concentration, however, the shear modulus depends on shear stress. (2) The log–log plots of zero shear modulus against polymer concentration and molecular weight fall on two straight lines with different slopes. The intersection of lines is considered to be the onset of elastically deformable entanglement network. We denote this inflection point as (C_c)_e or (M_c)_e. (3) The log–log plot of viscosity against polymer concentration does not show a change of slope at the critical concentration (C_c)_e. (4) By the application of the kinetic theory of rubberlike elasticity to the pseudo-network structure of concentrated polymer solution, in the range of C_c < C < (C_c)_e or M_c < M < (M_c)_e, the number of chain entanglement per molecule is kept one; moreover, in the range of C > (C_c)_e, or M > (M_c)_e, the number of chain entanglement increases to three.     

Evaluation of an onset of electrospun beadless poly(ethylene oxide) nanofibres

To evaluate the lowest polymer concentration within a solvent from which there appears beadless nanofibres during the process of electrospinning, is rather complicated. A widely used method is based on a determination of so called entanglement concentration c_e and the onsets of beadless nanofibres are characterized by multipliers of c_e subjected to used materials. However, a determination of c_e as an intersection point of two linear segments (in log–log coordinates specific viscosity vs. concentration) in a semi-dilute region is not applicable for all materials as for instance a solution of poly(ethylene oxide) (PEO) in water does not exhibit 'classical' three linear segments within the dilute and semi-dilute regions determining overlap and entanglement concentrations. For such cases a new approach for the evaluation of an initial concentration from which beadless nanofibres are produced is proposed. This method does not use the terms overlap and entanglement concentrations. The procedure is demonstrated using four PEO solutions differing in molecular weight. The relationship expressing initial concentration in dependence on PEO molecular weight containing no adjustable parameters is proposed.     

An empirical model relating the molecular weight distribution of high-density polyethylene to the shear dependence of the steady shear melt viscosity

An empirical model has been developed to relate molecular weight distribution to the shear dependence of the steady shear viscosity in high-density polyethylene melts. It uses a molecular weight, M_c, which partitions molecular weights into two classes; those below M_c contribute to the viscosity as they do at zero shear, and those above M_c contribute to the viscosity as though they were of molecular weight M_c at zero shear. Each individual molecular weight species contributes on the basis of its weight fraction. M_c is proposed to be a unique function of the shear rate. Using this method of treating the molecular weight distribution, and the zero shear relation for relating η0 to molecular weight, the calculated steady shear viscosities at various shear rates for polyethylene samples of widely varying polydispersities agree well with experimental results. The model makes no judgment on the existence or importance of entanglements in non-Newtonian behavior since it has no specific parameters involving an entanglement concept. Use of the model suggests that for the samples studied, only the upper portion of the molecular weight distribution contributes toward the experimentally observed decrease of steady shear viscosity with shear rate for shear rates of up to 10,000 sec^?1. The lower molecular weight species are assumed to behave in a Newtonian manner.     

Studies on hyperbranched polyurethane by multidetector size exclusion chromatography

Hyperbranched polyurethane (HP) and its linear analog (LPU) were studied by size exclusion chromatography (SEC), utilizing a combination of refractive index (RI), right angle light scattering (RALLS), and differential viscosity (DV) detectors. The relationships between retention volume (V_e), intrinsic viscosity (η), radius of gyration (R_g), and the molecular structure were investigated. It was shown that the hyperbranched polyurethane had lower V_e, η, and R_g than its linear analog when they had the same molecular weight. The branching parameter g and g′ were calculated. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2445–2450, 2002     

Effect of dispersity on the Tll (>Tg) transition in polystyrene

The presence of a high temperature (>T_g) relaxation in amorphous polystyrene has been investigated further. In the previous work,¹ the techniques of differential thermal analysis (DTA) and torsional braid analysis (TBA) were employed to study polystyrene as a function of “monodisperse” molecular weight. The occurrence of the T_ll transition appeared to be associated with the attainment of a critical viscosity level with also corresponded with a free volume level. An entanglement network developed at a critical value of molecular weight, M_c, giving a break in the T_ll-versus-M plots. The present work deals with the influence of dispersity on the T_ll transition, below and above M_c. A series of binary blends of “monodisperse” anionically polymerized polystyrenes with systematic changes in M?_n and heterogeneity index (M?_w/M?_n) was tested by TBA. The results show that when both components have molecular weights below M_c, single and average values of T_g and T_ll are observed which are linearly related to M?_n^?1, as predicted by free volume arguments. Although a single T_g is observed when one component has a molecular weight above and the other has a molecular weight below M_c, the components appear to undergo the T_ll relaxation independently. The results indicate that both the glass transition and the T_ll transition are basically governed by the same type of molecular motion but at different length ranges.     

Preparation of long‐chain branched poly(ethylene terephthalate): Molecular entanglement structure and toughening mechanism

Poly(ethylene terephthalate) (PET) was long‐chain branched (LCB) by ring‐opening reaction with both pyromellitic dianhydride and tetrahydrophthalic acid diglycidyl ester as chain extenders through reactive melt processing. It was found that with the increase of chain extenders dosage, the intrinsic viscosity of PET increased and melt index decreased greatly, while both the tensile strength and impact strength of PET were remarkably improved. The elastic modulus (G′) and viscous modulus (G″) were enhanced by chain branching. Compared with PET, the complex viscosities of LCB‐PET were much higher at full frequency range, and obvious shear thinning was presented. The Cole–Cole curve deviated from the semicircular shape and the curve end was inclined to upward in high viscosity region, indicating the formation of the multiple hierarchical structures. The molecular weight of the branch (M_B) was much greater than critical entanglement molecular weight (M _e), which essentially confirmed the existence of LCB structure and fairly strong molecular entanglement in the LCB‐PET molecular chain. When subjected to external force, the entanglement point, acting as physical crosslinking point between the molecules, was in favor of increasing the molecular interaction, reducing the molecular slippage, and bearing a large deformation. POLYM. ENG. SCI., 59:1190–1198 2019. © 2019 Society of Plastics Engineers     

Predicting chain conformation and entanglement of polymers from chemical structure

The characteristic ratio C_∞ and the entanglement molecular weight M_e are two key molecular parameters that control melt viscoelasticity, solid mechanical (brittle/ductile) behavior, and adhesion of polymers. We show that the characteristic ratio C_∞ and the entanglement molecular weight M_e can be predicted from chemical structure by group additivity with uncertainties usually less than ～ 7% for C_∞ and ～ 15% for M_e, comparable with the accuracies of experimental values.     

Rheological properties of concentrated polymer solution: Polybutadiene in good and θ solvents

The zero shear viscosity, η° of three polybutadiene samples having different molecular weights over a wide range of concentration (1.0–35.0% polymer) in good and θ solvents has been studied. Superposition of viscosity data has been made to give a single composite curve for each solvent by shifting them vertically by a factor (M°/M)^3.4, where M° represents the molecular weight of the reference sample. The shift factor is found to be proportional to M^3.4 in the region of higher concentration, which indicates that the 3.4-power law is valid for the data of polybutadiene. The double-logarithmic plots of relative viscosity η°_r as a function of c⁵M^3.4 yielded a single composite curve approximating a straight line with slope of unity at the higher values of the variables. The results indicate that over a considerable range of the variables (molecular weight and concentration) at a constant temperature, the relative viscosity is a single function of c⁵M^3.4. The results for double-logarithmic plots of zero shear specific viscosity η°_csp as a function of concentration confirmed those observed in polycholoroprene samples studied earlier that the η0_sp values in θ solvents at higher concentration region are found to be higher than those found in good solvents, whereas in the moderately concentrated region the values are just opposite in θ and good solvents. The viscosity crossover in θ solvents is not as sharp as is found in case of polychloroprene samples and that crossover, too, has taken place in the range of concentration of 11.7–31.6% polymer, which is comparatively higher than that of polychloroprene samples (6.06–21.0% polymer). The results indicate some relation between viscosity crossover and polymer polarity, supporting the idea of enhanced intermolecular association in poor solvents. To correlatethe viscosity data obtained in good and poor solvents, two methods, one given by Graessley and the other given by Dreval and coworkers involving the correlating variable c[η], were considered. The plots of relative viscosity η°, versus the correlating variable c[η] in benzene (good solvent) yielded one curve, but in the case of θ solvents (dioxane and isobutyl acetate), the same plots yielded three separate curves instead of a single curve, which is rather unusual. The appropriate correction on the correlating variable for chain contraction in the concentrated region in a good solvent moved the data to a common curve, especially in lower concentration region, but at the higher concentration region a slight overestimation of data seems to have been effected. On the other hand, the plots of log η as a function of correlating variable c[η] yielded a single curve for three samples in the good solvent benzene, but in poor solvents (diozane and isobutyl acetate) the same plots yielded three separate curves for three samples instead of a single curve, the reason for which is not known at present. However, the normalization of the correlating variable c[η] with Martin constant K_M reduced all experimental data of the polymer samples to a common curve. The correlation of the viscosity data by either of the two methods seems to be possible in the case of the nonpolar flexible polymer, polybutadiene.     

Effect of network morphology on adhesive performance in emulsion blends of acrylic pressure sensitive adhesives

High-gel containing latices and gel-free latex were blended at various weight ratios. The high-gel containing latices was made of poly(2-ethyl hexylacrylate-stat-acrylic acid) and the gel-free latex was made of poly(2-ethyl hexylacrylate-stat-acrylic acid-stat-isobutoxymethyl acrylamide) using semicontinuous emulsion polymerization. Films were cast at room temperature and dried at 121°C for 10 min. Adhesive performance was evaluated in terms of loop tack, peel, and shear holding power. It was found that interlinking the microgels by the linear polymer due to the isobutoxymethyl acrylamide-acrylic acid reaction in the film when heated gave synergistic effects in increasing shear. This interlinking could take place only if the molecular weight between crosslinks (M_c) of the microgels was greater than the entanglement molecular weight of the linear polymer (M_e), and if the weight average molecular weight of the linear polymer (M_w) was greater than 2 × M_e. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2109–2117, 2001     

A model for the zero shear viscosity

An empirical equation for the number of entanglements per molecule has been proposed, which applies over all the molecular weight range. On this ground a simple equation for the zero shear viscosity of monodisperse polymer melts, η₀, has been worked out that appears able to properly take into account the sharp transition of viscosity between the monomeric and the entanglement regimes. The molecular parameters appearing in the new viscosity equation are: the monomeric molecular weight m₀, the monomeric friction factor ζ₀, the molecular weight M, the average molecular weight between entanglements M_e, and the entanglement friction factor ζ_e^3.4. This last parameter was evaluated for a number of monodisperse polymers.     

Viscosity‐molecular weight relationship for cellulose solutions in either NMMO monohydrate or cuen

The intrinsic viscosities, [η], of nine cellulose samples, with molar masses from 50 × 10³ to 1 390 × 10³ were determined in the solvents NMMO*H₂O (N‐methyl morpholin N‐oxide hydrate) at 80°C and in cuen (copper II‐ethlenediamine) at 25°C. The evaluation of these results with respect to the Kuhn–Mark–Houwink relations shows that the data for NMMO*H₂O fall on the usual straight line in the double logarithmic plots only for M ≤ 158 10³; the corresponding [η]/M relation reads log ([η]/mL g⁻¹) = –1.465 + 0.735 log M. Beyond that molar mass [η] remains almost constant up to M ≈ 10⁶ and increases again thereafter. In contrast to NMMO*H₂O the cellulose solutions in cuen behave normal and the Kuhn–Mark–Houwink relation reads log ([η]/mL g⁻¹) = −1.185 + 0.735 log M. Possible reasons for the dissimilarities of the behavior of cellulose in these two solvents are being discussed. The comparison of three different methods for the determination of [η] from viscosity measurements at different polymer concentrations, c, demonstrates the advantages of plotting the natural logarithm of the relative viscosities as a function of c. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Solution properties of hydrophobically modified polyelectrolytes synthesized via solution and micellar copolymerization

Hydrophobically modified polyelectrolytes (HMPEs) were synthesized using sodium 2‐acrylamido‐2‐methyl‐propanesulfonate and N‐n‐dodecylacrylamide as monomers with the same feeding ratio via micellar and solution copolymerization. The effects of hydrophobic association and electrostatic interaction on the solution properties of the HMPEs were studied. Compared with HMPE obtained via solution copolymerization (s‐PAD), the hydrophobic interaction of HMPE obtained via micellar copolymerization (m‐PAD) is more obvious due to the micro‐blocky distribution of hydrophobic groups. The viscosity properties of m‐PAD in deionized water or brine follow well the scaling theory of polyelectrolytes. However, for s‐PAD, the concentration where zero‐shear viscosity (η₀) and solvent viscosity (η_s) follow η₀ ≈ 2η_s is more likely to be critical entanglement concentration (c_e) rather than critical overlap concentration (c*). It is suggested that modifying of the transition region from c* to c_e is valid and reasonable for s‐PAD. It is believed that the different solution properties of s‐PAD and m‐PAD should be attributed to the distributions of hydrophobic groups in the chains. Copyright © 2010 Society of Chemical Industry     

Dynamics of polymeric fluids in transient-state theory

Transient-state theory recently proposed has enabled us to describe the chain length dependence of viscosity of polymeric melts from the Rouse to entangling regimes by the single equation which also takes the factor of temperature into account. On the basis of this theory, this contribution attempts to treat the effect of temperature on viscosity and provides a molecular explanation to the coefficients of M-dependence in the WLF equation, obtaining the activation energy ΔE₀ and elastic interaction parameter a for example selected. A reinterpretation from a molecular viewpoint directly leads to the common observation of the M-dependence of the glass transition temperature. The mathematical expressions are developed for diffusion coefficient D_s, showing the scaling behavior for special cases as M⁻¹ and M^−2.4 below and above the entanglement coupling mass M_e, respectively. Any deviation from the scaling can be accounted by the quantum confinement effect a. The terminal relaxation time τ_D behaves in the same way as η above the onset of entanglement. It is found that both D_s and τ_D scale on temperature in the way analogous to the WLF correlation. In addition, an expression for Young's modulus is presented by a molecular deduction. The predictions are in consistence with existing experimental data via the adjustment of a which can correlate more findings difficult to be accommodated into conventional theories. © 1996 John Wiley & Sons, Inc.     

Characterization of polymer molecular weight distribution by transient viscoelasticity: Polytetrafluoroethylenes

The relationship between the relaxation time spectrum H(τ) in the terminal zone and the volume-fraction differential molecular-weight-distribution function P(M) is derived by considering binary chain contacts for stress transmission, where β and λ are constants for a given chemical type. This is used to determine the molecular-weight-distribution curves from the stress relaxation modulus spectrum (above the crystal melting point) at 370°C for a number of commercial and experimental poly(tetrafluoroethylenes) (PTFEs). It is found that PTFEs typically have bimodal molecular-weight distributions. The lower-molecular-weight peak conforms essentially to the “most-probable” distribution, and the higher-molecular-weight peak to the binary coupling distribution. The entanglement molecular weight M_e is 5490, and the number of main-chain atoms between entanglement points is 110, consistent with a flexible chain. The zero-shear melt viscosity at 370°C is η₀ = 1.79 × 10^?13 M_w^2.94±0.13, where η₀ is in Pa.s and M_w/M_e = 2,000 to 12,000. The monomeric friction coefficient is also determined.     

Investigation of the Tu(>Tg) relaxation in homopolymers and block copolymers of styrene by torsional braid analysis

Investigation of the T_u (>T_g) relaxation in amorphous polymers of styrene by the technique of torsional braid analysis is reviewed. For the most part the relaxation behaves like the glass transition (T_g) in its dependence on molecular weight, on average molecular weight in binary polystyrene blends, and on composition in a polystyrene homogeneously plasticized throughout the range of composition. Diblock and triblock copolymers also display a T > T_g relaxation above the T_g, of the polystyrene phase. Two results in particular suggest that the T_u relaxation is molecularly based. (1) The T_u temperature is determined by the number average molecular weight for binary blends of polystyrene when both components have molecular weights below M_c. (the critical molecular weight for chain entanglements). (2) Homopolymers, and diblock and triblock copolymers of styrene, have a T > T_g relaxation at approximately the same temperature when the molecular weight of the styrene block is equal to that of the homopolymer.     

Blends,hydrogen bonds,and orientation: Understanding the role of interactions

A review of past and present studies on orientation, rheology, and FTIR investigations on a hydrogen bond–forming polymer, poly(vinyl phenol) (PVPh), and its blends with polyethylene oxide (PEO), poly(methyl methacrylate) (PMMA), and poly(vinyl methyl ether) (PVME) is presented. Orientation is analyzed on the basis of deformation‐induced orientation and relaxation. For deformation, it is proposed from recent molecular modeling studies that orientation is similar for flexible backbone polymers of the types studied. To investigate relaxation, dynamical rheology analysis was performed previously on PVPh/PEO blends and global molecular weight between entanglement, M_e, and chain friction ζ were estimated. M_e remained close to that of the polymer forming the dominant network, a discontinuity being observed near 50 mole percent. Friction coefficient exhibited a maximum near that of the orientation function of this system. Near‐infrared measurements also showed a maximum in the number of interchain hydrogen bonds at this concentration, although broader than that of orientation or of the friction coefficient. For strongly interacting blends, it is proposed that a break in orientation behavior would be associated with the dominant network present, and therefore to M_e, whereas ζ will dictate whether orientation decreases or increases in a given network domain.     

Dielectric study on dynamics and conformation of poly(d,l-lactic acid) in dilute and semi-dilute solutions

Fractionated samples of d,l-poly(lactic acid) (PLA) were prepared and the dielectric normal mode relaxation was studied for dilute and semi-dilute solutions of the PLA in a good solvent benzene. Results indicate that in the dilute regime the normal mode relaxation time is proportional to [η]M_w in agreement with the Rouse-Zimm theory, where [η] and M_w denote the intrinsic viscosity and weight average molecular weight, respectively. The dielectric relaxation strength which is proportional to the mean square end-to-end distance 〈r²〉 increases with increasing M_w with the power of 2ν, where ν is the excluded volume parameter determined from [η]. The relaxation time in the semi-dilute regime increases with increasing concentration C due to increases of the entanglement density and the friction coefficient. The relaxation time corrected to the iso-friction state agrees approximately with the dynamic scaling theories. The relaxation strength decreases with increasing concentration indicating that 〈r²〉 decreases on account of the screening of the excluded volume effect. The concentration dependence of 〈r²〉 agrees approximately with the scaling theory proposed by Daoud and Jannink.     

Some rheological properties of molten polytetrafluoroethylene

Measurements of melt viscosity on samples of polytetrafluoroethylene of different molecular weight were carried out at 360°C by means of tensile creep tests in the linear viscoelasticity range. The apparent activation energy for viscous flow in the range between 330° and 380°C was estimated to be 20 kcal/mole. A value of about 7,500 was also determined for the average molecular weight between entanglement points (M_e), from the equilibrium compliance (D_e). Melt viscosity data were compared with zero strength time (ZST) values and a linear correlation was found on a bilogarithmic scale. The dependence of ZST on the applied stress and temperature was also studied and the results are discussed on the basis of Bueche's theory on the creep at rupture above the glass transition temperature.     

Variation of periodic crazing based on polymer blends of an ultra‐high and a low molecular weight poly(methyl methacrylate)

Periodic crazes are caused in a polymer film by the unique mechanical method using bending. Generation of a craze depends on entanglements of the molecular chains of a polymer. Therefore, control of composite morphology of periodic crazes was attempted by varying the entanglements of molecular chains. An effective entanglement network became sparse by polymer blends of an ultra‐high molecular weight polymethylmethacrylate (PMMA) and a low molecular weight PMMA. Consequently, the composite morphology of periodic crazes caused in the blend film varied. In other words, the periodic craze can be used for the evaluation of the effective entanglements. In addition, it was figured out that PMMA of which the number‐average molecular weight (M_n) is less than twice of the effective entanglement molecular weight (M_e^*) works as a plasticizer in the blend film. And also, it was revealed that the mechanical properties of the blend film decreased dramatically at M_n ≒ 6M_e^*. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44332.     

The dispersion of magnetic nanorods in poly(2‐vinylpyridine)

The dispersion of magnetic nanorods in poly(2‐vinylpyridine) (PVP) as a function of rod length, particle loading and molecular weight of PVP was investigated. The nanorods were organized into small spherical clusters at low particle loading. Further increasing the particle concentration caused an increase in the size of the aggregates. Additionally, the internal structure of the nanorods developed into a raft‐like structure, forming rectangular clusters. The incorporation of longer nanorods in the PVP amplified the magnetic interaction energy, which created conditions to induce extensive aggregation. The entanglement of the polymer also played an important role in the arrangement of the nanorods. This behavior could be categorized into two regimes, M_PVP > M_e and M_PVP < M_e, where M_PVP and M_e are the number‐average molecular weight and entanglement molecular weight of PVP, respectively: for M_PVP > M_e, PVP formed entanglements that prevented nanorods from extensive aggregation; for M_PVP < M_e, PVP could not form entanglements, and nanorods could move freely in the PVP, and thus significant rod aggregation occurred. Simple calculations to assess the contribution of the magnetic interaction, the van der Waals interaction and the free energy of mixing of the system to the arrangement of magnetic nanorods in the homopolymer are discussed. © 2013 Society of Chemical Industry