Concentration dependence of the viscoelastic properties of polystyrene-tricresyl phosphate solutions

Based on creep and creep-recovery measurements, the viscoelastic functions [J(t), J_r(t), J′(ω), J″(ω), G′(ω), G″(ω), and L(lnτ)] are presented for solutions of a narrow molecular-weight-distribution polystyrene in tri-m-tolyl phosphate in the concentration range of 1% to 100% polymer. For concentrations of 25% polymer and above, two maxima are exhibited by the retardation spectrum, L(lnτ). In the neighborhood of each of the maxima the retardation spectra of the more concentrated solutions can be superimposed by translations along both the logL and logτ axes. Reflecting the increasing width of the rubbery plateau with increasing polymer concentration, the dependence of the concentration time-scale shift factors is greater for the terminal region of response. The response of the solvent is seen at the lower concentrations and it is a less sensitive function of the concentration than that of the polystyrene. This behavior is associated with the previously reported observation of two glass-transition temperatures in the middle concentration range. For the higher concentrations, both the steady-state and rubbery-plateau compliances are inversely proportional to the square of the concentration.     

Dynamics of Polymer Networks with Strong Differences in the Viscous Characteristics of their Crosslinks and Strands

We study theoretically the relaxation properties of polymer networks, whose monomers and junction sites have different friction parameters (ζ and ζ_jun, respectively). For this, we focus on topologically regular cubic networks built from “bead‐and‐spring” Rouse chains. Setting σ = ζ_jun/ζ, we determine analytically both the eigenvalues and the eigenmodes of the model for arbitrary values of σ. This allows us to extend previous approaches (Macromolecules 2000 , 33, 6578) which were restricted by the condition σ = 3. We compute the frequency dependent storage, G′(ω), and loss, G″(ω), moduli (which for σ ≫ 3 or σ ≪ 3 display two plateaus and two maxima, respectively) and also the mean‐square displacements of the network junctions and of the beads; these turn out to obey power laws, whose validity ranges depend on σ.

     

Relaxation of Copolymeric Dendrimers Built from Alternating Monomers

Summary: In this study we extend our previous work concerning the Rouse dynamics of linear alternating copolymers (Macromolecules 2003 , 36, 486) to tree‐like structures and focus on copolymeric dendrimers built from monomers of two kinds A and B; as before, we let the monomers differ in their interaction with the solvent. In the framework of generalized Gaussian structures (GGS), we consider alternating arrangements of monomers over the dendritic structures. We develop a semi‐analytical method to determine for such structures (of arbitrary functionality, f, and number of generations, g), the eigenfrequencies (relaxation times). The method allows us to compute readily the storage, [G′(ω)] and the loss, [G″(ω)] moduli. These quantities show a multitude of features which mainly depend on the difference in the mobilities, or, equivalently, in the friction coefficients ζ_A and ζ_B of the A‐ and B‐beads. These features range from the presence of large plateau‐type regions in [G′(ω)] to the appearance of double‐peaks in [G″(ω)]. In contrast to linear alternating copolymers, the behavior of the dynamic moduli of copolymeric systems with dendritic topology can shed light into their composition, i.e. into the relative numbers of A‐ and B‐beads. We discuss these aspects in view of their experimental relevance.

A system under study: a dendrimer of third generation (g = 3) with functionality f = 3, composed of alternating beads.     

Temporal scaling analysis: Linear and crosslinked polymers

An ansatz that predicts the frequency dependence of viscoelastic moduli of polymer solutions was tested against literature data on linear polymers and polymer microgels. Excellent agreement was uniformly found between the ansatz and the experiment. The ansatz does not give a simple reduction scheme or a master plot; it systematizes large amounts of data to a few parameters. The dependence of these parameters on polymer concentration and solvent quality was examined. The ansatz satisfies Kronig–Kramer's relations; transformations of G′(ω) and G″(ω) for a given system lead to the same G(t). © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 375–386, 2002; DOI 10.1002/polb.10099     

Effect of branching and molecular weight on the viscoelastic properties of poly(butyl acrylate)

A series of poly(butyl acrylate) samples were prepared by emulsion polymerization with a range of molecular weights and degrees of chain branching. Characterization was performed with NMR (giving the fraction of branching, ranging from approximately 0 to 7%), gel permeation chromatography, viscometry, and determination of the gel fraction. The dynamic mechanical response, that is, the frequency dependence of the storage and loss moduli G′(ω) and G″(ω) was measured from 0.02 to 200 Hz. The occurrence of a significant insoluble fraction in the sample meant that full characterization of the molecular weight distribution was not possible, and so an unambiguous separation of the dependencies of the mechanical response on the degree of long‐chain branching (LCB) and short‐chain branching (SCB) and the molecular weight could not be made; however, trends dependent on the molecular weight alone were insufficient to model the results. At high frequencies, all trends in G′(ω) and G″(ω) could be ascribed to molecular weight dependencies; at low frequencies, the effects of both the molecular weight and total degree of branching could be inferred, with more highly branched samples showing lower storage and loss moduli. Although the relative amounts of SCB and LCB could not be determined, no dynamic features attributable to LCB were observed. The low‐frequency trends could be semiquantitatively fitted with reptation and retraction theory if it was assumed that an increased degree of SCB led to an increased tube size. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3335–3349, 2002     

Rheological technique for determining the order–disorder transition of block copolymers

A rheological technique is proposed for determining the thermally induced order–disorder transition of block copolymers. In the present investigation, a cone-and-plate rheometer was used to measure dynamic storage and loss moduli, G′(ω) and G″(ω), as a function of angular frequency ω of a commercial grade polystyrene-block-polyisoprene-block-polystyrene (SIS) tri-block copolymer (KRATON D-1107, Shell Development Company) in the temperature range from 140 to 240°C. For comparison purposes, dynamic viscoelastic properties of a commercial grade low-density polyethylene (LDPE) were also determined in the temperature range from 160 to 238°C. We have found that log G′ versus log G″ plots for the LDPE show no temperature dependence, whereas log G′ versus log G″ plots for the SIS block copolymer do show systematic temperature dependence in the temperature range 140–230°C. This observation leads us to conclude that the order–disorder transition of the SIS block copolymer takes place gradually as the temperature is raised from 140 to 230°C. This conclusion is in good agreement with that drawn from the study of Roe (Ref. 33), who employed the same block copolymer using small-angle x-ray scattering. It is not possible to reach such a conclusion using log G′(ω) versus log ω, log G″(ω) versus log ω, or log η′(ω) versus log ω plots in which η′ is the dynamic viscosity. We have demonstrated further that the use of frequency-temperature superposition is inappropriate for investigating the rheological behavior of block copolymer in the temperature range over which a thermally induced transition from an ordered structure to a disordered homogeneous phase occurs. We therefore suggest that when using information on dynamic viscoelastic properties, log G′ versus log G″ plots be used for determining the thermally induced order–disorder transition of block copolymers.     

Effect of the structure of latex particles on adhesion. Part II: Analogy between peel adhesion and rheological properties of acrylic copolymers

This article, the second part of this series, concerns the development of an analogy between the peel behavior of pressure-sensitive adhesives and the dynamic mechanical properties of the corresponding copolymers. The adhesive copolymers used were synthesized by emulsion polymerization processes. Their physical and dynamic mechanical properties were characterized and presented in Part I of this series. In this study, an analogy was built up between the force in a peel test as a function of peel velocity, F_p(v_p), and the loss modulus of the adhesive as a function of the angular frequency in a dynamic mechanical experiment, G″(ω). This was done by superimposing the curves of F_p versus v_p and those of G″ versus ωβ₀/β, where β₀/β is a shift factor with β being a parameter in the Kaelble theory and β₀ being some reference value of the Kaelble parameter. When the curves of F_p ～ v_p and those of G″ ～ ωβ₀ were plotted together, they followed the same trend of variation. This analogy between G″(ωβ₀/β) and F_p(v_p) was further confirmed by the fact that the apparent activation energies of the primary glass transition for G″(ω) and F_p(v_p) are virtually the same, suggesting that the analogy between G″(ω) and F_p(v_p) is dictated by the glass transition. The existence of the above-mentioned analogy between G″(ω) and F_p(v_p) shows that the performance of an adhesive can be evaluated or predicted from the dynamical loss modulus of the corresponding (co)polymer. ©1995 John Wiley & Sons, Inc.     

Solvent Vapor‐Induced Nanowire Formation in Poly(3‐hexylthiophene) Thin Films

Summary: Nanowire lengths and length‐to‐width aspect ratios in regioregular poly(3‐hexylthiophene) (P3HT) were simply controlled through changes in the solvent vapor pressure during solidification. It is demonstrated that the nanowires grew by rod‐to‐rod association, in which the molecular long axis of the P3HT chains appeared to be well‐oriented parallel to the silicon substrate (Si/SiO_x). The formation of the nanowires took place by one dimensional self‐assembly, governed by π‐π stacking of the P3HT units.

TEM high contrast images showing P3HT nanowires fabricated by spin‐coating under a solvent vapor pressure.     

Gelation Studies on a Radical Chain Cross‐Linking Copolymerization Process: Comparison of the Critical Exponents Obtained by Dynamic Light Scattering and Rheology

Summary: The sol–gel transition of a radical chain cross‐linking copolymerization system [N‐vinylcaprolactam/2‐hydroxylethyl methacrylate/allyl methacrylate] has been studied using in situ time‐resolved dynamic light scattering (DLS) and in situ rheology. A critical dynamic behavior was observed near the sol–gel transition, which was characterized by the presence of a power‐law spectra over three decades in the time–intensity correlation function g₂(t) − 1 ∼ t^−μ and over two decades in the oscillatory shear experiment G′(ω) ∼ G″(ω) ∼ ωⁿ. A comparison of the obtained critical exponents μ ≈ 0.62 and n ≈ 0.75 was made. The theory predicts a relationship between these exponents, but up to now no experimental comparison has been done. The experimental results favor the percolation model, with a fractal dimension d_f of the gel clusters of 1.67.

Double‐logarithmic plot of time–intensity correlation functions g₂(t) − 1 versus the delay time t.     

Comparison of Critical Exponents Determined by Rheology and Dynamic Light Scattering on Irreversible and Reversible Gelling Systems

Summary: The sol-gel transition of a radical chain cross-linking copoly-merization system [N-vinylcaprolactam/2-hydroxylethyl methacrylate/allyl-methacrylate] and various thermoreversible gelling systems (mixtures made of xanthan gum and locust bean gum as well as gelatin) have been studied using in-situ time-resolved dynamic light scattering (DLS) and in-situ rheology. A critical dynamical behavior was observed near the sol-gel transition, which is characterized by the presence of a power-law spectra in the time-intensity correlation function g₂(t)−1 ∝ t^−µ and in the low-amplitude oscillatory shear experiment G′(ω) ∝ G″(ω) ∝ ωⁿ. A comparison of the obtained critical dynamical exponents µ and n were made according to the theory by Doi and Onuki. This theory predicts a relation between these exponents, but up to now no detailed experimental comparison was done in the past. It was found that for all investigated systems n > µ.     

Influences of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile solutions around the sol-gel threshold

Viscoelastic experiments were performed to study the influence of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile (PAN) solutions around the sol-gel threshold. The dynamic critical parameters around the sol-gel threshold were determined using dynamic rheometer. The sol-gel transition takes place at a critical gel temperature at which the scaling law of G′(ω) ∼ G″(ω) ∝ ωⁿ holds, allowing an accurate determination of the critical gel temperature by means of the frequency independence of the loss tangent. Although the gel points of PAN solutions increase with increasing H₂O content, the results show that the scaling exponent n at the gel point is found to be universal for all ternary PAN solutions, which is independent of temperature and H₂O content, indicating the similarity of the fractal structure in the critical PAN gels. The gelation of ternary PAN solutions induced by adding a nonsolvent and by decreasing the temperature is demonstrated to be a thermoreversible process, which implies that the PAN gels are physical gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2637–2643, 2008     

Effect of endgroup modification on dynamic viscoelastic relaxation and motion of hyperbranched poly(ether ketone)s

Fluoro‐terminated hyperbranched poly(ether ketone) (FHPEK) was synthesized and its end groups were modified with alkyl compounds of different chain lengths, i.e., hexyloxy (C6), dodecyloxy (C12), and octadecyloxy, (C18), to produce alkyl‐modified HPEKs (HPEK‐C6, HPEK‐C12, and HPEK‐C18, respectively). Master curves were constructed by using the time‐temperature superposition principle. The horizontal shift factors, a_T, used for the construction of the master curves were fit using the William‐Landel‐Ferry (WLF) equation. From the fitting parameters, the apparent activation energy, E_a, was estimated. With increasing alkyl chain length, the E_a values were found to decrease in the order FHPEK > HPEK‐C6 > HPEK‐C12, and then increase for HPEK‐C18. The average relaxation time, τ_HN, was determined by fitting of the dynamic moduli G′(ω) and G″(ω) to the empirical Havriliak‐Negami equation. Similarly, the τ_HN values decreased in the order of FHPEK > HPEK‐C6 > HPEK‐C12, and then increased for HPEK‐C18. This indicates that the endgroup modification with short alkyl chains (C6, C12) increased the molecular mobility due to the internal plasticization effect of these alkyl chains. Modification with the longer alkyl chain (C18) retarded the molecular motion through an antiplasticization effect caused by summation of nonpolar hydrophobic interactions between long hydrocarbon chains. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2079–2089, 2008     

Gelation Studies: Comparison of the Critical Exponents Obtained by Dynamic Light Scattering and Rheology, 2

Summary: The sol–gel transition of two thermoreversible gelling mixtures made of xanthan gum and locust‐bean gum has been studied by using in situ, time‐resolved dynamic light scattering (DLS) and in situ rheology. A critical dynamical behavior was observed near the sol–gel transition, which was characterized by the presence of power‐law spectra over three and four decades in the time‐intensity correlation function g₂(t) − 1 ∼ t^−μ and over four and three decades in the oscillatory shear experiment G′(ω) ∼ G″(ω) ∼ ωⁿ. A comparison of the critical exponents obtained (μ₁ ≈ 0.36, μ₂ ≈ 0.32 and n₁ ≈ 0.62, n₂ ≈ 0.67) was made as a function of the dependence of the two mixing ratios according to the theory by Doi and Onuki. New experiments were also performed to compare the critical exponents on such a thermoreversible system.

Double‐logarithmic plot of the time‐intensity correlation functions g₂(t) − 1 versus the delay time, t, at a 90° scattering angle and at several temperatures of the mixture 1.     

Dielectric relaxation study of aniline,N-methylaniline and N,N-dimethylaniline and alcohol in 1, 4-dioxane using picosecond time-domain reflectometry

A time-domain reflectometry technique has been used to measure complex dielectric permittivity ε*(ω) = ε?(ω) ? jε″(ω) of 1-propanol–dioxane, 2-propanol–dioxane, aniline–dioxane, N-methylaniline–dioxane and N,N-dimethylaniline–dioxane mixtures in the frequency range of 10 MHz to 30 GHz. The complex permittivity spectrum has been fitted with a single relaxation time with a small amount of Davidson–Cole behaviour. The least squares fit method has been used to obtain the static dielectric constant (ε₀), relaxation time (τ), Bruggeman factor and Kirkwood correlation factor. The Luzar theoretical model is used to compute the binding energies and average number of hydrogen bond between co-solvent–co-solvent and co-solvent–dioxane molecules.     

Study of Intracellular Delivery of Doxorubicin from Poly(lactide‐co‐glycolide) Nanoparticles by Means of Fluorescence Lifetime Imaging and Confocal Raman Microscopy

The intracellular delivery of Doxorubicin (Dox) from poly(lactide‐co‐glycolide) (PLGA) nanoparticles stabilised with bovine serum albumin, in HepG2 cells, is studied via flow cytometry, fluorescence lifetime imaging microscopy (FLIM), confocal Raman microscopy (CRM) and cell viability studies. Flow cytometry shows that the initial uptake of PLGA and Dox follow the same kinetics. However, following 8 h of incubation, the fluorescence intensity and cellular uptake of Dox decreases, while in the case of PLGA both parameters remain constant. FLIM shows the presence of a single‐lifetime species, with a lifetime of 1.15 ns when measured inside the cells. Cell viability decreases by approximately 20% when incubated for 24 h with PLGA loaded with Dox, with a particle concentration of 100 µg · mL^?1. At the single‐cell level, CRM shows changes in the bands from DNA and proteins in the cell nucleus when incubated with PLGA loaded with Dox.

     

Glass Transition of Low‐Dimensional Polystyrene

Summary: A unified model is developed for the finite size‐effect on the glass‐transition temperature of polymers, T_g(D), where D denotes the diameter of particles or thickness of films. In terms of this model, T_g depends on both the size and interface conditions. The predicted results are consistent with the experimental evidence for polystyrene (PS) particles and films with different interface situations.

T_g(D) function of free‐standing PS films.     

Measurement of high frequency linear viscoelastic functions of a nitrile‐butadiene rubber compound by ultrasound spectroscopy

The storage and loss components of the complex wave modulus, M*(ω), measured on a nitrile‐butadiene rubber compound (NBR‐DIN 53538) by ultrasound spectroscopy at a temperature of 293.2 K, were combined with the components of the complex shear modulus, G*(ω), measured on the same sample in a commercial Rheometric Scientific ARES instrument with torsion geometry at different frequencies and temperatures, and superposed in a master plot using the time–temperature superposition principle. From the combined measurements the components of the complex bulk modulus, K*(ω), were obtained by means of the exact formula M*(ω) = K*(ω) + (4/3)G*(ω). Some of the features of the complex bulk modulus reported in the literature for polymeric materials are confirmed for the NBR‐DIN mixture. The maxima in G″(ω) and K″(ω) are separated by more than one order of magnitude in the frequency scale and furthermore, the shapes of the peaks are different. The simple idea, that, for many polymers, the mechanisms for relaxation in shear and in bulk are of the same basic nature appears not to be supported by the present data. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 91–102, 2007     

Equilibration and Deformation of Amorphous Polystyrene: Scale‐jumping Simulational Approach

A polymer sample‐preparation method (extended‐chain condensation, ECC) based solely on molecular‐dynamics simulations has been compared to a connectivity‐altering Monte Carlo method (coarse‐grained end‐bridging, CGEB). Since the characteristic ratio for the CGEB samples is closer to the experimental value, ECC results in polymer structures that are too compact. The stress–strain relations are different in the strain‐hardening regime. For CGEB samples, a stronger strain hardening is observed and the strain‐hardening modulus is more realistic; for the CGEB polystyrene (PS) sample G_R = 9 ± 1 MPa is found versus G_R = 4 ± 2 MPa for the ECC samples. These differences have to be attributed to a steeper increase in the contributions to the total stress from bond‐ and dihedral angles for CGEB than for ECC samples.

     

Effect of Chain Straightening on Plateau Modulus and Entanglement Molecular Weight of Ni‐diimine Poly(1‐hexene)s

Summary: In this communication, we report the first rheological study on the chain‐straightened Ni‐diimine poly(1‐hexene)s and investigate the unique effect of chain straightening on plateau modulus and entanglement molecular weight of this series of polymers. Two Ni‐diimine poly(1‐hexene) samples having different levels of chain straightening were prepared with a chain‐walking Ni‐diimine catalyst, (ArNC(An) C(An)NAr)NiBr₂ (An = acenaphthene, Ar = 2,6‐(i‐Pr)₂C₆H₃) at two different temperatures. Rheological analyses show that the chain‐straightened polymers exhibit significantly enhanced plateau modulus and reduced entanglement molecular weight compared to regular poly(1‐hexene)s by metallocene catalysis. Such an effect becomes more pronounced with an increase in the level of chain straightening.

Loss moduli G″(ω) versus reduced angular frequency in a linear, natural logarithm plot for the three polymers at the reference temperature of 100 °C.