Osmotic pressure,atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model

A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ → 0. In contrast, both contributions to the pressure due to intrachain nonbonded forces and due to forces between different chains change sign from high temperatures (T ≫ θ, θ the theta-temperature) where they are positive, to low temperature where both parts of the pressure become negative. It is shown that the total pressure has the expected behavior with temperature near the θ-temperature, i.e., Δp ≡ p_tot − k_B · T_p ∼ (T − θ). We study also the concentration and chainlength dependence of the various contributions to the pressure in the good solvent regime and interpret them with scaling predictions.     

Rigidity percolation model of polymer fracture

A theory of the fracture of polymers with network microstructure was developed that was based on the vector, or rigidity percolation (RP) model of Kantor and Webman, in which the modulus, E, is related to the lattice bond fraction p, via E ～ [p ? p_c]^τ. The Hamiltonian for the lattice was replaced by the strain energy density function of the bulk polymer, U = σ²/2E, where σ is the applied stress and p was expressed in terms of the lattice perfection via the bond density ν, with the entanglement molecular weight, ν = ρ/M_e and appropriate measures of crosslink density for rubber, thermosets, and carbon nanotubes. The stored mechanical energy, U, was released by the random fracture of νD_o[p ? p_c] over stressed hot bonds of energy D_o ≈ 330 kJ/mol. The polymer fractured critically when p approached the percolation threshold p_c, and the net solution was obtained as σ = (2EνD_o [p ? p_c])^1/2 with a fracture energy, G_1c ～ [p ? p_c]. The fracture strength of amorphous and semicrystalline polymers in the bulk was well described by, σ = [ED_oρ/16 M_e]^1/2, or σ ≈ 4.6 GPa/M_e^1/2. Fracture by disentanglement was found to occur in a finite molecular weight range, M_c < M < M*, where M*/M_c ≈ 8, such that the critical draw ratio, λ_c = (M/M_c)^1/2, gave the molecular weight dependence of the fracture as G_1c ～ [(M/M_c)^1/2 ? 1]². The critical entanglement molecular weight, M_c, is related to the percolation threshold, p_c, via M_c = M_e/(1 ? p_c). Fracture by bond rupture was in accord with Flory's suggestion, G/G* = [1 ? M_c/M], where G* is the maximum fracture energy. Fracture of an ideal rubber with p = 1 was determined not to occur without strain hardening at λ > 4, such that the maximum stress, σ = E (λ ? 1/λ) = 3.75E. The fracture properties of rubber were found to behave as σ ～ ν, σ ～ E, and G_1c ～ ν. For highly crosslinked thermosets, it was predicted that σ ～ (Eν)^1/2, σ ～ (X ? X_c)^1/2, and G_1c ～ ν^?1/2, where X is the degree of reaction of the crosslinking groups and X_c defines the gelation point. When applied to carbon nanotubes (SWNT and MWNT) of diameter d and hexagonal bond density ν = j/b², the nominal stress as a function of diameter is σ(d) = [16 ED_o(p ? p_c) j/b]^1/2/d ≈ 211/d (GPa.nm) and the critical force, F_c(d) ≈ 166 d (nN/nm), in which j = 1.15, b = 0.142 nm, E ≈ 1 Tpa, and D_o = 518 kJ/mol. For polymer interfaces with Σ chains per unit area of length L and width X ～ L^1/2, G_1c is then ～ [p ? p_c], where p ～ ΣL/X. The results predicted by the RP fracture model were in good agreement with a considerable body of fracture data for linear polymers, rubbers, thermosets, and carbon nanotubes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 168–183, 2005     

Twinkling fractal theory of the glass transition: Rate dependence and time–temperature superposition

The twinkling fractal theory (TFT) of the glass transition temperature T_g provides a new method of analyzing rate effects and time–temperature superposition in amorphous materials. The rate dependence of T_g was examined in the light of new experimental and theoretical evidence for the nature of the dynamic heterogeneity near T_g. As T_g is approached from above, dynamic solid fractal clusters begin to form and eventually percolate rigidity at T_g. The percolation cluster is a solid fractal and to the observer, appears to “twinkle” as solid and liquid clusters interchange in dynamic equilibrium with a vibrational density of states g(ω) ∼ ω. The solid-to-liquid twinkling frequencies ω_TF are controlled by the Boltzmann population of intermolecular oscillators in excited energy levels of their anharmonic potential energy functions U(x) such that ω_TF = ω exp −B(T*² − T²)/kT in which T* ≈ 1.2T_g. An oscillator changes from a solid to a liquid when a thermal fluctuation causes it to expand beyond its inflection point in the anharmonic potential. This leads to a continuous solid fraction P_s near T_g given by P_S ≈ 1−[(1 − p_c) T/T_g] where p_c ≈ 1/2 is the rigidity percolation threshold. Since g(ω) is continuous from very low to very high frequencies, the complex twinkling dynamics existing near T_g produces a continuous relaxation spectrum with many different length scales and times associated with the fractal clusters. The twinkling frequencies control the kinetics of T_g such that for a given observation time t when the rate γ > 1/t, only those parts of the twinkling spectrum with ω > γ can contribute to relaxation or percolation upto time t. The most important results in this article are as follows: The TFT describes the rate dependence of T_g, both for DSC thermal heating/cooling rates and DMA frequencies as the classic T_g − lnγ law as T_g(γ) = T_go + (k/2B) ln γ/γ_o in which the constant B = 0.3 cal/mol K². The constant B appears quite universal for the 17 thermoset polymers investigated in this study and 18 linear polymers investigated by others. Many other amorphous metal and ceramic glass materials exhibited the same rate law but required a new B value approximately half that for polymers. The same B = 0.3 value was also used to successfully describe the TTS shift factors using the twinkling fractal frequencies ω_TF = ωexp −B(T*² − T²)/kT, as ln a_T(TFT) = exp B(T_R² − T²)/kT, which gave comparable results with the classical WLF equation, log a_T = [−C₁(T − T_R)]/[C₂ + (T − T_R)]. The advantage of the TFT over the WLF is that C₁ and C₂ are not universal constants and must be determined for every material, whereas the TFT uses one known constant B which appears to be the same for all polymers. The TFT has also been found to describe the strong and fragile nature of the viscosity behavior of liquids and the rate and temperature dependence of the yield stress in polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2578–2590, 2009     

Simulation of first- and second-order transitions in asymmetric polymer mixtures

The critical properties of dense asymmetric binary polymer mixtures are studied by grand canonical simulations within the framework of the 3-dimensional bond fluctuation lattice model. The monomers interact with each other via a potential ranging over the entire first peak of the pair distribution. An asymmetry is realized by giving the ratio of interactions λ = ∈_AA/∈_BB between monomers of the A-species and of the B-species a value different from 1. Using multiple histogram extrapolation techniques for the data analysis, the two phase region, which is a line of first-order transitions driven by the chemical potential difference, and the critical point are determined for a mixture of chains with 32 monomers each. At a critical potential difference Δμ_c unmixing occurs below a critical temperature T_c. It is found that Δμ_c is proportional to the asymmetry (1 - λ) and that the quantity 4k_BT_c/(3 + λ)∈ is independent of the asymmetry, consistent with the prediction of the Flory theory.     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

Relation of the decay of free radicals in irradiated polyethylene to the molecular motion of the polymer and the configurations of the free radicals

Decay reactions of the free radicals produced in irradiated polyethylene (high-density and low-density materials) were examined in connection with the molecular motion of the matrix polymer. Three temperature regions, in which the free radicals decay very rapidly, at around 120, 200, and 250°K, were designated T_A, T_L, and T_B, respectively. The decay of the free radicals at these temperatures had activation energies in high-density polyethylene of 0.4 kcal/mole for T_A, 9.4 kcal/mole for T_L, and 18.4 kcal/mole for T_B. In low-density polyethylene these quantities were 0.7 kcal/mole for T_A, 23.1 kcal/mole for T_L, and 24.8 kcal/mole for T_B. Comparison of time constants for the decay reactions and for molecular motion of the matrix polymer indicate that the decay in T_A and T_B is closely related to molecular motion in the amorphous regions of the polymer. The decay of the free radicals at T_L in high-density polyethylene is due to molecular motion associated with local mode relaxation at lamellar surfaces, while that of low-density polyethylene is due to local mode relaxation in the completely amorphous region. Steric configurations of the free radicals which decay in the respective temperature regions were also investigated.     

Magnetic Structures of the Rare-Earth Platinum AluminidesRPtAl (R=Ce, Pr, Nd)

The rare-earth (R) platinum aluminidesRPtAl crystallize in the orthorhombic TiNiSi-type structure (space group Pnma,Z=4), where magnetic rare-earth atoms form a network of chains parallel to thea-axis and parallel to theb-axis. Magnetic structures and phase transitions ofRPtAl (R=Ce, Pr, Nd) compounds were investigated by systematic measurements of magnetic susceptibility, specific heat, and neutron diffraction on polycrystalline samples. The results reveal a large magnetocrystalline anisotropy and magnetic structures that are dominated by a ferromagnetic component parallel to one of the two chain directions: thea-axis for CePtAl and PrPtAl and theb-axis for NdPtAl. The complex magnetism of CePtAl with three successive magnetic phase transitions (T_C=5.9 K,T₂=4.3 K,T₃=2.5 K) and two coexisting propagation vectors (k₁=0 forT≤T_C, k_2i=[0, 0.46, 0] forT₂≤T≤T_C, k₂=[0, 1/2, 0] forT≤T₂) is confirmed to be exceptional amongRPtAl compounds. PrPtAl has a nonmagnetic crystalline-electric field (CEF) ground-state singlet separated by 21 K from the first-excited state CEF singlet and magnetic exchange interactions are strong enough to induce long-range magnetic order (Curie temperatureT_C=5.8 K, propagation vector k₁=0, magnetic group Pnm′a′, ordered saturation momentm₁=1.00(7)μ_B). NdPtAl is a simple ferromagnet (T_C=19.2 K, k₁=0, Pn′ma′,m₁=2.08(4)μ_B).     

Solvent induced phenomena in a dendronized linear polymer

The properties of a dendronized linear polymer (DP) in dilute solutions depending on solvent quality and temperature are described. The polymer has a contour length of L _c?=?1,060 nm. The sample of the fourth generation (PG4) was analyzed in the thermodynamically good solvents dioxane, chloroform, and methanol. The wormlike macromolecule has a persistence length l _p?=?7 nm in dioxane and a cross-section radius determined by small angle X-ray scattering (SAXS) of R _{c (SAXS)}?=?2.8 nm. The bulk density of PG4 determined by SAXS was compared with solution density. Evidence for substantial swelling of the cross-section was found. Toluene acts as a thermodynamically poor solvent (θ solvent). Above the θ temperature T _θ , a strong temperature dependence of the size and the Young’s modulus E was observed. Following Odijk, E/k _B T ～1 was found. Below T _θ , a regime characterized by unswelling of the wormlike chains was observed. The results suggest that DPs can be described as soft colloid filaments, which are subject to commonly observed interactions in colloidal systems. A phase diagram indicates a regime below T _θ in which fluctuations of osmotic pressure inside the filaments result in periodic undulation of the chains. In summary, introducing a dense dendritic shell around the backbone converts conventional polymers into molecular colloids.

The configurational free energy of a polymer chain

The configurational, or elastic, free energy A_el of a polymer chain is discussed in terms of the Fourier configurational approach. The importance of accounting for all degrees of freedom of the chain is shown in comparison with affine mean-field theories and with scaling theories of chain expansion and contraction. In case of strong contraction the chain does show neither affinity nor self-similarity, and we get A_el ∼ N^1/3, N being the number of chain bonds. Conversely, in case of good-solvent expansion we find A_el ∼ N. The same result holds in the vicinity of the Θ-temperature, where A_el is also proportional to [(T − Θ)/T]².     

Halogenide der Seltenerdmetalle Ln4X5Z. Teil 3: Das Chlorid La4Cl5B4 – Präparation,Struktur und Verwandtschaft zu La4Br5B4, La4I5B4

Rare Earth Halides Ln₄X₅Z. Part 3: The Chloride La₄Cl₅B₄ – Preparation, Structure, and Relation to La₄Br₅B₄, La₄I₅B₄ La₄Cl₅B₄ is synthesized by reaction of LaCl₃, La metal and boron in sealed Ta containers at 1050 °C < T < 1350 °C. It crystallizes in the monoclinic space group C2/m with a = 16.484(3) Å, b = 4.263(1) Å, c = 9.276(2) Å and β = 120.06(3)°. Ce₄Cl₅B₄ is isotypic, a = 16.391(3) Å, b = 4.251(1) Å, c = 9.180(2) Å and β = 120.20(3)°. The La atoms form strings of trans-edge shared La octahedra, and the B atoms inside the strings form B₄-rhomboids, which are condensed to chains via opposite corners. The Cl atoms interconnect the channels according to La₂La_4/2Clⁱ⁻ⁱ_6/2Cl^i−a_2/2Cl^a−i_2/2. The crystal structures of the bromide and the iodide are comparabel, however, the interconnection of the strings is different in the three structure types, as 14 Cl, 13 Br and 12 I atoms surround the La₆ octahedra.     

Stress overshoot of polymer solutions at high rates of shear; Polystyrene with bimodal molecular weight distribution

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γ_σm and γ_Nm, corresponding to the peaks of σ and N₁ lay on the universal functions of γ˙τ_R, respectively, proposed for dilute solutions in pure solvent. Here τ_R is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γ_σm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τ_R < 10⁻². This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γ_σm and γ_Nm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000     

Flow of polymer chains and segregation in a flow field with a hybrid simulation

Effects of a flow field (E) on segregation and flow of polymer chains are studied in two dimensions using a hybrid (discrete‐to‐continuum) simulation. The flow rate (j) of polymer chains is found to increase monotonically with E, a linear response in the low field regime followed by a slow approach to saturation in the high field regime. The effective chain permeability (ϕ_c = j/E) varies nonmonotonically on increasing the field E, with a maximum (ϕ_cm) at a characteristic value of the field (in the range 0.2 < E < 2); ϕ_cm depends on the chain length. Chain aggregates exhibit an anisotropic mass distribution due to the field with a molecular bridging at high fields. The longitudinal component of the radius of gyration (R_gx) exhibits a crossover from a random walk (RW) (R_gx ˜ L_c^1/2) at E = 0 to an elongated conformation (R_gx ˜L_c) at E ⪈ 0.2; the transverse component changes from R_gy ˜ L_c^1/2 to R_gy ˜ L_c^1/3. The width of the radial distribution function (ρ(r)) of the monomers increases while its peak varies nonmonotonically with E and is consistent with the observation of anisotropic mass distribution.     

Electrophilic aromatic substitution. 14. [1] A kinetic,NMR, and Raman study of the aluminum chloride-catalyzed reaction of p-toluene-sulfonyl chloride with benzene and toluene in dichloromethane

Vacuum line kinetic studies of the reaction of p-toluenesulfonyl chloride and benzene or toluene, using aluminum chloride as the catalyst and dichloromethane as the solvent were determined at 25°C by means of gas chromatography. The reaction is first-order in arene, tosyl chloride, and in AlCl₃ as catalyst. Noncompetitive results are k_T/k_B=22±7 with a product sulfone isomer distribution: ortho, 14±1%; meta, 4.3±0.2%; and para 82±1%. With hexadeuteriobenzene k_H/k_D was determined to be 1.8±0.1. Rate constant ratios and product isomer distributions were also determined competitively: with AlCl₃, k_T/k_B=30±2; % ortho, 13±1; % meta, 4.0±0.5; % para, 84±3; with SbCl₅, k_T/k_B=40±4; % ortho 10.3±0.4; % meta, 4.7±0.2; and % para, 85.0±0.5. The k_T/k_B ratio for AlCl₃ and the meta sulfone product percentages for both AlCl₃ and SbCl₅ are considerably higher than those reported in the literature. NMR and Raman studies suggest a molecular complex between p-tosyl chloride and AlCl₃, with coordination through oxygen as the dominant species and the probable electrophile in CH₂Cl₂. A reaction mechanism consistent with the kinetic and spectroscopic results is proposed. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 367–372,1998     

The effects of aromatic solvents on the photopolymerization rates of isoprene,ethyl methacrylate,and styrene

The photochemical polymerization rates of isoprene, ethyl methacrylate, and of styrene in various aromatic solvents were measured. The average lifetimes of propagating radicals were measured by the rotating sector method. The polymerization rate constants, K_p, were determined and compared with dipole moments (μ) and Hammett σ constants for the aromatic solvents. Linear correlations of log(k_p/k_{p, benzene}) vs. μ and σ were obtained.     

Kinetics and mechanism of the aminolysis of thiophenyl methylacetates in acetonitrile

The aminolysis of Z‐thiophenyl methylacetates (C₂H₅C(O)SC₆H₄Z) with X‐benzylamines in acetonitrile has been investigated at 45°C. The reaction is found to proceed by a stepwise mechanism in which the rate‐determining step is the breakdown of the zwitterionic tetrahedral intermediate, T^±, with possibly a hydrogen‐bonded four‐center‐type transition state. These mechanistic conclusions are drawn based on (i) the large magnitude of β_X (= 1.2 ∼ 2.5) and β_z (= −0.9 ∼ −1.5), (ii) the normal kinetic isotope effects (k_H/k_D ≅ 1.2) involving deuterated benzylamines (XC₆H₄CH₂ND₂), (iii) a large positive ρ_xz (= 2.4) and (iv) adherence to the reactivity‐selectivity principle in all cases. The extremely large β_X (β_nuc) values can be accounted for by the loss of a strong localized cationic charge on the N atom of benzylamines in the expulsion from the T^±. The pK_a^o (≥ 10.0) is high due to a large ratio of the expulsion rates of the amine (k_−a) to thiophenolate (k_b) (k_−a/k_b) from the T^±. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 485–490, 2000     

Electron or hole liquids in high-T c cuprates: evidence for d-wave order parameter

Phillips and Jung [J.C. Phillips and J. Jung (2002). Phil. Mag. B, 82, 1163] refute nodal properties of the gap function Δ_k and propose an isotropic s-wave picture with electron–phonon interaction as the mechanism for high-T _c superconductivity in the cuprates. Here, we compare and contrast predictions of various physical properties with the gap function Δ_k reflecting three scenarios: (i) isotropic s-wave pairing, (ii) extended s-wave with eight line nodes as championed quite recently by Zhao [G.M. Zhao (2001). Phys. Rev. B, 64, 024503], and (iii) d-wave pairing. By referring to (a) scanning tunnelling microscopy imaging of a Zn impurity, supported by our own subsequent theoretical study, (b) linear decrease of T _c with non-magnetic impurity concentration, and (c) calculations on the extended s-wave scenario applied to tunnelling conductance, strong evidence for nodal properties of Δ_k is given. The contentions of Phillips and Jung [J.C. Phillips and J. Jung (2002). Phil. Mag. B, 82, 1163] should therefore be treated with considerable caution, isotropic s-wave behaviour being truly exceptional among the high-T_c cuprates.     

Long periods in slow-cooled linear and branched polyethylene: Part II

It is shown that the long periods L in slow-cooled polyethylene materials obey the general law L = L⁰ + αr_w, where r_w is the weight average dimension of the coil before crystallization, and L⁰ is a parameter of the order of l_c, the crystalline core thickness, which increases as the cooling rate V decreases. α is a parameter independent of M and V but decreasing with the number of long-chain branches per molecule. The two terms in the above relation are, respectively, the contributions of crystalline and amorphous layers. For cooling rates from 800°C/min to 0.2°C/min, it is shown that the temperature T_c of crystallization is constant; hence the change of morphology (long period, crystalline core thickness, crystallinity) cannot be explained by supercooling. The increase in long period and crystallite thickness in slow-cooled materials with decreasing cooling rate is interpreted in terms of annealing of the crystallized materials between the crystallization temperature T_c and the secondary transition temperature T_αc. Crystallization proceeds by a two-step process of solidification and annealing. During the annealing stage, the mobility of the chains in the crystalline phase is due to defects; the kinetics of thickening is then governed by the mobility (or nucleation) of the defects appearing above T_αc. In the proposed model of crystallization, the assumption that the energy of activation is proportional to T_αc explains the observed laws L ≡ l_c ≡ log t_a, where the annealing time t_a is equal to (T_c ? T_αc)/V. The model applies also to polymers crystallized from the melt and subsequently annealed.     

Study on Cd2+ Determination Using Bud-like Poly-L-Tyrosine/Bi Composite Film Modified Glassy Carbon Electrode Combined with Eliminating of Cu2+ Interference by Electrodeposition

A bud-like poly-L-tyrosine/Bi modified glassy carbon electrode (p-Tyr/Bi/GC) was prepared by CV and in situ Bi plating, whose conductivity and membrane morphology were characterized by CV, EIS and SEM, respectively. The p-Tyr membrane can effectively promote the enrichment of Cd²⁺. The optimal Tyr concentration and scanning number for p-Tyr/GC preparation were 2.0 mmol ⋅ L⁻¹ and 35, while the optimal Bi³⁺ concentration, pH and Cd²⁺ accumulation potential in test medium were 3.0 μmol ⋅ L⁻¹, 6.5 and −1.3 V, respectively. The linear equation of p-Tyr/Bi/GC's response to Cd²⁺ (1.0 nmol ⋅ L⁻¹ to 2.0 μmol ⋅ L⁻¹) was i_p (μA) = −0.6809 + 100.2c (μmol ⋅ L⁻¹) (R² = 0.9985) with a detection limit of 0.11 nmol ⋅ L⁻¹ (3S/N). The elimination of interference caused by Cu²⁺ in sample was studied by electrodeposition. The p-Tyr/Bi/GC electrode was successfully used for detecting Cd in rice samples with good reliability and accuracy. The developed Cd²⁺ sensor exhibits high sensitivity, wide linear range and low detection limit, especially the designed method of eliminating Cu²⁺ interference has the characteristics of high selectivity, simple operation and wide application range.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

Elongational flow studies on flexible polymer chains in a pseudo-solvent

The dynamics of isolated high molecular weight (M_H) polymer chains dissolved in a nonentangled semidilute solution of a low molecular weight (M_L) polymer were investigated by monitoring the elongational flow birefringence. Because of its nonentangled nature, a low molecular weight matrix polymer solution is regarded as a pure solvent (a binary pseudo-solvent). A ternary solution consisting of a small amount of a high molecular weight probe polymer and the binary pseudo-solvent is effectively a dilute solution of the probe polymer. It was observed that the birefringence from the orientation and/or stretching of the probe polymer chains starts to increase rather abruptly at a certain critical strain rate, , and the spatial birefringence pattern is localized along the elongation axis, characteristics that are reminiscent of the coil-stretch transition of flexible polymer chains in a simple dilute solution. The relaxation time for the chain extension, _el, defined as the reciprocal of the critical strain rate , was determined at various temperatures, matrix polymer concentrations c_L, and test chain molecular weights M_H. It was found that _el varied with molecular weight as _el~M_H^a , with a ranging from 1.3 to 1.8, which is roughly consistent with the molecular weight dependence of the non-free-draining Zimm relaxation time. A scaled relaxation time _elkT/, which can be used to estimate the radius of gyration R_g of the probe polymer, decreased with increasing c_L, indicating contraction of the high molecular weight polymer due to a screening of the excluded volume effect caused by the matrix polymer in the pseudo-solvent.