Simultaneous determination of levofloxacin hemihydrate and ambroxol hydrochloride in tablets by thin-layer chromatography combined with densitometry

This paper describes the application of thin-layer chromatography (TLC) combined with densitometry to simultaneous determination of levofloxacin hemihydrate (LEV) and ambroxol hydrochloride (AMB) in bulk and tablets. The separation was achieved on aluminum sheet of silica gel 60 F ₂₅₄ using chloroform: methanol: toluene: ammonia (10: 6: 3: 0.8 v/v/v/v) as mobile phase. Quantification was carried out densitometrically at 245 nm. This system was found to give compact spots for LEV (R _f value of 0.4) and AMB (R _f value of 0.7). The calibration curves for LEV and AMB was found to be linear between 9960–16600 ng/spot (r ² = 0.999) and 600–1000 ng/spot (r ² = 0.999), respectively. The mean percentage recoveries from tablets for LEV and AMB were 99.45% and 99.58%, respectively. The TLC-densitometry method has many advantages, such as simplicity, reasonable sensitivity, rapidity, and low cost, and it can be successfully used in routine analysis of both these drugs in tablet formulations.     

Differential Pulse Polarography for a First‐Order EC Process and Its Diagnostic Parameters

Theoretical expressions for differential pulse polarography (DPP) for a reversible electron transfer coupled with an irreversible follow‐up first‐order chemical reaction (E_rC_i) is derived approximately. The peaks as given by the current expressions are analyzed in terms of several parameters such as a ratio of anodic‐to‐cathodic peak‐currents (i_p^a/i_p^c), a separation of peak‐potentials (E_p^c?E_p^a), and a ratio of anodic‐to‐cathodic half‐peak‐widths (W_1/2^a/W_1/2^c) in order to characterize the E_rC_i process and distinguish it from other types of electrode processes. The anodic peak is found to be more susceptible to the post kinetics than the cathodic peak. The new parameter of W_1/2^a/W_1/2^c ratio is much more sensitive to the post kinetics than the peak separation (E_p^c?E_p^a). The peak current ratio (i_p^a/i_p^c) and the peak‐width ratio (W_1/2^a/W_1/2^c) have comparable sensitivities to the kinetics. Hence, W_1/2^a/W_1/2^c ratio is a better diagnostic parameters than (E_p^c?E_p^a) which has a poor sensitivity. This phenomenon is different from cyclic voltammetry (CV) in which E_p^c?E_p^a is as sensitive as i_p^a/i_p^c. The new criteria for EC with DPV is tested and successfully applied to several Co(III) complex systems, including coenzyme B₁₂. The homogeneous rate constant (k) for the follow‐up step is estimated from the measurements of the experimental values of the parameters. The present treatment is valid quantitatively at lower values of k, yielding relatively larger errors for higher k values (k>10 s^?1).     

Topological studies on IRC paths of X+H2→XH+H reactions

Topological properties of potential energy and electronic density distribution on five reaction paths X+H₂→XH+H (X=H, N, HN, H₂C, NC) are investigated at the level of UMP2/6–311G(d,p). It has been found that in the region of the reaction paths studied, where B(r_c)|_s>0 [B(r_c)|_s is the product of ρ(r_c) and ∇²ρ(r_c) at the point of reaction process, i.e., B(r_c)|_s=ρ(r_c)∇² ρ(r_c)] is basically the same as the region of V′(s)<0[V′(s) is the second derivative of potential energy with respect to the reaction coordinate, i.e., V′(s)=d²V/ds²], and the point with maximum B(r_c)|_s is almost coincident with the point of minimum V′(s). It can be concluded from the calculated results that there is a good correlation between the topological properties of potential energy and electronic density distribution along the reaction path. The structure transition state of such collinear reactions may be determined by topological analysis of electronic density. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1167–1174     

Characterization of the Surface Redox Process of Adsorbed Cercosporin (CER) at Glassy Carbon Electrodes by Anodic Stripping Square‐Wave Voltammetry

The adsorptive accumulation of cercosporin (CER) at glassy carbon electrodes is studied by square‐wave voltammetry (SWV). The Freundlich adsorption isotherm resulted in being the best one to describe the specific interaction of CER with glassy carbon electrodes by using a fitting procedure of experimental fractional surface coverage vs. the CER bulk concentration (c*_CER). SWV was also used to generate Q vs. c*_CER and I_{p, n}. vs. c*_CER calibration plots from pure commercial reagent solutions. Theoretical detection limits of 1.8×10^?7 and 9.7×10^?8 M were calculated from Q. vs. c*_CER and I_{p, n} vs. c*_CER plots, respectively. The lowest concentration value measured experimentally from calibration plots performed at a f =40 Hz for a signal to noise ratio of 2 : 1 was 3.7×10^?8 M, being this value two orders of magnitude smaller than that obtained previously by us from the diffusion controlled CER reduction peak. I_{p, n}./f vs. f plots from SW voltammograms performed at different c*_CER as well as different accumulation times showed the so‐called “quasi‐reversible maxima”. A splitting of the voltammetric peak was also observed by increasing the SW amplitude at a given frequency. A value of (?0.260±0.011) V was determined for the formal potential of the adsorbed redox couple from the split voltammetric peak. A full characterization of the surface redox process was obtained by applying the methods of the “quasi‐reversible maximum” and the “split SW peak”. In 1 M HClO₄ aqueous solution, the formal rate constant and the anodic transfer coefficient were (3.5±0.5)×10² s^?1 and (0.50±0.03), respectively. Besides, the number of electrons exchanged during the redox reaction was calculated as n≈1.     

Effects of composition drift on the effectiveness of random copolymer reinforcement at polymer–polymer interfaces

Random copolymer layers are surprisingly effective at reinforcing polymer–polymer interfaces. One hypothesis is that composition drift during synthesis can account for the higher than expected toughening. To test this hypothesis, we polymerized a series of poly(d‐styrene‐r‐2‐vinylpyridine) (dPS_f‐r‐PVP_1?f) copolymers with various fractions (f) of deuterated styrene to only 10% completion to avoid composition drift. The fracture energies (G_c) of polystyrene/dPS‐r‐PVP/poly(2‐vinylpyridine) interfaces with relatively thick layers of dPS‐r‐PVP were measured. G_c decreased relative to interfaces reinforced with composition‐drifted dPS‐r‐PVP. Conversely, G_c increased when two or more copolymers were blended together. In such samples, the copolymers form distinct layers with multiple interfaces characterized by the difference in f (Δf) between adjacent layers. We find that G_c is governed by Δf_max, the largest difference in adjacent compositions, and, therefore, by the width of the narrowest interface (w_min). G_c increases strongly as w_min increases from 3 to 5 nm. Remarkably, these w_min values are about half the entanglement spacing in bulk polystyrene. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2363–2377, 2001     

Estimation of the agglomeration structure for conductive particles and fiber‐filled high‐density polyethylene through dynamic rheological measurements

A study on the correlation between electrical percolation and viscoelastic percolation for carbon black (CB) and carbon fiber (CF) filled high‐density polyethylene (HDPE) conductive composites was carried out through an examination of the filler concentration (?) dependence of the volume resistivity (ρ) and dynamic viscoelastic functions. For CB/HDPE composites, when ? was higher than the modulus percolation threshold (?_G ～ 15 vol %), the dynamic storage modulus (G′) reached a plateau at low frequencies. The relationship between ρ and the normalized dynamic storage modulus (G_c^′/G_p^′, where G_c^′ and G_p^′ are the dynamic storage moduli of the composites and the polymer matrix, respectively) was studied. When ? approached a critical value (?_r), a characteristic change in G_c^′/G_p^′ appeared. The critical value (G_c^′/G^′_p)c was 9.80, and the corresponding ?_r value was 10 vol %. There also existed a ? dependence of the dynamic loss tangent (tan δ) and a peak in a plot of tan δ versus the frequency when ? approached a loss‐angle percolation (?_δ = 9 vol %). With parameter K substituted for A, a modified Kerner–Nielson equation was obtained and used to analyze the formation of the network structure. The viscoelastic percolation for CB/HDPE composites could be verified on the basis of the modified equation, whereas no similar percolation was found for CF/HDPE composites. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1199–1205, 2004     

Axial force fluctuations in long-chain molecules

The fluctuations Δf in the axial force f acting on a long-chain molecule whose end-to-end displacement r is fixed are computed for a freely jointed model in which the covalent bonds are represented by stiff linear springs. It is found that the relative fluctuation Δf/f remains large regardless of the length of the chain. A time-dependent computer simulation of the model serves both to verify the theoretical calculation of Delta;f and to provide physical insight. The result helps to clarify the difference in behavior of the strain ensemble (r is fixed and f fluctuates) and the stress ensemble (f is fixed and r fluctuates) for which, in the absence of excluded volume, the strain ensemble predicts that f = 0 for r = 0, while for the stress ensemble with f = 0 it is found that 〈r²〉₀ > 0.     

The Laplacian of the electronic density at the valence-shell charge concentration (VSCC): A comparative study of effective core potential and full-electron calculations in Mo compounds. II

The effective core potential (ECP), using a basis set of different qualities, and ab initio full-electron (FE) calculations were carried out for MoS⁻²₄, MoO⁻²₄, and MoOCl₄ molecules. The topology of − ▿²p(r_cp) (the negative Laplacian of the charge density at its critical points) in the atomic valence shell was studied. Results clearly indicate that semicore (ECP2) approaches are able to reproduce, in a qualitative way, the topology of the Laplacian distribution with respect to those obtained by the FE method. Modifications of basis sets, such as introduction of polarization functions on the ligands, affect the electronic charge distribution (number of critical points in MoOCl₄) for FE as well as for ECP2 approaches. The ECP2 scheme predicts correctly the order of − ▿²p_x(r_cp) (X = O, S, Cl, Mo) in the valence shell; nevertheless, it fails in the relative magnitudes of − ▿²p_Mo(r_cp) between Mo compounds in respect to FE calculations. A scaling factor consistently improves the values of − ▿²p(r_cp) and p(r_cp), which are larger than those obtained with FE, particularly the − ▿²p(r_c) values. © 1996 John Wiley & Sons, Inc.     

原子配分参数、配分连接性指数及其应用

结构决定性质，性质反映结构，这是化学、生物学等学科的一条基本规律。因此，分子的微观结构与性质之间存在着密切关系。物质的理化性质、生物活性等数据的获取，迄今主要来自于实验。如能建立结构与性能之间的数量关系用以估算与预测分子的性质，这无疑是一项十分有意义的工作。拓扑指数法以其计算简单、准确性高、应用范围广而在上述领域中发挥重要作用犤１～４犦。拓扑指数是对分子结构进行的定量描述，使分子之间的结构差异定量化。自Wiener提出第一个拓扑指数（W）犤５犦以来，迄今已有２００余种拓扑指数问世。其中一部分能够有效地…     

Calculation of the formation constant of the 1:1 complex between manganese(II) and the anion of 2-mercaptopyridine N-oxide (pyrithione) by polarographic measurements

Polarograms of mixtures of Mn^II and the anion of 2-mercaptopyridine N-oxide (pyrithione) in neutral media do not show separate waves for the metal ion, either complexed or not, nor for the ligand, free or in the complex. The two-electron reduction of Mn^II is shown to be an E_rE_i process in the absence of ligand and C_rE_rE_i process in the presence of ligand, with a fast previous reaction. From measurements made at constant Mn^II concentration and variable ligand concentration it is shown that the 1:1 complex is formed. The logarithm of the formation constant of this complex is obtained from these and other measurements, this value being log K_f = 3.76 ± 0.03.     

Injection effect on the sensitivity in an isothermal titration calorimeter

By using electrical calibrations and with the injection of liquids with very different heating capacities (water and cyclohexane), it is made a thorough evaluation of the ‘injection effect’ in terms of the parameter ρc _p f (ρc _p – volumetric heat capacity, f – injection flow) in an isothermal titration calorimeter. This effect can be evaluated accurately in the case of non-volatile liquids, however, when dealing with volatile liquids, the uncertainty in their determination increases because of the vaporization heat.     

Perturbed structures generated using coordinates derived from compliance constants in internal vibrations for QTAIM dual functional analysis: Intrinsic dynamic nature of interactions

Perturbed structures for QTAIM dual functional analysis (QTAIM‐DFA) are proposed to generate using the coordinates corresponding to the compliance force constants in internal vibrations (CIV). In QTAIM‐DFA, total electron energy densities H_b( r _c) are plotted versus H_b( r _c) – V_b( r _c)/2 at bond critical points (BCPs) of interactions in question, where V_b( r _c) are potential energy densities at BCPs. Each plot of an interaction based on the data from both perturbed structures and fully optimized one takes the form (θ_p, κ_p), where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ_p values evaluated with CIV are equal to those obtained by partial optimizations with the interaction distance in question being fixed suitably, within the calculation errors. Very high applicability of CIV is demonstrated to generate the perturbed structures for QTAIM‐DFA. Dynamic nature of interactions based on (θ_p, κ_p) with CIV is called “intrinsic dynamic nature of interactions.”     

Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

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Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

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Notation g ^c (y);g ^m (Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g _o ^c ;g _o ^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty _f - gco(y, y _ef,y _f) molar free enthalpy of the crystal corey _co - g ₀ ^ex ((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g ^f(y_ef,g _o ^ex ) molar free enthalpy of the longitudinal layers of the folded chain crystals - g ^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h _o ^1c ,h _o ^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h _o ^m -h _o ^c molar heat of fusion of the unit - C _p=C _p ^m -C _p ^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h ^D molar defect enthalpy of local defects within the crystal lattice - h ^D molar defect enthalpy of the unit - s _o ^c ,s _o ^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s _c ^m conformational entropy of a chain in the melt - s _gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s _n ^c nematic configurational entropy - T absolute temperature - T _M melting temperature of extended chain crystals of infinite size - T _M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T _M (y, y _f) melting temperatureof folded chain crystals of the thicknessy _f composed of chains of the lengthy - T _M(y _f) melting temperature of folded chain crystals of the thicknessy _fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y _f height of lamelliform folded chain crystals - f=(y/y _f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy _f - y _co thickness of the crystal core of the simplified twophase model - y _et average thickness of the surface layers of folded chain crystals - N _c number of crystallized units of a chain of the lengthy - x _c molar number of crystallized units of a chain of the lengthy - x _nc molar number of noncrystallized units - excess free enthalpy parameter - (y _f) thickness distribution of the fold heightsy _f With 15 figures and 2 tables     

Zum Scherverhalten unzerstörter adsorbierter tensidmodifizierter Gelantineschichten

Zusammenfassung Untersucht wurde das grenzflächenrheologische Verhalten unzerstörter 0.2% Gelatine/Natrium-dodecylsulfat (10^–4, 10^–5 M/l)-Adsorptionsschichten bei Scherung an der Phasengrenze Luft/Lösung. Bei der Ermittlung der rheologischen Parameter muß eine Fließgrenze berücksichtigt werden, unterhalb derer lediglich spontan- und verzögert-elastisches Verhalten zu beobachten ist. Das Kriechdeformationsverhalten wurde mit einem Schofield-Scott-Blair-Modell beschrieben. Eine Analyse zur Modellierung des Fließvorganges ergab, daß Messungen bei diskontinuierlichen Scherbedingungen, bei denen die Fließgrenze nicht im gesamten Bereich der Scherung überschritten wird, wegen des dabei realisierten großen Meßeffekts für die Parameterbestimmung am geeignetsten sind. Die das Fließverhalten der Phasengrenzschicht beschreibenden Parameter weisen eine geringe Streuung (< 10%) auf, Die Ignorierung der Fließgrenze führt zu einer scheinbaren Erhöhung der plastischen Grenzflächenscherviskosität.Der Zusatz von Natrium-dodecylsulfat zu Gelatine bewirkt im untersuchten Konzentrationsbereich mit steigender Tensidkonzentration neben dem Auftreten der Fließgrenze eine erhebliche Erhöhung aller rheologischen Parameter, welche sich nicht additiv aus den Parametern der Einzelkomponenten ergibt. Das Ansteigen der rheologischen Parameter wird als Strukturverfestigung interpretiert.

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The surface-rheological behaviour of undestroyed 0.2% gelatine/sodium-dodeylsulfate (10^–4, 10^–5 M/l)-adsorption-layers at the interface air/liquid was investigated. For the determination of the rheological parameters a yield value must be taken into account. By stressing the structure below this yield value only instantaneous and retarded-elastic deformations were detected. The creep behaviour of the investigated structures was described by a Schofield-Scott-Blair-model. At discontinuous shear-conditions the yield value is not reached in the whole range of shearing. Analysing the flow-process it was shown, that using those conditions a high measuring effect is realized for the determination eached of the rheological parameters.The rheological parameters describing the creep-process deviate from its average by < 10%. Ignoring the yield value causes an apparent increasing of the plastic surface viscosity.The addition of SDS to the gelatine causes the yield value and an increasing of all rheological parameters in the investigated concentration-range. This increasing is not additiv and leads to an interpretation of a strong rise of solidity of the surface structure.

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Abkürzungen A ₁ eine die Fließgrenzef ₁ berücksichtigende Scherspannung, def. durch (30) - A ₂ eine die Fließgrenzef ₂ berücksichtigende ScherspannungF — Kraft - G ₁ ^s Schermodul der spontanen Elastizität - G ₂ ^s Schermodul der verzögerten Elastizität - M Drehmoment - S effektive Scherspannung - f ₁ Fließgrenze der plastischen Viskosität - f ₂ Fließgrenze der elastischen Viskosität - r Radialkoordinate - r ₁ Ringradius - r ₂ Gefäßradius - r _O1 kritischer Radius fürf ₁ - r _O2 kritischer Radius fürf ₂ - t Zeit - t _O Expositionszeit, Zeitpunkt der Entlastung des Systems - x Deformation - Deformation in rad - _O spontan-elastische Deformation - ^* irreversible Deformation - ₁ ^s plastische Grenzflächenscherviskosität - ₂ ^s elastische Grenzflächenscherviskosität - Retardationszeit ₂ ^s /G ₂ ^s     

Silolene-Bridged zirconocenium polymerization catalysts

A new silolene-bridged compound, racemic (1,4-butanediyl) silylene-bis (1-η⁵-in-denyl) dichlorozirconium ( 1 ) was synthesized by reacting ZrCl₄ with C₄H₈Si (IndLi)₂ in THF. 1 was reacted with trialkylaluminum and then with triphenylcarbenium tetrakis (penta-fluorophenyl) borate ( 2 ) to produce in situ the zirconocenium ion ( 1 ⁺). This “constraint geometry” catalyst is exceedingly stereoselective for propylene polymerization at low temperature (T_p = ?55°C), producing refluxing n-heptane insoluble isotactic poly(propylene) (i-PP) with a yield of 99.4%, T_m = 164.3°C, δH_f = 20.22 cal/g and M?_w = 350 000. It has catalytic activities of 10⁷?10⁸ g PP/(mol Zr · [C₃H₆] · h) in propylene polymerization at the T_p ranging from ?55°C to 70°C, and 10⁸ polymer/(mol Zr · [monomer] · h) in ethylene polymerization. The stereospecificity of 1 ⁺ decreases gradually as T_p approaches 20°C. At higher temperatures the catalytic species rapidly loses stereochemical control. Under all experimental conditions 1 ⁺ is more stereospecific than the analogous cation derived from rac-dimethylsilylenebis (1-η⁵-indenyl)dichlorozirconium ( 4 ). The variations of polymerization activities in ethylene and in propylene for T_p from ?55°C to +70°C indicates a Michaelis Mention kinetics. The zirconocenium-propylene π-complex has a larger insertion rate constant but lower thermal stability than the corresponding ethylene π-complex. This catalyst copolymerizes ethylene and propylene with reactivity ratios of comparable magnitude r_E ? 4r_p. Furthermore, r_E.r_p ? 0.5 indicating random copolymer formation. Both 1 and 4 activated with methylaluminoxane (MAO) exhibit much slower polymerization rates, and, under certain conditions, a lower stereo-selectivity than the corresponding 1 ⁺ or 4 ⁺ system. © 1994 John Wiley & Sons, Inc.     

Anharmonic effects on theoretical IR line shapes of H-bonds

In the spirit of Y. Maréchal and A. Witkowski's [J. Chem. Phys. 48 (1968) 2697] work, one revisits, for weak H-bonds, the dependence of the angular frequency ω and of the equilibrium position q_e of the υ_X–H high frequency mode q, on the position coordinate Q of the low frequency υ_X–HY mode. One considers: ω=ω^o+bQ+cQ² and q_e=gQ+fQ². That leads to the anharmonic potential U: U=k₁q²+∑k_rQ^r+∑∑k_nmqⁿQ^m+k₁₅qQ⁵. Here k_r and k_mn (r=2–5, n=1,2 and m=1–4) are interrelated through b, c, g and f. By aid of the Hamiltonian involving U, we find the direct damped auto correlation function of υ_X–H, which, by Fourier transform, gives the IR spectral density (SD). When only b≠0, the SD is nothing but that given in a previous paper [P. Blaise, O. Henri-Rousseau, Chem. Phys. 243 (1999) 229]. When the adiabatic approximation is performed, this SD becomes that of N. Rösch and M. Ratner [J. Chem. Phys. 61 (1974) 3444] which reduces in turn to that of Maréchal and Witkowski in the absence of damping. With respect to b≠0, c produces a narrowing of the SD if c>0 and a subtle broadening if c<0. Besides, g induces the same narrowing for g>0 and g<0, while f gives subtle changes very sensitive to the sign of f and to the values of b, c and g. The situation b<0 and f>0 which is physically the most probable, leads to SDs which are the most evoking experimental profiles.     

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     

Temperature Modulated DSC (TMDSC) Applications and Limits of Phase Information, cp Determination and Effect Separation

The ADSC (Alternating DSC [1]) technique superimposes upon the conventional constant heating rate a periodically varying modulation [2–8]. The modulation creates high instantaneous heating rates which increases sensitivity. The low underlying constant heating rate is used to get better resolution. With ADSC it is possible to separate overlapping thermal effects without loss of sensitivity and to determine heat capacities under quasi-isothermal conditions. It has been reported that there are also some limitations for the use of the modulation techniques, i.e. that the accuracy of c_p determination is reduced at higher modulation frequencies due also to thermal diffusivity within the sample itself [9, 10]. In this contribution, the limitations given by the measuring system itself will be discussed. A key value is the limit frequency of the sensor arrangement. In the Mettler Toledo DSC821^c this frequency is approximately 1/3 Hz. From these findings the following recommendations amongst others can be given: for light mass crucibles, 30 s periods are reasonable with amplitudes not exceeding the heating/cooling rates possible. A blank and a calibration measurement will eliminate cell asymmetry and will enhance the accuracy of c_p measurements even at higher modulation frequencies. This revised version was published online in August 2006 with corrections to the Cover Date.