Pulsed NMR observation of ultradrawn polypropylene

Proton spin-spin relaxation times have been measured as a function of temperature for ultradrawn polypropylene with draw ratios λ up to 24. The three relaxation times T_2a (the longest), T_2i (intermediate), and T_2c (the shortest), observed for all the samples, have been ascribed to the relaxations of the amorphous, constrained amorphous, and crystalline components, respectively. T_2i and T_2a, which reflect the changes in structure and mobility in the noncrystalline regions, decrease with increasing λ; T_2i becomes saturated at λ > 9, whereas T_2a shows a substantial decrease up to λ = 24. The continued decrease in T_2a indicates that the constraint on the amorphous segments keeps increasing up to the highest λ. The associated mass fractions F_a, F_i, and F_c also change with λ. At λ < 9, the increasc in F_i with increasing λ is accompanied by a decrease in F_a, with F_c remaining unchanged. At higher λ, however, F_a is almost constant, and stepwise rises in F_c at about λ = 12 and 24 are accompanied by corresponding drops in F_i. It seems that, in this high draw ratio range, some of the taut molecules are fully extended and are in sufficiently good lateral register to transform into crystalline bridges. This conjecture is supported by the similarity in the λ dependence of F_c and the mass-fraction crystallinity obtained from the heat of fusion.     

Thermochemical properties of RE (Gly)4 Im (ClO4) 3 2H2O (RE = La,Pr, Nd,Sm, Eu)

The enthalpies of solution in water for five new light rare earth ternary complexes RE(Gly)₄Im(ClO₄)₃ 2H₂O (RE = La, Pr, Nd, Sm, Eu; Gly‐glycine; Im‐imidazole) were measured by means of a Calvet microcalorimeter. The empirical formula of enthalpy of solution (Δ_solH), relative apparent molar enthalpy (πL_i), relative partial molar enthalpy (L_i) and enthalpy of dilution (Δ_dllH_1,2) were drawn up by the data of enthalpies of solution of these complexes. From three plots of the values of standard enthalpy of solution Δ_sol H?, πL_i, L_i) versus the values of ionic radius (r) of the light rare earth elements, the grouping effect of lanthanide was observed, showing that the coordination bond between rare earth ion and ligand possesses a certain extent of the property of a covalent bond. The standard enthalpies of solution in water of similar complexes, Ce(Gly)₄Im(ClO₄)₃.2H₂O were estimated according to the plot of Δ_solH?, versus r.     

Conformation of nonideal hyperbranched polymer in ABn (n = 2, 4) type polymerization

The conformation of hyperbranched polymers from one pot polymerization with AB_n (n = 2, 4) type monomers, applying the reactive 3D bond fluctuation lattice model, are systematically studied using scaling relation R ～ N^λ, where R is the radius of gyration or the hydrodynamic radius of a hyperbranched polymer with the degree of polymerization N. The exponent λ was calculated at various monomer concentrations and group conversions. When the concentration of monomers with the equal reactivity of B groups increases from 0.1 to 0.9, the exponents λ_g and λ_h (corresponding to the radius of gyration and hydrodynamic radius, respectively) are in the ranges of 0.51–0.37 and 0.41–0.34 at the full conversion of A groups. Especially, we find that λ_g decreases linearly with the reaction conversion increasing. The ratio of z‐average radius, R_gz/R_hz, ranges from 1.08 to 1.32 and indicates that hyperbranched polymer is soft macromolecule with penetrable structure. In the case of AB₂ type monomer with unequal reactivities, λ displays complicated dependence on the reaction conversion and the reactivity ratio. The results of our simulation are consistent with those of experiments and theories, and valuable in better understanding the fundamental properties of hyperbranched polymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 610–616, 2010     

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.     

Initial Radical Separation after Photolysis of 2,2′‐Azobis(isobutyronitrile) (AIBN) in Solution: Modeling the Primary Cage Effect for Polar Radicals

There is a contradiction as to the initial spatial separation r_i of the two transient 2‐cyanoprop‐2‐yl radicals (Me₂ ? CN) formed by flash photolysis of 2,2′‐azobis(isobutyronitrile) (AIBN) in solvents of various viscosities. The cage effect, expressed in terms of the in‐cage termination probability of the resulting radicals, is predicted correctly by classical Langevin models assuming a decrease of r_i with increasing viscosity. However, the electron‐spin polarization of the radicals escaping the primary cage clearly indicates that the initial separation distance r_i is independent of the solution viscosity. This obvious discrepancy can be reconciled by accounting for the strong electric dipole moments of these radicals and the resulting inter‐radical dipole? dipole interaction potential. We propose a primary‐caging model for polar radicals in solution based on an attractive inter‐radical mean‐force potential. The model is applied to the flash photolysis of AIBN and shown to describe properly the viscosity dependence of both the in‐cage termination probability (cage effect) and the electron‐spin polarization of the escaping 2‐cyanoprop‐2‐yl radicals.     

Photoelectron Spectra and Electronic Structures of Some Acceptor‐Substituted Cyclopropanes: Linear Correlation of Substituent Effects on MO Energies with Molecular Structures

The relationship between electronic and geometrical structures in acceptor‐substituted cyclopropanes has been investigated by B3LYP DFT calculations and photoelectron (PE) spectroscopy. The spectra of cyclopropanecarbaldehyde ( 2 ), cyclopropanecarboxylic acid ( 3 ), cyclopropanecarboxylic acid methyl ester ( 4 ), nitrocyclopropane ( 5 ), isothiocyanatocyclopropane ( 6 ), cyanocyclopropane ( 7 ), and 1,1‐dicyanocyclopropane ( 8 ) have been analyzed. The first ionization potential (IP₁) of compounds 2 – 5 was found to be 0.1–0.4 eV higher than that of the analogous isopropyl derivatives indicating—contrary to expectation—that in these compounds the cyclopropyl group acts as a weaker electron donor than an isopropyl group. In the other compounds, IP₁ values are 0.4–1.1 eV lower than in the open‐chain congeners. The Walsh orbitals ω_S and ω_A of the three‐membered ring are substantially stabilized to different extents by interactions with substituent orbitals, and this is reflected in shortened distal and elongated vicinal C? C bonds. Although the nitro group in compound 5 causes large stabilizations of both ω_S and ω_A, their energy difference Δω remains rather small; this is in agreement with a relatively small difference Δr of the C? C bond lengths. For the investigated monosubstituted cyclopropanes 2 – 7 , the largest effects with respect to Δω and Δr are caused by the formyl group in carboxaldehyde 2 . Comparison of the results for nitriles 7 and 8 indicates that the effects of the cyano groups are additive. A linear relationship between Δω and Δr was established by B3LYP DFT calculations on geometrically distorted cyclopropane ( 1 ) and from the PE data of 2 – 8 .     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

聚二烯丙基二甲基氯化铵在质子交换膜表面静电自组装过程的热力学研究

本文通过热化学方法设计了PDDA滴定质子交换膜,并研究了高分子的静电自组装过程。通过非线性拟合数据分析,求出了自组装过程的焓变（ ）和结合常数（K）。根据该反应过程中的热力学参数,可知自组装过程是“焓驱动”反应。热量的放出代表着能量的降低,有利于反应的发生;而自由度的减小不利于反应的发生。对于每个离子键的形成,单分子DDA的焓变超过了PDDA,这是因为小分子能够更加自由地结合到膜上,而高分子PDDA有一定的位阻效应。     

Solitonic waves in polyene dications and principles of charge carrier localization in π‐conjugated organic materials

The quantum‐chemical investigations by ab initio method (restricted Hartree–Fock/6‐31G**) have been performed for a series of unsubstituted, monosubstituted, and disubstituted neutral polyenes and their double charged cations. The waves of charge alternation (characterized by the difference in the electron densities at the nearest carbon atoms or Δq function) and bond length alternation (characterized by the lengths difference of the nearest carbon–carbon bonds or Δl function) are reported. Comparisons are made with the corresponding monocationic polymethine molecules. We found that ionization by two electrons results in formation of two solitonic waves of charge alternation, rather than superposition of two overlapping solitonic waves into one. These waves behave similar to two independent elastic particles, which do not penetrate into each other despite the special confinement by the length of chromophore π‐system. In monosubstituted polyene dication, Δq and Δl functions contain two waves each; however, only one wave is mobile and sensitive to a change of the chemical nature of the terminal group, whereas the second wave remains practically unchanged. The introduction of one oxymethyl or phenyl terminal groups leads to a relatively small shift of the mobile wave from the center to a direction of the terminal group. The effect of the amino or tropilium terminal groups is much more pronounced and leads to a shift of the mobile wave to the end of the molecule. In disubstituted polyene dication, both solitonic waves become mobile and shift symmetrically to both ends. The general principles of the charge localization described in this study may be used in molecular design and fine‐tuning of the charge transport properties in plastic photovoltaics and other organic semiconducting materials. © 2012 Wiley Periodicals, Inc.     

Chiral Lithiated Allylic α‐Sulfonyl Carbanions: Experimental and Computational Study of Their Structure,Configurational Stability,and Enantioselective Synthesis

X‐ray crystal structure analysis of the lithiated allylic α‐sulfonyl carbanions [CH₂?CHC(Me)SO₂Ph]Li ? diglyme, [cC₆H₈SO₂tBu]Li ? PMDETA and [cC₇H₁₀SO₂tBu]Li ? PMDETA showed dimeric and monomeric CIPs, having nearly planar anionic C atoms, only O?Li bonds, almost planar allylic units with strong C?C bond length alternation and the s‐trans conformation around C1?C2. They adopt a C1?S conformation, which is similar to the one generally found for alkyl and aryl substituted α‐sulfonyl carbanions. Cryoscopy of [EtCH?CHC(Et)SO₂tBu]Li in THF at 164 K revealed an equilibrium between monomers and dimers in a ratio of 83:17, which is similar to the one found by low temperature NMR spectroscopy. According to NMR spectroscopy the lone‐pair orbital at C1 strongly interacts with the C?C double bond. Low temperature ⁶Li,¹H NOE experiments of [EtCH?CHC(Et)SO₂tBu]Li in THF point to an equilibrium between monomeric CIPs having only O?Li bonds and CIPs having both O?Li and C1?Li bonds. Ab initio calculation of [MeCH?CHC(Me)SO₂Me]Li ? (Me₂O)₂ gave three isomeric CIPs having the s‐trans conformation and three isomeric CIPs having the s‐cis conformation around the C1?C2 bond. All s‐trans isomers are more stable than the s‐cis isomers. At all levels of theory the s‐trans isomer having O?Li and C1?Li bonds is the most stable one followed by the isomer which has two O?Li bonds. The allylic unit of the C,O,Li isomer shows strong bond length alternation and the C1 atom is in contrast to the O,Li isomer significantly pyramidalized. According to NBO analysis of the s‐trans and s‐cis isomers, the interaction of the lone pair at C1 with the π* orbital of the CC double bond is energetically much more favorable than that with the “empty” orbitals at the Li atom. The C1?S and C1?C2 conformations are determined by the stereoelectronic effects n_C–σ_SR* interaction and allylic conjugation. ¹H DNMR spectroscopy of racemic [EtCH?CHC(Et)SO₂tBu]Li, [iPrCH?CHC(iPr)SO₂tBu]Li and [EtCH?C(Me)C(Et)SO₂tBu]Li in [D₈]THF gave estimated barriers of enantiomerization of ΔG^≠=13.2 kcal mol^?1 (270 K), 14.2 kcal mol^?1 (291 K) and 14.2 kcal mol^?1 (295 K), respectively. Deprotonation of sulfone (R)‐EtCH?CHCH(Et)SO₂tBu (94 % ee) with nBuLi in THF at ?105 °C occurred with a calculated enantioselectivity of 93 % ee and gave carbanion (M)‐[EtCH?CHC(Et)SO₂tBu]Li, the deuteration and alkylation of which with CF₃CO₂D and MeOCH₂I, respectively, proceeded with high enantioselectivities. Time‐dependent deuteration of the enantioenriched carbanion (M)‐[EtCH?CHC(Et)SO₂tBu]Li in THF gave a racemization barrier of ΔG^≠=12.5 kcal mol^?1 (168 K), which translates to a calculated half‐time of racemization of t_1/2=12 min at ?105 °C.     

Bond Length Alternation Observed Experimentally: The Case of 1H-Indazole

Bond length alternation is a chemical phenomenon in benzene rings fused to other rings, which has been mainly predicted theoretically. Its physical origin is still not clear and has generated discussion. Here, by using a strategy that combines microwave spectroscopy, custom-made synthesis and high-level ab initio calculations, we demonstrate that this phenomenon is clearly observed in the prototype indazole molecule isolated in the gas phase. The 1H-indazole conformer was detected by rotational spectroscopy, and its 17 isotopologues resulting from single and double heavy atom substitution (¹³C and ¹⁵N) were also unambiguously observed. Several experimental structures were determined and, in particular, the most useful semi-experimental equilibrium structure (r_e^SE), allowed determination of the heavy atom bond lengths to milli-Ångstrom precision. The experimentally determined bond length alternation is estimated to correspond to 60:40 contributions from the two resonant forms of 1H-indazole.     

Conformational structure of peptides containing dehydroalanine: Formation of β‐bend ribbon structure

α,β‐Unsaturated amino acids (dehydroamino acids) have been found in naturally occurring antibiotics of microbial origin and in some proteins. Due to the presence of the C_αC_β double bond, the dehydroamino acids influence the main‐chain and the side‐chain conformations. The lowest‐energy conformational state of the model tripeptides, Ac–X–ΔAla–NHMe, (X=Ala, Val, Leu, Abu, or Phe) corresponds to ϕ₁=−30°, ψ₁=120° and ϕ₂=ψ₂=30°. This structure is stabilized by the hydrogen bond between CO of the acetyl group and the NH of the amide group, resulting in the formation of a 10‐membered ring. In the model heptapeptide containing ΔAla at alternate position with Ala, Abu, and Leu, the lowest‐energy conformation corresponds to ϕ=−30° and ψ=120° for all the Ala, Abu, and Leu residues and ϕ=ψ=30° for all ΔAla residues. A graphical view of the molecule in this conformation reveals the formation of three hydrogen bonds involving the CO moiety of the ith residue and the NH moiety of the i+3th residue, resulting in a 10‐membered ring formation. In this structure, only alternate peptide bonds are involved in the intramolecular hydrogen‐bond formation unlike the helices and it has been named the β‐bend ribbon structure. The helical structures were predicted to be the most stable structures in the heptapeptide Ac–(Aib–ΔAla)₃–NHMe with ϕ=±30°, ψ=±60° for Aib residues and ϕ=ψ=±30° for ΔAla residues. The computational results reveal that the ΔAla residue does not induce an inverse γ‐turn in the preceding residue. It is the competitive interaction of small solvent molecules with the hydrogen‐bonding sites of the peptide which gives rise to the formation of an inverse γ‐turn (ϕ₁=−54°, ψ₁=82°; ϕ₂=44°, ψ₂=3°) in the preceding residue to ΔAla. The computational studies for the positional preference of ΔAla in the peptide containing one ΔAla and nine Ala residues reveals the formation of a 3₁₀ helical structure in all the cases with the terminal preferences for ΔAla, consistent with the position of ΔAla in the natural antibiotics. The extended structures is found to be the most stable for poly‐ΔAla. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 15–23, 1999     

Origin of the variation with vibrational and rotational state of the fine-structure constants in O2, SO and S2

Calculations of the spin—orbit part λ_SO of the fine-structure parameter λ have been performed at several internuclear distances for the molecules O₂, SO and S₂ in their ground (X ³Σ^?) states. Only the interaction with the lowest ¹Σ⁺ state was considered and two-centre integrals were neglected. λ_SO is found to make the dominant contribution to λ. The variation of the matrix elements in λ_SO with internuclear distance has been derived and when combined with expressions for the variation of the energy denominator in λ_SO enables the coefficients for the vibrational and rotational dependence of λ to be estimated. Excellent agreement with experiment is found.     

Alternation Tendency in Copolymerization

The number fractions of the alternate diads and triads and the average length of the alternate sequence may be used as the indices of the alternation tendency of binary copolymerizations. It is shown that these indices take on maximum values when the monomer feed ratio is such that [M₁]/[M₂] = (r₂/r₁)^1/2. The physical significance of the customary measure of the alternation tendency r₁r₂ is discussed.     

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

The problem of bond length alternation in linear extended ϕ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes C_NH_N with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.     

Defect Chemistry of Singly and Doubly Doped Ceria: Correlation between Ion Transport and Energetics

Earlier studies have shown a strong correlation between the enthalpy of formation, ΔH_f,ox, and the ionic conductivity, σ_i, near room temperature in doped ceria systems, which are promising solid electrolytes for intermediate‐temperature solid oxide fuel cells (IT‐SOFCs). The present work demonstrates that this correlation holds at the operating temperature of IT‐SOFCs, 600–700 °C. Solid solutions of Ce_1?xNd_xO_2?0.5x, Ce_1?xSm_xO_2?0.5x, and Ce_1?xSm_0.5xNd_0.5xO_2?0.5x are studied. The ΔH_f,ox at 702 °C is determined by considering the excess heat content between 25 and 702 °C combined with the value of ΔH_f,ox at 25 °C. Both σ_i and ΔH_f,ox show maxima at x=0.15 and 0.20 for the singly and doubly doped ceria, respectively, suggesting that the number of mobile oxygen vacancies in these solid solutions reaches a maximum near those compositions. An increase in temperature results in a shift of the maximum in both ΔH_f,ox and σ_i towards higher concentrations. This shift results from a gradual increase in dissociation of the defect associates.     

Polymer complexes. LXXVIII. Synthesis and characterization of supramolecular uranyl polymer complexes: Determination of the bond lengths of uranyl ion in polymer complexes

The UO₂(II) polymer complexes (1–5) of azo dye ligands 5(4`‐derivatives phenylazo)‐8‐hydroxy‐7‐quinolinecarboxaldehyde (HL_x) were prepared and characterized by elemental analysis, ¹H NMR, IR spectra, thermal analysis and X‐ray diffraction analysis (XRD). The molecular geometrical structures and quantum chemical of the ligands (HL_x) and their tautomeric forms (D and G) were calculated. Molecular docking between the HL_x ligands and their tautomeric form with two receptors of the breast cancer (1JNX) and the prostate cancer (2Q7K) was discussed. From the histogram of the HOMO–LUMO energy gap (ΔE) and the estimated free energy of binding of the receptors of prostate cancer (2Q7K) and breast cancer (1JNX) for the ligands (HL_x), it is observed that the ΔE values of the ligands (HL_x) increases in the order HL₂ < HL₃ < HL₄ < HL₁ < HL₅. The electronic structures and coordination were determined from a framework for the modeling of the formed polymer complexes. From the IR spectra of the polymer complexes, the symmetric stretching frequency υ₃ values of UO₂²⁺ were used for the determination of the force constant (F_U‐O (in 10^?8 N/?)) and the bond length (R_U‐O (?)) of the U–O bond by using Wilson, G. F. matrix method, McGlynn & Badger's formula and El‐Sonbati equations. The plot of the bond distance r_U‐O (r₁, r₂, r₃, and r_t) vs. υ₃ was showed straight lines with increase in the value of υ₃ and decrease in r_U‐O.     

Homogeneous Fermi liquid with ‘artificial’ repulsive inverse square law interparticle potential energy

A good deal is known by now on the so-called jellium model of the homogeneous electron liquid. However, much of the quantitative progress at experimentally realizable densities has come from quantal computer simulation. Therefore, we here consider a homogeneous Fermion liquid with ‘artificial’ repulsive interaction λ/(r_ij )² between Fermions i and j at separation r_ij . We discuss first of all the way the static structure function S(q), essentially the Fourier transform of the pair correlation function, is changed because of non-zero λ from the ‘Fermi hole’ form due entirely to Pauli principle effects between parallel spin Fermions. Unlike jellium with e ²/r_ij repulsive interactions, S(q) is proportional to q at long wavelengths, whereas the plasmon in jellium annulls the q term and S(q) is quadratic in q as q tends to zero. However for λ/(r_ij )² interactions, the coefficient of q appearing in the Fermi hole structure factor, is renormalized by particle repulsions. Then some discussion is given of Fermion quasiparticle lifetimes τ as the Fermi surface is approached. Arguments are presented that τ^?1 is proportional to |E???E _F| as E tends to the Fermi energy. This is already interesting, in fact, in connection with the jellium model and therefore an approximate analytic form of τ is finally derived.     

A Comparison of Dose Metrics to Predict Local Tumor Control for Photofrin‐mediated Photodynamic Therapy

This preclinical study examines light fluence, photodynamic therapy (PDT) dose and “apparent reacted singlet oxygen,” [¹O₂]_rx, to predict local control rate (LCR) for Photofrin‐mediated PDT of radiation‐induced fibrosarcoma (RIF) tumors. Mice bearing RIF tumors were treated with in‐air fluences (50–250 J cm^?2) and in‐air fluence rates (50–150 mW cm^?2) at Photofrin dosages of 5 and 15 mg kg^?1 and a drug‐light interval of 24 h using a 630‐nm, 1‐cm‐diameter collimated laser. A macroscopic model was used to calculate [¹O₂]_rx and PDT dose based on in vivo explicit dosimetry of the drug concentration, light fluence and tissue optical properties. PDT dose and [¹O₂]_rx were defined as a temporal integral of drug concentration and fluence rate, and singlet oxygen concentration consumed divided by the singlet oxygen lifetime, respectively. LCR was stratified for different dose metrics for 74 mice (66 + 8 control). Complete tumor control at 14 days was observed for [¹O₂]_rx ≥ 1.1 mm or PDT dose ≥1200 μm J cm^?2 but cannot be predicted with fluence alone. LCR increases with increasing [¹O₂]_rx and PDT dose but is not well correlated with fluence. Comparing dosimetric quantities, [¹O₂]_rx outperformed both PDT dose and fluence in predicting tumor response and correlating with LCR.     

Elastic behavior of ring polymer chains

In this article, the conformational properties and elastic behaviors of ring polymers in the process of tensile elongation are investigated with the Monte Carlo method and the bond fluctuation model. The ratio of the mean‐square diameter <d²> to the mean‐square radius of gyration <S²> increases with the elongation ratio, λ, and the instantaneous shape of ring polymers is more symmetric than that of linear chains in the process of tensile elongation. Here <d²> for ring polymers rather than the mean‐square end‐to‐end distance <R²> for linear polymers is defined as the average of squared distances between two segments separated by N/2 bonds, where N represents the total number of bonds. Local quantities, that is, the mean‐square bond length <b²> and the mean bond angle <θ> increase with λ, especially for short ring chains. The <d²> and <S²> have the same relationship with the chain length, N, that is, <d²> ～ N^1.130±0.020 and <S²> ～ N^1.160±0.013 for a different λ. Some thermodynamics properties are also addressed here. The average energy per bond <U> decreases with λ and the average Helmholtz free energy and elastic force f increase with λ, especially for short ring chains. Comparisons with linear chains are also made. These investigations may provide insight into the elastic behaviors of ring polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 223–232, 2005