Role of diffusion in gel permeation chromatography

A theory is developed that describes the diffusion of solute into the gel particles during a gel permeation chromatographic experiment. The particles are treated as homogeneous spheres of radius a, into which diffusion takes place with diffusion coefficient D_s. The concentration in the mobile phase at any level at any time is supposed to be uniform throughout the cross-section of the column. It is shown that in the usual columns the effect of diffusion in the mobile phase is unimportant. A determinative quantity in the process is the parameter a²/D_st, where t is the time. For large values of a²/D_st an explicit expression for concentration versus time in the mobile phase at the end of the column is derived [eq. (26) and Fig. 1]. It shows a relatively long tail at large efflux volumes V, where the concentration varies at V^?3/2. For arbitrary values of a²/D_st the first three moments of the concentration versus time curve are calculated [eqs. (33)–(37)]. Pronounced skewness of the curve is found unless a²/D_st is small.     

Static dipole and quadrupole polarizabilities of alkaline earth atoms

Static dipole and quadrupole polarizability (α_d and α_q, respectively) values of coupled Hartree–Fock quality have been calculated for the alkaline earth atoms Be(2s), Mg(3s), Ca(4s), and Sr(5s) using a method based on the many-body perturbation theory. The present values of α_d and α_q for Be and α_d for Mg are in excellent agreement with the other available results of similar accuracy. The CHF calculations of α_d for Sr and α_q for Mg, Ca, and Sr are being reported for the first time.     

Isentropic Compressibility Changes of Mixing for 1,3-Dioxolane or 1,4-Dioxane + Water + Propanol Ternary Mixtures

Speed of sound data, u_ijk, of 1,3-dioxolane or 1,4-dioxane(i) + water(j) + propan-1-ol or propan-2-ol(k) ternary mixtures and their sub-binary mixtures, u_ij, of 1,3-dioxolane or 1,4-dioxane(i) + water or propan-1-ol or propan-2-ol(j) and water(i) + propan-1-ol or propan-2-ol(j) mixtures have been measured over the entire composition range at 308.15 K. Isentropic compressibility changes of mixing, (κ_s^E)_ij and (κ_s^E) _ijk, for the binary and ternary mixtures have been determined by employing the observed speeds of sound data and densities (calculated from their molar excess volumes data). The (κ_s^E) _ij and (κ_s^E) _ijk values have also been predicated by the graph theoretical approach and the Flory theory. It has been observed that (κ_s^E) _ij and (κ_s^E) _ijk predicted by the graph theoretical approach compare well with their corresponding experimental values.     

6,12-二乙炔基茚并[1,2-b]芴系列衍生物的非线性光学性质

采用密度泛函理论(DFT) CAM-B3LYP方法对6,12-二乙炔基茚并[1,2-b]芴系列衍生物的极化率(α_s)和第二超极化率(γ_s)进行研究. 结果表明, 此类分子具有较大的γ_s值. 用乙炔基硅烷基和氧原子取代茚并[1,2-b]芴分子6,12位的氢原子后, 分子的几何构型发生改变, 进而影响其非线性光学(NLO)性质. 连接乙炔基硅烷基的分子α_s值和γ_s值均增大, 而连接氧原子的分子α_s值和γ_s值均减小. 茚并[1,2-b]芴环2,8位取代基R(R=H, F, CH₃)的不同, 对分子的γ_s值也有一定的影响, R为CH₃时分子的α_s值和γ_s值均较大. 由含时密度泛函理论(TD-DFT)方法计算的吸收光谱分析可知, 与茚并[1,2-b]芴系列分子相比, 引入乙炔基硅烷基的分子共轭性增强, 最大吸收波长红移; 引入氧原子的分子几何结构扭曲, 共轭性降低, 最大吸收波长蓝移.     

Ab initio CPHF calculations of the static polarizability and second hyperpolarizability of small molecules: Comparisons between standard and moderately large basis sets augmented with diffuse functions

Static polarizability and second hyperpolarizability have been calculated for a number of small molecules? CO₂, OCS, CS₂, C₂H₂, C₂H₆, C₃H₈, cyclo-C₃H₆, C₃H₄, C₃H₆, SiH₄, Si₂H₆? in the framework of the coupled-perturbed Hartree-Fock (CPHF ) theory. The linear and nonlinear coefficients have been calculated with standard Gaussian basis sets and 3-21G bases moderately enlarged with diffuse functions. It is shown that the parallel component of the polarizability saturates rapidly, which suggests that a 3-21G basis containing s and p diffuse functions is sufficient to reproduce α_zz. For the α_xx and α_yy components, a 3-21G basis with s, p, and d diffuse functions is required. In general, the concordance between α computed with this basis set and the experimental static polarizability is at least of the order of 80%. On the contrary, the computation of the second hyperpolarizability with the same basis set for CO₂, CS₂, and C₂H₂ gives values that are 30% too low, compared to the experimental value. Better results are observed for ethane, propane, and cyclopropane for which the error is lower than 50%. The better agreement observed for the saturated compounds can probably be explained by their saturated character.     

Ab initio reaction path for cisplatin interaction with L‐cysteine and L‐methionine

Ab initio calculations are used to track the reaction pathway of interaction between cisplatin and the sulfur‐containing amino acids cysteine (Cys) and methionine (Met). Structures of all reactive species as well as thermodynamic and kinetic properties were calculated and discussed based on the role played by the level of theory. Twenty‐three different levels of theory were examined including HF, DFT, and perturbation theory at MP2 and MP4(SDQ) orders. The rate constant for a second‐order associative ligand exchange mechanism (k₂) was calculated by means of transition state theory. This quantity is quite sensitive to small fluctuation of activation free energy, therefore is a good benchmark to assess the performance of different methods of calculations. The k₂ values predicted by DFT methods were in best agreement with experiment, found equal to (10²k₂ in M^?1 s^?1) 3.42 for Met (PBE1PBE) and 1.90 for Cys (B3P86). The experimental values are 3.6 and 2.2 for Met and Cys, respectively. The solvent effect plays a primary role to the kinetic properties, accounting for ～30% of the activation Gibbs free energy. The outcomes from the present study promptly show the adequacy of distinct theoretical approaches to describe the reactivity of cisplatin, thus might be useful for further studies involving other Pt(II) complexes. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Excess Isentropic Compressibilities for 1,3-Dioxolane or 1,4-Dioxane <Emphasis Type="Italic">+</Emphasis> Water <Emphasis Type="Italic">+</Emphasis> Formamide or N,N-Dimethylformamide Ternary Mixtures at 308.15 K

Speeds of sound, u_ijk, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + formamide or dimethylformamide (k) ternary mixtures and of their binary subsystems, u_ij, of 1,3-dioxolane or 1,4-dioxane (i) + formamide or dimethylformamide (j), and water (i) + formamide or dimethylformamide (j) have been measured over the entire composition range at 308.15 K. The experimental data have been used to evaluate the excess isentropic compressibilities of binary (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using their densities calculated from molar excess volume data. The Moelwyn-Huggins concept [M. L. Huggins, Polymer 12, 389 (1971)] of interaction between the surfaces of components of a binary mixture has been employed to evaluate the excess isentropic compressibilities (using the concept of connectivity parameter of third degree of a molecule, ³ξ, which in turn depends on its topology) of binary mixtures, and this method has been extended to predict excess compressibilities of ternary mixtures. Values of (κ_s^E)_ij and (κ_s^E)_ijk have also been calculated by the Flory theory. It was observed that (κ_s^E)_ij and (κ_s^E)_ijk predicted by the Moelwyn-Huggins approach compare well with calculated and experimental values.     

Molecular modeling of hydration properties of hydrophobic ions Li<Superscript>+</Superscript>@C<Subscript>60</Subscript> and K<Superscript>+</Superscript>@C<Subscript>60</Subscript>

The Gibbs free energies of solvation (ΔG _s) and the electronic structures of endohedral metallofullerenes M⁺@C₆₀ (M⁺= Li⁺, K⁺) were calculated within the framework of the density functional theory and the polarizable continuum model. In water environment, the equilibrium position of K⁺ is at the center of the fullerene cavity whereas that of Li⁺ is shifted by 0.14 nm toward the fullerene cage. The Li⁺ cation is stabilized by interactions with both the fullerene and solvent. The equilibrium structures of both endohedral metallofullerenes are characterized by very close ΔG _s values. In particular, the calculated ΔG _s values for K⁺@C₆₀ are in the range from −124 to −149 kJ mol⁻¹ depending on the basis set and on the type of the density functional. Molecular dynamics simulations (TIP3P H₂O, OPLS force field, water sphere of radius 1.9 nm) showed that the radial distribution functions of water density around C₆₀ and M⁺@C₆₀ are very similar, whereas orientations of water dipoles around the endohedral metallofullerenes resemble the hydration pattern of isolated metal ions.     

Salting-in of alcohols in aqueous solutions by tetraalkylammonium bromides at the freezing temperature

The freezing-point depression of the ternary systems tetraalkylammonium bromides-t-butanol-water for the first five homologs of R₄NBr was measured. In the case of Bu₄NBr, the effect of size of the alcohol (methahol ton-butanol) was also investigated. From the corresponding freezing-point data for the binary systems the apparent salting constants were calculated. The true salting constantsk _s were obtained by extrapolation to infinite dilution. These are all very close to zero at the freezing temperature. From the corresponding thermochemical data the temperature dependence ofk _s was calculated, and above 5°C all the R₄NBr salts int-butanol; the salting-in increases with temperature and with the size of the hydrophobic cations. The scaled-particle theory is at present the only one which can account semiquantitatively for the temperature dependence of the salting-in effect. On leave of absence from Chemistry Department, The University, Sheffield S3 7HF, England To whom correspondence should be addressed.     

Equilibrium dielectric properties of butanediols

Experimental investigations of static dielectric permittivity (ɛ _s ) for 1,3-, 1,4-, and 2,3-butanedilos determined in the temperature range from 283 to 423 K at 1 MHz and a density of (ρ) are presented. The values of the experimental correlation factor, g _exp, which characterizes the correlation of the orientation of molecules in a liquid due to short-range oriented intermolecular interactions, are calculated according to the Onsager-Kirkwood-Frohlich theory. Its values are used for the judgment of a character of a short-range orientation order in a liquid.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Dynamic viscosity of dilute aqueous solutions of poly(acrylic acid) at frequencies of 2–500 kHz

The dynamic viscosity of aqueous solutions of poly(acrylic acid) at a polymer concentration of ca. 0.15 g/100 ml has been measured at frequencies from 2 to 500 kHz as a function of degree of polymerization P, degree of neutralization α, and salt (NaCl) concentration C_s. Relaxation spectra have been obtained from the dynamic viscosity. The spectra in the short relaxation time region can be approximated by the Zimm theory for the conformational relaxation of nonionic polymers. The maximum relaxation time τ₁ of the Zimm spectra is proportional to P² and depends rather moderately on α and C_s. Increased deviation is found, however, in the long relaxation time region, in particular for high values of P and α and low values of C_s. The major part of the deviation is interpreted in terms of rotational relaxation of a molecule as a whole. The rotational relaxation time τ_R is proportional to P³ and increases with increasing α and decreasing C_s. The remaining part of the excess spectra located between τ₁ and τ_R is ascribed to the deviation of the conformational relaxation from the Zimm theory arising from ionization of the polymer.     

Rheology of polystyrene/poly(vinyl methyl ether)blends near the phase transition

Mixtures are expected to show anomalous behavior in their viscoelastic properties close to a critical point. In this study, the reheological behavior of blends of polystyrene and poly (vinyl methyl ether) below, close to, and above the phase separation temperature T_s was investigated. Rheological measurements were carried out at three different compositions in the melt. Below and far from T_s, a satisfactory superposition of the storage and loss moduli G' and G″ was observed at all temperatures and frequencies. Close to T_s deviations were observed for G' at low frequencies (the so-called terminal zone). Above T_s G″ values was still observed over the whole range of frequencies and temperatures. The deviations observed for G' near T_s can be interpreted as due to the presence of significant concentration fluctuations. Plots of log (G'/G″²) as a function of temperature were shown to be sensitive to this anomalous behavior.     

X-ray scattering by water molecules studied by using synchrotron radiation

The energy spectra of free water molecules were measured at scattering angles 2θ ranging from 10.5° to 75.7°, using an angle-dispersive-type diffractometer and synchrotron radiation as an X-ray source. A silicon (111) monochrometer was used to obtain incident X-rays with the wavelengths of (1.543/n) Å (n = 1,3,4,5). Observed inelastic scattering peaks are clearly separated from eleastic ones at s values [s = (4π/λ) sin Å] larger than 8 Å^?1. The increase of the separation with an increasing s value was consistent with the classical theory of the Compton shift. The total (elastic plus inelastic) intensities were obtained over a range of s = 0.74–5.0 Å^?1. Experimental difference intensities Δσ_ee and Δσ_ne were obtained separately by combining the X-ray and high-energy electron scattering data. The experimental results are in reasonable agreement with the theoretical intensities calculated from SCF and CI molecular wave functions with a basis set of double-zeta plus polarization functions. © 1994 John Wiley & Sons, Inc.     

Topological Investigations of Some Cyclic Ether-Water-Alkanol Ternary Mixtures: Molar Excess Volumes

Molar excess volumes, V_ijk^E, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + propan-1-ol or + propan-2-ol (k) ternary mixtures have been determined dilatometrically over the entire composition range at 308.15 K. The resulting data have been analyzed in terms of (1) the graph theoretical approach (which involves the topology of the mixture constituents), (2) the Sanchez and Locombe theory and (3) the Flory theory. It was observed that V_ijk^Evalues predicted by the graph theory compare reasonably well with their corresponding experimental values. However, although V_ijk^E values calculated by the Sanchez and Lacombe and Flory theories are of same sign and magnitude, the qualitative agreement is poor.     

A Simple Equivalent Bond Orbital Model for the Rationalization of the C2s-Photoelectron Spectra of the Higher n-Alkanes,in Particular of Polyethylene

The higher homologues of n-alkanes H(CH₂)_NH with N > ∽ 13 yield photoelectron spectra in which the C_2s-bands merge to form a double humped, unresolved C_2s-band system in the interval of I=15 to 25 eV [1]. It is shown that with the help of an equivalent bond orbital model one can derive a closed formula, which gives the individual C_2s-band positions I=?ε_j in function of N and j with sufficient accuracy, assuming the validity of Koopmans' approximation. The calculated I values (j=1 to N) folded with an appropriate shape function for the individual C_2s-bands reproduce the observed Franck-Condon envelope of the C_2s-band system within narrow limits of error. However, a comparison of the observed total width of the C_2s-band system with the computed one, indicate that for large n-alkanes (N≥ ∽ 13), the simplification which consists of taking into account only the interaction matrix elements between vicinal bond orbitals [2], is no longer a satisfactory one.     

ESR single-crystal study of radical and radical-pair formation in some γ-irradiated vinyl monomers

Single crystals of methyl methacrylate (MMA), methyl acrylate (MA), and acrolein (A) have been prepared by a low-temperature technique. After irradiation with γ-rays at 77°K the paramagnetic species were identified by ESR spectroscopy. MMA gave a seven-line single spectrum from radicals formed by hydrogen addition. The hyperfine coupling constants are slightly anisotropic with a mean value of 22 G. Radical pairs were observed as ΔM_s = 1 and ΔM_s = 2 transitions; the hyperfine coupling was 11 G. From the strongly anisotropic dipolar interaction, upper limits for the distances between the pair components were calculated to be 5.45 Å and 6.3 Å. MA gave a five-line main spectrum with the same hyperfine coupling values and two radical pairs, one with a distance 5.9 Å between the components. In a there was also a strongly anisotropic interaction. The hyperfine coupling of the ΔM_s = 2 transition was 9.8 G. The number of radical pairs compared to the total number of radicals increases only slightly with the radiation dose. This makes it likely that pair formation occurs in the spurs and blobs formed by the γ-radiation. At an increased temperature the radical pairs disappeared; the spectrum of MMA changed to that characteristic of propagating polymer radicals.     

Structure and photoelectron spectral properties of I(-)·nCO2 clusters: an ab initio study

Structures and photoelectron spectral properties of I^??nCO₂ (n=1–7) clusters are presented at the level of second‐order Møller–Plesset perturbation theory with relativistic corrections. Triple split‐valence 6‐311++G(d,p) basis set functions are employed herein. It is observed that the CO₂ molecules approach the I^? anion from one side in all the clusters and that I^??nCO₂ clusters prefer the surface structure. The calculated vertical detachment energy of these clusters is in excellent agreement with the reported experimentally measured values (within 4 %). Efforts are also made to extract vertical detachment energy of large size of clusters, including the bulk. The extracted vertical detachment energy values for larger clusters (n=8–13) by employing the microscopic theory‐based expression are also close (within 4 %) to that of the experimentally measured values.     

New Architectures for Side Chain Liquid Crystalline Polymers with Chiral Smectic C Mesophases

All attempts at synthesizing side chain liquid crystalline polymers (SCLCPs) with chiral smectic C (s_c*) mesophases simply functionalize one terminal group of the mesogen with a chiral substituent and attach the other terminus to the polymer backbone through a spacer. If a s_c* mesophase is observed, it is usually in the less desirable s_c*-s_A phase sequence. We propose that SCLCPs with laterally attached (vs terminally attached) mesogens offer an ideal architecture for obtaining s_c* meso- phases. This is because extended mesogens symmetrically disubstituted with long n-alkoxy groups can be attached to the polymer backbone through a chiral spacer. Thus, mesogens which typically form the desirable s_c*-n phase sequence can be used, and the chiral group can be introduced at the center of the mesogen which should result in high values of spontaneous polarization. We are not only using mesogens which exhibit s_c*-n phase sequences, but are also attempting to induce smectic layering into laterally attached systems which typically form nematic mesophases by electron-donor-acceptor interactions and immiscible hydrocarbon/fluorocarbon components. Smectic layering was successfully induced in 2,5-bis[(4'-n-alkoxybenzoyl)oxy]toluenes when the n-alkoxy substituents were terminated with perfluorinated segments.     

Thermodynamic and transport properties of binary liquid mixtures of cyclohexanol with isomeric chlorotoluenes

Densities (ρ) at different temperatures from 303.15 to 318.15 K, speeds of sound (u) and viscosities (η) at 303.15 K were measured for the binary mixtures of cyclohexanol with 2-chlorotoluene, 3-chlorotoluene and 4-chlorotoluene over the entire range of composition. The excess volumes (V^E) for the mixtures have been computed from the experimental density data. Further, the deviation in isentropic compressibilities (Δκ_s) and deviation in viscosities (Δη) for the binary mixtures have been calculated from the speed of sound and viscosity data, respectively. The V^E values and Δκ_s values were positive and Δη data were negative for all the mixtures over the whole range of composition at the measured temperatures. The calculated excess functions V^E, Δκ_s and Δη were fitted to Redlich–Kister equation. The excess functions have been discussed in terms of molecular interactions between component molecules of the binary mixtures.