Diffusion and equilibrium swelling of macromolecular networks by their linear homologs

Polydimethylsiloxane (PDMS) networks having strands of molecular weight in the range 11,000–36,000 have been prepared by endlinking linear PDMS molecules of these molecular weights with a tetrafunctional linking agent. Absorption of a series of homologous linear PDMS molecules by the resulting PDMS networks has been investigated. The diffusion coefficients at 70°C were found to be rather large, 1 × 10^?12–6 × 10^?12 m²/s, and approximately inversely proportional to the molecular weight of the diffusing liquid, over the range 5000–38,000. The amount of liquid absorbed at equilibrium was relatively small, 10–80%, in good agreement in all cases with an especially simple version of the Flory–Huggins theory when the heat of mixing is made vanishingly small and only entropic terms are retained.     

Fractional moments and moments of time in boundary diffusion of random coil polymers

Equations for the evaluation of experiments in free diffusion of random coil polymers in dilute solution are derived. Moments of the concentration function with respect to the cell co-ordinate of whole or fractional order are employed. Weight-average diffusion coefficients raised to any positive power and hence negative moments of the molecular weight distribution can be obtained. Among the latter is M_n. Theta conditions are not required. For a narrow-distribution polymer, the linear concentration effect is eliminated in a simple way without additional experiments. Corresponding equations referring to moments with time as the variable of integration are deduced. These should be applied to experiments in bounded diffusion. The statistical weight in the averages is the reciprocal of the weight given by using moments of the cell co-ordinate. Thus the series of weight averages of diffusion coefficients raised to a negative power and positive moments of the molecular weight distribution are obtainable.     

Concentration dependence of the diffusion coefficient of polydisperse polystyrene in dilute solution

The concentration dependence of the diffusion coefficients (D) of two different polystyrenes in toluene was measured. The concentration dependence of D of a standard monodisperse sample (M = 498,000) for concentrations up to 1 · 25 g/dl is not linear. The dependence is adequately described by the theory of dilute polymer solutions up to about 0·7 g/dl and the second virial coefficients of the osmotic pressure can be evaluated. For a polystyrene sample having a broad molecular weight distribution, the concentration dependence of four different average diffusion coefficients was determined so indirectly characterizing the molecular weight distribution. These dependences are not linear and differ from each other owing to the different sensitivity of the individual averages to high-molecular and low-molecular weight fractions. The apparent distribution of the diffusion coefficients becomes narrower with increasing concentration. When evaluating polydispersity from the free diffusion data obtained in good solvents, it is necessary to determine directly the differential diffusion coefficients; an extrapolation of the integral diffusion coefficients can be misleading.     

Simulation of size-exclusion chromatography distribution coefficients of comb-shaped molecules in spherical pores comparison of simulation and experiment

Simulations of the distribution coefficients of linear polymers and regular combs with various spacings between the arms have been performed. The distribution coefficients were plotted as a function of the number of segments in order to compare the size exclusion chromatography (SEC)-elution behavior of combs relative to linear molecules. By comparing the simulated SEC-calibration curves it is possible to predict the elution behavior of comb-shaped polymers relative to linear ones. In order to compare the results obtained by computer simulations with experimental data, a variety of comb-shaped polymers varying in side chain length, spacing between the side chains and molecular weights of the backbone were analyzed by SEC with light-scattering detection. It was found that the computer simulations could predict the molecular weights of linear molecules having the same retention volume with an accuracy of about 10%, i.e. the error in the molecular weight obtained by calculating the molecular weight of the comb-polymer based on a calibration curve constructed using linear standards and the results of the computer simulations are of the same magnitude as the experimental error of absolute molecular weight determination.     

Precise measurement of the self-diffusion coefficient for poly(ethylene glycol) in aqueous solution using uniform oligomers

Uniform poly(ethylene glycol) (PEG) oligomers, with a degree of polymerization n=1-40, were separated by preparative supercritical fluid chromatography from commercial monodispersed samples. Diffusion coefficients, D, for separated uniform PEG oligomers were measured in dilute solutions of deuterium oxide (D(2)O) at 30 degrees C, using pulsed-field gradient nuclear magnetic resonance. The measured D for each molecular weight was extrapolated to infinite dilution. Diffusion coefficients obtained at infinite dilution follow the scaling behavior of Zimm-type diffusion, even in the lower molecular weight range. Molecular-dynamics simulations for PEG in H(2)O also showed this scaling behavior, and reproduced close hydrodynamic interactions between PEG and water. These findings suggest that diffusion of PEG in water is dominated by hydrodynamic interaction over a wide molecular weight range, including at low molecular weights around 1000.     

Diffusion des additifs du polyethylene—I: Influence de la nature du diffusant

Chemical efficiency and stabilizer migration are the most important factors to be considered in connection with the ageing of polyethylene. This paper gives diffusion coefficients and solubilities for various industrial additives in low density polyethylene. The results, together with activation energies for diffusion, allow study of the diffusion process. It seems that it is necessary to consider deformations of the diffusing molecules and the polymer molecules. Additives of low molecular weight diffuse as gases, those of high molecular weight behave like polymer chains in self-diffusion.     

Probing the dimensions of semi-rigid inner functionalised U-shaped bis-porphyrin cavities

The synthesis of a series of open U-shaped bis-porphyrin cavity molecules is described, with bridged bicyclic backbones to confer rigidity, and a pendant substituted aromatic probe unit suspended on the inside of the cavity. The dimensions and flexibility of the bis-zincporphyrin cavity were probed using several different techniques. Initially the molecular ruler concept was employed, using flexible bidentate ligands as guests with a range of possible linear dimensions. Secondly, NMR methods were employed with rigid bidentate ligand guests of fixed lengths, and thirdly diffusion based NMR methods were utilised. The range of inter-porphyrin distances estimated by these methods suggests that these types of open-cavity systems have a surprising degree of flexibility.     

The application of the perrin–agishev model for calculation of the translational diffusion coefficients of liquid dichloroalkanes

The article presents the translational diffusion coefficients calculated for dichloroalkanes series C _n H_{2 n} Cl₂ (where n =?6, 8, 10, 12) in the liquid state, with the use of the Perrin and Agishev model. It has been shown that the molecules of dichloroalkanes assume a mutually parallel arrangement in three possible coordinations. The model of arrangement, orientations and packing of the molecules has been presented. The activation parameters of the compounds studied have been discussed. The physical and structural properties of the liquids studied (macroscopic density, electron density and molecular weight) are correctly described within the van der Waals model predicting their orientations and packing. The formulae linking the diffusion, viscosity and temperature for the liquids have been presented. The assumption that each molecule can be approximated by an ellipsoid of the semiaxes lengths a, b and c has been justified. The translations become slower with increasing volume and weight of the molecule. The diffusion coefficients decrease with increasing molecular weight.     

气体在无定型聚异戊二烯中扩散的分子动力学模拟

采用分子动力学模拟方法研究了多个温度下氧气、氮气及甲烷在无定型顺式1,4-聚异戊二烯中的扩散系数。在模拟过程中,使用COMPASS力场作为分子力场。应用COMPASS力场的势能函数,聚合物的密度及玻璃化转变温度的计算结果与实验值有较好吻合。在278-378 K的温度范围内,通过3或1.5 ns时长的正则系综动力学模拟,计算了不同温度下氧气、氮气及甲烷的扩散系数。结果表明,根据爱因斯坦关系式计算得到的扩散系数与实验结果比较接近。对气体扩散系数与温度的关系进一步研究,发现在278-378 K温度范围内,甲烷的扩散系数随温度变化的半对数曲线图是非线性的,而氧气和氮气的扩散系数随温度变化的半对数曲线图是线性的。本文研究结果有助于理解温度对气体扩散的影响机制,并为高温下气体在天然橡胶中扩散系数的测定及天然橡胶热氧老化建模分析提供依据。     

Molecular dynamics and composition of crude oil by low‐field nuclear magnetic resonance

Nuclear magnetic resonance (NMR) techniques are widely used to identify pure substances and probe protein dynamics. Oil is a complex mixture composed of hydrocarbons, which have a wide range of molecular size distribution. Previous work show that empirical correlations of relaxation times and diffusion coefficients were found for simple alkane mixtures, and also the shape of the relaxation and diffusion distribution functions are related to the composition of the fluids. The 2D NMR is a promising qualitative evaluation method for oil composition. But uncertainty in the interpretation of crude oil indicated further study was required. In this research, the effect of each composition on relaxation distribution functions is analyzed in detail. We also suggest a new method for prediction of the rotational correlation time distribution of crude oil molecules using low field NMR (LF‐NMR) relaxation time distributions. A set of down‐hole NMR fluid analysis system is independently designed and developed for fluid measurement. We illustrate this with relaxation–relaxation correlation experiments and rotational correlation time distributions on a series of hydrocarbon mixtures that employ our laboratory‐designed downhole NMR fluid analyzer. The LF‐NMR is a useful tool for detecting oil composition and monitoring oil property changes. Copyright © 2016 John Wiley & Sons, Ltd.     

Measuring the mutual diffusion coefficient for dodecyl acrylate in low molecular weight poly(dodecyl acrylate) with laser line deflection (Wiener's Method) and the fluorescence of pyrene

Diffusion of small molecules into glassy polymers is quite complicated and almost always non-Fickian. Little work has been done with the diffusion of low molecular weight polymers that are liquids at room temperature (such as poly(dodecyl acrylate)) into their miscible monomers. We have studied three molecular weights under 20 000 to determine if poly(dodecyl acrylate) diffusion into dodecyl acrylate could be treated with Fick's law and if so to determine the values of the diffusion coefficients. We compare two methods for measuring the diffusion of dodecyl acrylate into poly(dodecyl acrylate): We used laser line deflection (Wiener's method) and improved upon the method from published reports. We also used the dependence of pyrene's fluorescence on the viscosity to measure the concentration distribution, and thus to extract the diffusion coefficient. After an initial relaxation period, diffusion in all cases followed Fick's law with a single concentration-independent diffusion coefficient. Comparison of the diffusion coefficients obtained by both methods yielded the same order of magnitude for the diffusion coefficients (10(-7) cm2/s) and showed the same trend in the dependence on the average molecular weight of the polymer (a decrease in the diffusion coefficient with an increase in the molecular weight).     

Chemistry of Anthracene–Acetylene Oligomers XXV: On‐Surface Chirality of a Self‐Assembled Molecular Network of a Fan‐Blade‐Shaped Anthracene–Acetylene Macrocycle with a Long Alkyl Chain

An anthracene cyclic dimer with two different linkers and a dodecyl group was synthesized by means of coupling reactions. The calculated structure had a planar macrocyclic π core and a linear alkyl chain. Scanning tunneling microscopy observations at the 1‐phenyloctane/graphite interface revealed that the molecules formed a self‐assembled monolayer that consisted of linear striped bright and dark bands. In each domain, the molecular network consisted of either Re or Si molecules that differed in the two‐dimensional chirality about the macrocyclic faces, which led to a unique conglomerate‐type self‐assembly. The molecular packing mode and the conformation of the alkyl chains are discussed in terms of the intermolecular interactions and the interactions between the molecules and the graphite surface with the aid of MM3 simulations of a model system.     

Diffusion with molecular association in chloroform + triethylamine and chloroform + dioxane mixtures

The Taylor dispersion method is used to measure the binary mutual diffusion coefficients of chloroform + triethylamine and chloroform +1,4-dioxane at 25°C. The components of these mixtures associate, forming chloroform-triethylamine and chloroform-dioxane, (chloroform)₂-dioxane molecular complexes. A modified Hartley-Crank equation is developed to express the binary diffusion coefficient as a weighted average of the diffusion coefficients of the free molecules and the molecular complexes. Counterintuitively, the contribution made by each molecular complex to the overall diffusion coefficient vanishes when the concentration of the complex reaches its maximum value. The measured and fitted diffusion coefficients agree within 3% or better over the complete composition range.     

New thermal diffusion coefficient measurements for hydrocarbon binary mixtures: viscosity and composition dependency

New thermal diffusion coefficients of binary mixtures are measured for n-decane-n-alkanes and 1-methylnaphthalene-n-alkanes with 25 and 75 wt % at 25 degrees C and 1 atm using the thermogravitational column technique. The alkanes range from n-pentane to n-eicosane. The new results confirm the recently observed nonmonotonic behavior of thermal diffusion coefficients with molecular weight for binary mixtures of n-decane- n-alkanes at the compositions studied. In this work, the mobility and disparity effects on thermal diffusion coefficients are quantified for binary mixtures. We also show for the binary mixtures studied that the thermal diffusion coefficients and mixture viscosity, both nonequilibrium properties, are closely related.     

Distinct Diffusion in Macromolecule‐Solvent Mixtures

Summary: The specificity of interactions between pairs of molecules cannot be explicitly given by experimental transport coefficients such as intra‐ or mutual diffusion coefficients. But a microscopic interpretation of the transport properties exists, where distinct diffusion coefficients (DDCs) are related to preferential, correlated motion among distinct molecules. Since in general the DDCs do not play the role of an indicator for molecular self‐association phenomena if not compared with some appropriate standard, here we propose DDCs of hard spheres at the second order of volume fraction as new standard coefficients. The analysis based on these novel DDCs is designed to study intermolecular interaction between macromolecule and solvent. Comparisons of the novel non‐ideal with previous ideal reference states were done, and their combined use is shown to reinforce information conveyed by the usual velocity correlation analysis. The comparison of novel hard sphere standards with real DDCs, corresponding to an homologous chemical series of poly(ethylene glycol)‐water mixtures, provides a look at this polymer‐solvent mixture in a dilute and semi‐dilute regime.

Comparison between real (calculated by using Equation (5)–(7) and experimental data) and hard‐sphere based distinct diffusion coefficients for PEG 200 (1: Dequation/tex2gif-stack-1.gif; 2: Dequation/tex2gif-stack-2.gif and 3: Dequation/tex2gif-stack-3.gif).     

Diffusion coefficients and activation energies of diffusion of low molecular weight migrants in Poly(ethylene terephthalate) bottles

Poly(ethylene terephthalate) (PET) is nowadays the packaging material of choice for beverages. Therefore knowledge about the diffusion coefficients at a certain temperature or activation energies of diffusion of potential migrants in the polymer is of interest, especially for the definition of the basic parameter set for migration modelling of PET. In this study, the diffusion coefficients of acetaldehyde, benzene and tetrahydrofuran in PET bottle materials were determined from kinetic migration experiments at four different temperatures. The activation energies for tetrahydrofuran and benzene were determined to be 106.8 kJ mol⁻¹ and 101.4 kJ mol⁻¹, respectively. The activation energy for acetaldehyde is significantly lower (75.7 kJ mol⁻¹) which is due to the lower molecular weight of this molecule compared to benzene and tetrahydrofuran. The results were compared with literature data of diffusion coefficients of other low molecular weight molecules in PET. From the results it is evident that the current migration model with the default modelling parameters for PET does not describe realistically the diffusion coefficients in PET. The migration of small molecules like acetaldehyde will be underestimated whereas higher molecular weight compounds will be overestimated by the current migration model. Whereas the overestimation is useful for compliance evaluation of PET bottles, for more realistic migration calculations, e.g. for exposure estimations, such overestimation is not desirable. Therefore, more accurate modelling parameters should be established. The key parameters for more realistic migration modelling are the activation energies of diffusion in the polymer.     

Diffusion of Quinine with Ethanol as a Co-Solvent in Supercritical CO2

This study aims at contributing to quinine extraction using supercritical CO₂ and ethanol as a co-solvent. The diffusion coefficients of quinine in supercritical CO₂ are measured using the Taylor dispersion technique when quinine is pre-dissolved in ethanol. First, the diffusion coefficients of pure ethanol in the supercritical state of CO₂ were investigated in order to get a basis for seeing a relative change in the diffusion coefficient with the addition of quinine. We report measurements of the diffusion coefficients of ethanol in scCO₂ in the temperature range from 304.3 to 343 K and pressures of 9.5, 10 and 12 MPa. Next, the diffusion coefficients of different amounts of quinine dissolved in ethanol and injected into supercritical CO₂ were measured in the same range of temperatures at p = 12 Mpa. At the pressure p = 9.5 MPa, which is close to the critical pressure, the diffusion coefficients were measured at the temperature, T = 343 K, far from the critical value. It was found that the diffusion coefficients are significantly dependent on the amount of quinine in a small range of its content, less than 0.1%. It is quite likely that this behavior is associated with a change in the spatial structure, that is, the formation of clusters or compounds, and a subsequent increase in the molecular weight of the diffusive substance.     

Investigation on extremely dilute solution of PEO by PFG-NMR

The technique of pulsed-field gradient nuclear magnetic resonance (PFG-NMR) was applied to study the solution properties of a series of low molecular weight poly(ethylene oxide). The self-diffusion coefficients of solutions from semi-concentrated to extremely diluted were measured, leading to a critical concentration. When the concentration of solution is higher than the value of critical concentration, the diffusion coefficient of the solute decreases as the concentration increases and remains the same when the concentration is lower than it. This critical concentration agrees well with the definition of dynamic contact concentration (C _s) and confirms indirectly the Flory's scaling law between the molecular weight and D ₀. In addition, the influences of molecular weight and terminal groups on C _s were discussed. All the diffusion coefficients determined at extremely dilute condition were equivalent to the diffusion coefficients at infinite concentration (D ₀), from which the polymer coil size was estimated.     

Relation between pore sizes of protein crystals and anisotropic solute diffusivities

The diffusion of a solute, fluorescein, into lysozyme protein crystals with different pore structures was investigated. To determine the diffusion coefficients, three-dimensional solute concentration fields acquired by confocal laser scanning microscopy (CLSM) during diffusion into the crystals were compared with the output of a time-dependent 3-D diffusion model. The diffusion process was found to be anisotropic, and the degree of anisotropy increased in the order: triclinic, tetragonal and orthorhombic crystal morphology. A linear correlation between the pore diffusion coefficients and the pore sizes was established. The maximum size of the solute, deduced from the established correlation of diffusion coefficients and pore size, was 0.73 +/- 0.06 nm, which was in the range of the average diameter of fluorescein (0.69 +/- 0.02 nm). This proves that size exclusion is the key mechanism for solute diffusion in protein crystals. Hence, the origin of solute diffusion anisotropy can be found in the packing of the protein molecules in the crystals, which determines the crystal pore organization.     

Pivotal steps towards quantification of molecular diffusion coefficients by NMR.

Using nuclear magnetic resonance (NMR) spectroscopy with a pair of pulsed field gradients (PFGs), Stajeskal and Tanner successfully measured molecular diffusion coefficients in solution in 1965. This method has since been used extensively in various applications, especially after the PFG was implemented in commercial NMR probes. Due to the nonuniformity of the PFG and radio frequency (RF) fields, molecules distributed throughout the sample experience different PFG and RF fields and contribute unevenly to the measured diffusion coefficients, resulting in considerable errors in conventional NMR diffusion experiments. By selective excitation of a central sample region with an offset-independent adiabatic inversion pulse and a PFG, a uniform RF field can be assumed, and the PFG can be represented as a linear approximation. Under these conditions, the molecules diffuse as if they were all experiencing the same effective gradient g(e), leading to a Gaussian signal decay as a function of the PFG strength. Quantitative measurement of molecular diffusion coefficients is therefore made possible. From the diffusion coefficient of a 90 % H(2)O/10 % D(2)O sample, it is convenient to calibrate g(e) with a Java program. In a similar way the nonlinearity of the PFG can be corrected.