Characterization of macromolecules in liquid solutions by thermal diffusion. I. Dependence of the soret coefficient on the nature of the dispersing medium

Experiments have been carried out on thermal diffusion of macromolecular particles dispersed in various liquids, with the object of checking some predictions of the radiation-pressure theory of Soret effect in liquids and of establishing a method of physical characterization of macromolecules in liquid solutions. The experimental results confirm the importance of the ratio G between thermal conductivity K and (phase) velocity v of high-frequency elastic waves of the materials composing the mixture in determining the thermodiffusive behavior of a liquid solution. We have shown that the migration of the macromolecular component takes place in the same direction in which thermal energy is flowing or opposite to it, depending on whether G of the dispersed particles is smaller or larger relative to the G of the liquid. Another aspect of the same phenomenon may be observed when macroscopic pieces of nonmetallic materials are suspended in a liquid, and heat is made to flow through this solid plunger and the surrounding liquid. The experiments performed with molecular solutions and with macroscopic plungers mutually complement and confirm each other. Anomalous results obtained in the case of solutions of polyvinylpyrrolidone in methanol are also discussed, and the possibility that this might be the consequence of the existence of a marked velocity dispersion in the high-frequency region of the spectrum of thermal waves in both water and methyl alcohol is indicated. Finally the possibility is hinted that thermal diffusion might have been responsible for the phenomena of molecular selection and evolution which ultimately led to the origin of life on our planet.     

Characterization of thermal diffusion in polymer solutions by thermal field-flow fractionation: Dependence on polymer and solvent parameters

The thermal diffusion coefficient D_T has been obtained for 17 polymer-solvent combinations, each of them spanning a range of polymer molecular weights, using thermal field-flow fractionation. The polymers examined include polystyrene, poly(alpha-methyl)styrene, polymethylmethacrylate, and polysioprene. The solvents include benzene, toluene, ethylbenzene, tetrahydrofuran, methylethylketone, ethylacetate, and cyclohexane. Although D_T was confirmed as essentially independent of polymer molecular weight, it was found to vary substantially with the chemical composition of polymer and solvent. The results were used to evaluate several thermal diffusion theories; the agreement with theory was generally found to be unsatisfactory. Attempts were then made to correlate the measured thermal diffusion coefficients with various physicochemical parameters of the polymers and solvent. A good correlation was found in which D_T increases with the thermal conductivity difference of the polymer and solvent and varies inversely with the activation energy of viscous flow of the solvent.     

Characterization of dehydroascorbic acid solutions by liquid chromatography/mass spectrometry.

The composition of a commercial dehydroascorbic acid (DA) solution at pH 2 was investigated by liquid chromatography/mass spectrometry (LC/MS) and liquid chromatography/tandem mass spectrometry (LC/MS/MS) to establish the nature of its different forms and its decomposition products. In freshly prepared solutions, dimeric forms of DA and the hydrated bicyclic hemiketal of DA are the species mainly present in solution. In the presence of light, the initial dimeric species disappears over time to give other dehydrated dimers some of which decompose to the monomer. The comparison of these data with similar data obtained for ascorbic acid (AA) solutions under the same experimental conditions revealed that, in the presence of light, the aging of such AA solutions gives rise to only the hemiketal form of DA, and that no dimeric species of DA were formed. The presence of the hemiketal form of DA was not revealed by analysis of the same AA solutions using the conventional LC/UV technique. The natural form of DA from the oxidation of AA is the hydrated bicyclic form.     

A theory of the diffusion coefficient in a liquid metal : II

Abstract

Calculations are reported of the diffusion coefficient and frequency spectrum of the velocity autocorrelation function for a model of liquid sodium using long-range oscillatory interionic potentials. They are based on a theory of the associated memory function which employs a previously known expression for the timedependent pair distribution function. The latter is introduced to try to solve the difficult problem of describing the relative motion of two atoms, but the results are not consistent with the information obtained from molecular dynamics calculations.

On the basis of a physical argument, a modified theory of the pair distribution is then employed and shown to produce results which are in much better agreement with those obtained from computer experiments. Some information is thereby obtained about the relative motion of atoms in a liquid.     

Application of molecular dynamics simulations in molecular property prediction II: diffusion coefficient

In this work, we have evaluated how well the general assisted model building with energy refinement (AMBER) force field performs in studying the dynamic properties of liquids. Diffusion coefficients (D) have been predicted for 17 solvents, five organic compounds in aqueous solutions, four proteins in aqueous solutions, and nine organic compounds in nonaqueous solutions. An efficient sampling strategy has been proposed and tested in the calculation of the diffusion coefficients of solutes in solutions. There are two major findings of this study. First of all, the diffusion coefficients of organic solutes in aqueous solution can be well predicted: the average unsigned errors and the root mean square errors are 0.137 and 0.171 × 10(-5) cm(-2) s(-1), respectively. Second, although the absolute values of D cannot be predicted, good correlations have been achieved for eight organic solvents with experimental data (R(2) = 0.784), four proteins in aqueous solutions (R(2) = 0.996), and nine organic compounds in nonaqueous solutions (R(2) = 0.834). The temperature dependent behaviors of three solvents, namely, TIP3P water, dimethyl sulfoxide, and cyclohexane have been studied. The major molecular dynamics (MD) settings, such as the sizes of simulation boxes and with/without wrapping the coordinates of MD snapshots into the primary simulation boxes have been explored. We have concluded that our sampling strategy that averaging the mean square displacement collected in multiple short-MD simulations is efficient in predicting diffusion coefficients of solutes at infinite dilution.     

Influence of bonded-phase coverage in reversed-phase liquid chromatography via molecular simulation II. Effects on solute retention

Particle-based Monte Carlo simulations were employed to examine the molecular-level effects of bonding density on the retention of alkane and alcohol solutes in reversed-phase liquid chromatography. The simulations utilized octadecylsilane stationary phases with various bonding densities (1.6, 2.3, 2.9, 3.5, and 4.2mumol/m(2)) in contact with a water/methanol mobile phase. In agreement with experiment, the distribution coefficient for solute transfer from mobile to stationary phase initially increases then reaches a maximum with increasing bonding density. A molecular-level analysis of the solute positional and orientational distributions shows that the stationary phase contains heterogeneous regions and the heterogeneity increases with increasing bonding density.     

Experimental study of the concentration dependence of the soret coefficient by thermal field-flow fractionation: the case of polystyrene in decalin

Summary Thermal field-flow fractionation separates polymers with high selectivity according to their Soret coefficient,S _τ, hence, according to their molar mass, and therefore consitutes an efficeint physicochemical tool for the determination of the Soret coefficient of a given polymer in the carrier liquid from its retention time. However, the polymer concentration in the sample influences the retention time and, hence, the value ofS _τ derived from it. An experimental study of the influence of sample concentration on retention,S _τ, and peak shape was performed for the polystyrene-decalin system over a relatively large temperature domain and for various molar masses. It is found that the retention time and the value ofS _τ increase with increasing sample concentration, the more so as the cold wall temperature is lower. This appears to be in contradiction with the general non-equilibrium thermodynamic expression derived for polymer-solvent systems with positive second virial coefficients, such as the present system over the temperature range investigated. There seems to be a temperature for which the dependence ofS _τ on sample concentration vanishes. This temperature is about 375 K for the polystyrene-decalin system. As the sample concentration increases, the peak barycentre and the standard deviation increases. As the peaks are fronting, the skewness is negative and becomes more negative as the sample concentration increases. The peak skewness appears to be a good indicator of the onset of sample concentration effects. The threshold concentration, for which these effects begin to become significant, decreases with increasing molar mass.     

Dependence of diffusivity on density and solute diameter in liquid phase: a molecular dynamics study of Lennard-Jones system

Investigations into the variation of self-diffusivity with solute radius, density, and degree of disorder of the host medium is explored. The system consists of a binary mixture of a relatively smaller sized solute, whose size is varied and a larger sized solvent interacting via Lennard-Jones potential. Calculations have been performed at three different reduced densities of 0.7, 0.8, and 0.933. These simulations show that diffusivity exhibits a maximum for some intermediate size of the solute when the solute diameter is varied. The maximum is found at the same size of the solute at all densities which is at variance with the prediction of the levitation effect. In order to understand this anomaly, additional simulations were carried out in which the degree of disorder has been varied while keeping the density constant. The results show that the diffusivity maximum gradually disappears with increase in disorder. Disorder has been characterized by means of the minimal spanning tree. Simulations have also been carried out in which the degree of disorder is constant and only the density is altered. The results from these simulations show that the maximum in diffusivity now shifts to larger distances with decrease in density. This is in agreement with the changes in void and neck distribution with density of the host medium. These results are in excellent agreement with the predictions of the levitation effect. They suggest that the effect of disorder is to shift the maximum in diffusivity towards smaller solute radius while that of the decrease in density is to shift it towards larger solute radius. Thus, in real systems where the degree of disorder is lower at higher density and vice versa, the effect due to density and disorder have opposing influences. These are confirmed by the changes seen in the velocity autocorrelation function, self part of the intermediate scattering function and activation energy.     

Rotational diffusion of 9,10-diphenylanthracene in di-n-butyl phthalate solutions of polystyrenes by the fluorescence polarization method: Dependence on polymer concentration and molecular weight

A versatile double-beam polarization fluorimeter has been constructed for measuring the polarization of fluorescence from polymer solutions, melts, and glasses. Polarizations can be determined over a range of temperatures from ?20 to +80°C in a controlled atmosphere with a precision of ±0.001 to ±0.005 for the studies reported herein. Data collected at different temperatures for 1.5 × 10^?5M solutions of 9,10-diphenylanthracene (PA) in di-n-butyl phthalate (BP) fit a relation of the Perrin type, 1/P = (1/P₀) + (ST/_η1), where P is the polarization, T is the absolute temperature, and _η1 is the solvent viscosity. The constants P₀ and S were 0.400 ± 0.005 and (7.4 ± 0.3) × 10^?3 P/°K, respectively. Polarizations were also determined at 25.0 ± 0.1°C for BP solutions containing 1.5 × 10^?5M PA and polystyrenes at various weight fractions w₂ and molecular weights M. Rotational friction coefficients ζ_r deduced from these data showed no dependence on M from 5.1 × 10⁴ to 8.6 × 10⁵ g/mole, and a gradual increase as w₂ was varied from 0 to 0.1. It is concluded from these results that PA is an especially attractive emitter for rotational diffusion studies in nonaqueous systems, and that the abrupt changes in ζ_r with w₂ and M observed for some other emitter–polymer systems and attributed to onset of coil overlap are not universal characteristics of such systems.     

Effect of molecular weight on the diffusion coefficient of carbon dioxide in polystyrene

The permeability and time lag at pressures below 1 atm were measured for carbon dioxide in five polystyrene samples with different molecular weights at 25 to 40°C. The apparent permeability coefficient decreases with increasing carbon dioxide pressure and also decreases with increasing molecular weight of polystyrene, whereas the apparent diffusion coefficient calculated from time lag increases with pressure and is independent of molecular weight. Parameters for the partial-immobilization model were determined from the apparent diffusion and permeation coefficients by using a nonlinear least-squares optimization program without using sorption data. The results suggest that the void-saturation constant C′_H decreases as the molecular weight of the polymer increases or as the chain-end free volume decreases. The significance of these observation and their interpretation is discussed in terms of free-volume theory for glassy polymers.     

Measurement of the diffusion coefficient of atomic chlorine in molecular chlorine

A scheme for measuring the diffusion coefficients of reactive atomic species through their radiative recombination reactions is proposed. The method was employed to measure the rate of diffusion of chlorine atoms in chlorine molecules and led to an observed value for the diffusion coefficient of 0.149 ± 0.025 cm² s⁻¹ at 298 K and 1 atm.     

Dependence of molecular polarizability on the orientational order in nematic liquid crystals

The dispersion dependences of refractive indices in the visible range were used to obtain experimental values of the Lorentz tensor components L _j and the mean molecular polarizability $ \bar \gamma $ \bar \gamma for five nematic liquid crystals belonging to two homological series. The dependence of L _j components on the homologue number, mesophase temperature, birefringence value, and the orientational order of molecules in the nematic phase and upon a nematic-smectic A phase transition was revealed. The effect of the isotropization of the Lorentz tensors and the local field tensor with decreasing birefringence and molecular polarizability anisotropy Δγ was confirmed. The quadratic dependence $ \bar \gamma $ \bar \gamma (S) on the molecular orientational order parameter S in the nematic phase was found. It was invariant with respect to the nematic-smectic A transition. The dependences $ \bar \gamma $ \bar \gamma (S) and Δγ(S) are explained within molecular statistical theory as consequences of the correlation between orientational and conformational degrees of freedom of molecules. These conformational degrees of freedom are related to the internal rotation of molecular fragments, which affects the electronic conjugation of the fragments and the oscillator strengths of molecular transitions.     

Calculation of the diffusion coefficient in a liquid based on the force covariance function

Methods of optimal use of statistical information on the Brownian motion of molecules in a liquid for calculating the diffusion coefficient are considered. Relationships between covariance functions for the displacement of a molecule, its velocity, and the force acting on the molecule are established. It is proposed the method of calculation of the diffusion coefficient estimates should be made using the force covariance function, which enables to reduce the time of simulation of the molecular motion. The proposed method is used for callculating diffusion coefficients for some systems.     

Investigation of the diffusion coefficient of polymers and micelles in aqueous solutions using the Soret effect in cw-laser thermal lens spectrometry

The concentration gradient (Soret effect) induced in cw-laser thermal lens spectrometry subsequently to the formation of the thermal gradient (thermal lens effect) has been investigated in aqueous solutions of various macromolecular species including micelles, mixed micelles and polymers. It is shown that the build-up of the concentration gradient is much shorter than that in classical Soret experiments, reaching steady-state values in less than 1 min. The time evolution of the Soret signal has been used to derive mass-diffusion times from which mass-diffusion coefficients were calculated. Our data are in agreement with previous results obtained from quasi-elastic light scattering studies for the micellar solutions and calculated from a known molecular weight-dependent power law for polymer solutions.     

Li在液态Al中扩散系数的测定研究

首次尝试利用开路电位-浓度曲线法测定合金的浓度, 并用阳极计时电位法快速测定Li在液态Al中的扩散系数。720℃下Li在液态Al中的扩散系数DLi/Al=4.94×10ˉ^5cm^2·gˉ^1,与根据Stokes-Einstein方程计算得到的理论值DLi/Al=4.85×10ˉ^5cm^2·sˉ^1相吻合。     

Dependence of thermal diffusion effects in liquids on the physical properties of the dispersing phase

A generalization of the radiation-pressure theory of thermal diffusion in liquids explains the genesis of the forces acting in a condensed phase when heat flows through it. The analytical expressions obtained make it possible to connect such forces originated by the radiation pressure of thermal waves with the transport of matter taking place in solutions or suspensions of particles and also with the ultimate result of this transport, that is, the steady-state concentrations of the dispersed phase in the hot and in the cold regions of the nonisothermal solution. The form in which the theoretical results are laid down lends itself to direct and unambiguous experimental verification. The confrontation with a few data found in the literature lends support to the theory.     

Excess entropy scaling for the diffusion coefficient in expanded liquid metals

Molecular-dynamics simulation is used to compute the pair correlation function and the velocity autocorrelation function of Cs and Rb along the liquid-vapor coexistence curve, from which the excess entropy S(ex) and the diffusion coefficient D are deduced. The numerical results of both physical properties are correlated and a scaling law between the excess entropy and the reduced diffusion coefficient D(*)(=D/D(0)) is investigated for different expressions of the reduction parameter D(0). The choice of thermodynamic states along the liquid--vapor coexistence curve gives us the possibility to extend the investigation of the relation between the reduced diffusion coefficient and the excess entropy over a wide area and to test the adequacy of the scaling law confidently.     

Star polymer diffusion in concentrated solutions: Dependence on functionality via the coupling model

The coupling model is formulated in terms of the dynamic constraint entropy, S_c(t), and subsequently compared with measured tracer diffusion coefficients D for linear, 3-arm star, and 12arm star polystyrenes in solutions of poly (vinyl methyl ether) (PVME) /o-fluorotoluene. Inequalities between the dynamic constraint entropies, S_cf and S_cf′(t), respectively, for f-arm and f′-arm stars, enable us to explain the experimental observation that at constant arm molecular weight, the ratio D_star/D_linear decreases substantially with increasing concentration above the entanglement concentration for the PVME. This work indicates that not only the reptation model, but also the coupling model, can account for the experimental observation that in entangled solutions the mechanism for diffusion depends on diffusant architecture.     

Dependence of thermal diffusion factor of binary mixtures to the thermodynamic state by NEMD simulation

In this paper, we investigate the dependence of thermal diffusion factor and thermal conductivity to the temperature, density and mole fraction in Lennard–Jones binary mixtures of isotopes, noble gases and SF₆–noble gases by non-equilibrium molecular dynamics simulations.The results for the isotopic mixtures indicated that the density has a crucial effect on the dependence of thermal diffusion factor on the temperature. For isotope system at low density, thermal diffusion factor increased with temperature then remains constant at higher temperatures and the slope of thermal diffusion factor vs. temperature is positive while at higher density, thermal diffusion factor decreased with temperature and then fluctuate. For noble gas mixtures, thermal diffusion factor reduces with increasing of temperature and remain constant at high temperatures. For SF₆–Ar system, thermal diffusion factor has a negative slope and reduced with increasing of temperature, but remain nearly constant at high temperatures. For Xe–SF₆ thermal diffusion factor changed sign and the slope of thermal diffusion factor vs. temperature was negative. The results also show that thermal conductivity increases with temperature for all systems.The dependence of thermal diffusion factor to mole fraction of heavier component also investigated. The inverse of thermal diffusion factor versus mole fraction of heavier component is linear for isotope mixtures at thermodynamic conditions: (a) Low temperature, large mass ratio and all densities. (b) High temperature, large mass ratio and low densities. For Ne–Kr mixture, the inverse of thermal diffusion factor shows a linear dependence to the mole fraction of heavier component in moderate temperatures and all densities. For SF₆–Ar and Xe–SF₆ mixtures, the inverse of thermal diffusion factor has linear behaviour at moderate temperatures and low density and high temperature and low density, respectively.