Segment Distribution Function Research Articles

The Association Thermodynamics Modeling of Asphaltene Precipitation

In this work, the authors introduce an association asphaltene deposition modeling through application of continuous thermodynamics for crude oil mixture. It is assumed that a binary system forms consist of a nonprecipitating crude oil solvent system and a precipitating asphaltene component in which pure asphaltene component only participate in deposition phase. A simple association factor as an association term has been incorporated in set of equations for minimization of Gibbs free energy, which was obtained from molecular weight distribution (fractional molecular weight) and association ability of system. For characterization of asphaltenes, asphaltene segment distribution function and the association term are applied at equilibrium condition. The association parameters of asphaltene component are adjusted with the experimental data at different conditions. In this study, experimental data from the Iranian crude oil reservoir was used to examine the proposed asphaltene model. It has been shown that the calculated results are in good agreement with experimental data.

Flow-Induced Conformational Changes in Gelatin Structure and Colloidal Stabilization

Flow can change the rate at which solutes adsorb on surfaces by changing mass transfer to the surface, but moreover, flow can induce changes in the conformation of macromolecules in solution by providing sufficient stresses to perturb the segmental distribution function. However, there are few studies where the effect of flow on macromolecules has been shown to alter the structure of macromolecules adsorbed on surfaces. We have studied how the local energy dissipation alters the adsorption of gelatin onto polystyrene nanoparticles ( r = 85 nm). The change in the nature of the adsorbed layer is manifest in the change in the ability of the nanoparticles to resist aggregation. Circular dichroism spectroscopy was used to assess conformational changes in gelatin, and dynamic light scattering was used to assess the colloid stability. Experiments were conducted in a vortex jet mixer where energy density and mixing times have been quantified; mixing of the gelatin and unstable nanoparticles occurs on the order of milliseconds. The adsorption of the gelatin provides steric stabilization to the nanoparticles. We found that the stability of the gelatin-adsorbed nanoparticles increased with increasing mixing velocities: when the mixing velocities were changed from 0.9 to 550 m/s, the radius of the nanoclusters (aggregates) formed 12 h after the mixing decreased from 2620 to 600 nm. Increasing temperature also gave rise to similar trends in the stability behavior with increasing temperature, leading to increasing colloid stability. Linear flow birefringence studies also suggested that the velocity fields in the mixer are sufficiently strong to produce conformational changes in the gelatin. These results suggest that the energy dissipation produced by mixing can activate conformational changes in gelatin to alter its adsorption on the surfaces of nanoparticles. Understanding how such conformational changes in gelatin can be driven by local fluid mechanics and how these changes are related to the adsorption behavior of gelatin is very important both industrially and scientifically.

Topological effect in ring polymers investigated with Monte Carlo simulation

We studied equilibrium conformations of ring polymers in the melt over the wide range of segment number up to 1000 by the Monte Carlo simulations and the bond fluctuation model, and estimated Flory's scaling exponent nu. The radial distribution function of segments for the ring polymers in the melt is obtained. We have found that nu for ring polymers is decreased with increasing segment number N, and nu goes down to 0.365 when N reaches 1000, whose value is apparently smaller than the theoretically predicted one, i.e., 25. Those values are in contrast to the well established nu value of 0.5 for linear polymers in the melt. This is because ring polymer chains in the melt are squeezed both by their own topological effect and the compression effect by the neighboring ring polymer coils which are also squeezed at bulk state. The difference in our result and the theory may be due to the fact that the estimation of topological entropy loss was ignored in the theoretical prediction, while it has been taken into consideration in the present study. If polymer coils repel each other in melt at N --> infinity, we have the limiting nu value of 13, so we conclude that nu is in the range of 13 < or = nu << 0.365 when the molecular weight of a ring polymer is high enough.

Scattering Functions of Polymeric Core−Shell Structures and Excluded Volume Chains

General expressions for the scattering functions of polydisperse particles with an arbitrary number of concentric shells of lamellar, cylindrical, or spherical symmetry are derived. For shells consisting of dense polymer layers or brushes with algebraic density profiles, φ(r) ∼ rα, it is possible to obtain closed analytical expressions by taking advantage of the mathematical properties of hypergeometric functions. The same formalism can be employed to derive a closed expression for the form factor of polydisperse excluded volume chains assuming a des Cloizeaux-type segment distribution function.

Interpretation of water isotherm hysteresis for an activated charcoal using stochastic pore networks

Water vapor adsorption equilibria on activated carbons typically exhibit hysteresis. The size and shape of the hysteresis loop which separates the adsorption and desorption branches is a strong function of the pore size and interconnectivity of the pores. Neither conventional pore filling models nor statistical thermodynamics approaches provide a means for predicting the extent of hysteresis from only adsorption measurements. This work uses the Kelvin Equation in conjunction with the structural concept of a stochastic pore network to describe measured water isotherms on BPL carbon. Using a pore segment distribution function determined from the adsorption branch, it is shown that totally random assemblies underestimate the extent of hysteresis. It is possible, however, to closely fit the measured BPL-water hysteresis loop using a patchy heterogeneity in which a proportion of the larger pores are preferentially located on the exterior, mid-range pores are concentrated in a sub-surface layer and some large pores form shielded voids behind much smaller pores.

Electronic excitation transport on isolated, flexible polymer chains in the amorphous solid state randomly tagged or end tagged with chromophores

The transport of electronic excitations among chromophores which are randomly tagged or end tagged on finite flexible polymer chains in the amorphous solid state is described. First, the previously reported first order cumulant expansion treatment of excitation transport among chromophores randomly distributed in solution is extended to treat finite volume systems with nonrandom chromophore distributions. The method is demonstrated by considering chromophores randomly distributed in a finite sphere. The results are in good agreement with a previous treatment of this problem using a density expansion. The probability of finding the initially excited chromophore, still excited at time t, Gs(t), is calculated. Gs(t) is directly related to fluorescence depolarization and other observables. Gs(t) is then calculated for a finite flexible polymer chain in a polymer blend which is randomly tagged in low concentration with chromophores. The method permits any form of the polymer pair correlation function to be used. A specific model, a Gaussian segment distribution function, is employed, and an explicit time domain expression is obtained. This expression is compared to previous theoretical treatments which did not contain adequate descriptions of the pair correlation function. Greatly improved agreement with experiment is obtained. Excitation transfer on an end tagged coil is a limiting case of the random tagged problem. In addition, the energy transport aspect of the end tagged problem is treated exactly and the two approaches are compared.

Segment distribution in self-similar patterns and backbone structure of percolation clusters

A distribution function of segments in self-similar patterns is investigated and determined from the fractal dimensionality D of the pattern and that D' of the segments. On the basis of scaling assumptions, the critical behaviour of the segment distribution is studied. Critical exponents are introduced and expressed in terms of D and D'. The general theory is applied to link distribution in the backbone of an infinite percolation cluster. Critical exponents for link distribution are also introduced and evaluated explicitly.

Generalized hydrodynamical equations obeying the entropy principle

Three generalizations of classical hydrodynamic theories that are compatible with equilibrium thermodynamics and that are suitable for an appropriate macroscopic dynamical theory of polymeric liquids are considered. The strain tensor, the stress tensor and the chain segment distribution function (introduced in the network theory of polymeric liquids) are accepted as new state variables. We find that the generalized hydrodynamic equations are compatible with equilibrium thermodynamics provided certain conditions restricting the freedom of choice of constitutive relations are satisfied. In some particular cases the conditions are known from other considerations. We say that a dynamical theory is compatible with equilibrium thermodynamics, or equivalently, that it obeys the entropy principle if the properties listed in section 2.1 are satisfied.

Generalized Rouse–Zimm theory for polymer solutions

AbstractGeneralized Rouse–Zimm equations are derived using a local equilibrium ansatz for the segment distribution function. The relaxation frequencies depend on excluded‐volume effects and other interactions such as entanglement in semidilute solutions through exact static correlation functions. For the case of ring polymers general expressions are given for diffusion coefficients and mean‐square displacements. By use of the “blob” model, explicit results are presented for a dilute good‐solvent system.

Der einfluβ der molmassenverteilung und der kettenabstandsverteilung auf die streufunktion von polymeren in lösung

Universal expressions of the scattering function for coils with uniform and non-uniform expansion, gaussian and non-gaussian chain segment distribution functions and various types of molar mass distributions are given. Facilities to determine the parameters of the functions are discussed. Comparison of the calculated scattering functions with experimental data, for vinyl-polymers in good and poor solvents and for cellulose derivatives in solution, lead to the following statements: (1) Up to now light scattering measurements do not have the precision necessary to predict the form of the chain segment distribution function. Nevertheless measurements on vinyl-polymers in good solvents indicate non-gaussian chain segment distribution functions. (2) The experimental determined scattering function for vinyl-polymers in poor solvents and cellulose derivatives in solution correspond to the calculated scattering function for coils with uniform expansion and gaussian chain segment distribution function within experimental error.

Normal Stress Effect in Concentrated Polymer Solutions

Fixman's equation for stress tensor in polymer solutions consists of three terms: the term due to solvent, the term of 1st power of c ( P 1 ) and that of 2nd power of c ( P 2 ) where c is the number concentration. In this paper, it is shown that P 1 is split into two terms, P 1 0 linear in c and P ' 1 quadratic in c . As far as Dirac delta function for excluded volume potential and a special segment distribution function are employed, the sum of P ' 1 and P 2 does not contribute to normal stress functions.

The effect of multiple scattering on structural parameters determined from X-ray small-angle scattering

The effect of small-angle multiple scattering on a number of general structural parameters and on the segment distribution function has been studied using a representative correlation function of the type γ = exp (−r/lp). The results show that size parameters can be severely underestimated if the presence of multiple scattering is not taken into consideration and that the exact form of the segment distribution function is considerably affected even if the contributions from multiple scattering are relatively small.

On obtaining the segment distribution function from light‐scattering data

On obtaining the segment distribution function from light‐scattering data

Comments on carpenter's consideration “on obtaining the segment distribution function from light scattering data”

Comments on carpenter's consideration “on obtaining the segment distribution function from light scattering data”

Rubber Elasticity

Rubber elasticity is treated in terms of a general random network bead-spring model which expresses chain connectivity through Dirac delta functions. In contrast to the classical theory, the present starting point is the segmental distribution function, from which, besides elasticity, most polymer properties are deducible, e.g., relaxation spectra, intrinsic viscosities, etc. The method is that developed by Fixman and by Imai. The salient results are: (a) macroscopic observables correspond to mean-square vector quantities; (b) rubber elasticity is a function only of the strain invarient I1 (not of I2); in particular: (c) the C2 term of the Mooney–Rivlin equation reflects effects of network connectivity (e.g., the functionality of cross links), not of I2; (d) The new one-parameter stress–strain equation here derived fits classical data on one- and two-dimensional strain. The quantity corresponding to the “front factor” in the classical equation is ∼ 1.8, in reasonable agreement with measurements by Ferry et al.

Viscosity of chain polymers in solution

AbstractA theory is developed for the intrinsic viscosity of chain molecules in solution. The molecules are assumed to be composed of many repeating units called segments, which are distributed spherically around the center of each molecule. An integral equation similar to, yet different from, that of Kirkwood and Riseman is set up. This equation does not require the replacement of the Oseen hydrodynamical interaction tensor by its diagonal element and yields a new viscosity formula. This formula is rather general and is characterized by the Fourier transform of the segment distribution function and the eigenvalue λ(k) of the Oseen tensor expressed in momentum space. In the absence of hydrodynamical interactions between segments the formula is reduced to the Debye formula for the Staudinger empirical law. In the presence of interactions the eigenvalue λ(0) characterizes the viscosity. This eigenvalue is related to the average characteristic length of a chain molecule, through which the molecular‐weight dependence of the viscosity comes in.

Rotatory Diffusion Constant of a Chain Molecule

The rotatory diffusion constant of a chain molecule of spherical configuration is evaluated by the method which the author developed recently for the intrinsic viscosity. The theory is simpler than that given by Riseman and Kirkwood and yields a more general result in terms of the moment of the segment distribution function. The general result reduces to a simple expression for a flexible chain in terms of the molecular constants based on a pearl-necklace model. The relation between the intrinsic viscosity and the rotatory diffusion constant is proved to be the same as Riseman and Kirkwood's. This is due to the same flow mechanism underlying the viscosity and diffusion phenomena.