Segment Density Distribution Research Articles

Remarks on smoothed-density theories for flexible chains with three-segment interactions

Abstract The Orofino-Flory (OF) type smoothed-density theories for the end-distance expansion factor αR and the second virial coefficient A2 of flexible chains with three-segment interactions are inconsistent with first-order perturbation calculations unless the ternary cluster integral β3 is zero. It is shown in the present paper that the inconsistency arises from the factorization approximation to segment density distribution functions invoked in the smoothed-density model and that a proper treatment of such functions leads to expressions consistent with the perturbation calculations but different from the OF type equations. Thus, for non-zero β3 and near the Θ point the previous smoothed-density or mean-field theories retain no valid place, even though those for A2 account for a few experimental findings (at or below the Θ temperature) that two-parameter theories fail to explain. In particular, the prediction of a coil-globule transition by the OF type equations has no theoretical significance. It is also shown by a perturbation calculation that when both binary and ternary cluster integrals are vanishingly small, αR for an infinitely long chain is expressed in terms of a single excluded-volume variable up to second order in β3 with the same numerical coefficients as those in the two-parameter theory.

Conformations of polymer melts between parallel surfaces: comparison of the Scheutjens-Fleer lattice theory with Monte Carlo simulations

Conformations of chains in polymer melts confined between parallelsolid surfaces are examined by means of lattice Monte Carlo (MC) simulations and the Scheutjens-Fleer self-consistent-field (SCF) lattice theory for the purpose of comparing SCF predictions directly with simulation. The effects of surface chain end interactions on conformational properties of the chains are investigated by considering nonadsorbing, weakly adsorbing, and strongly adsorbing chain ends. Quantitative agreement between MC simulations and SCF theory is found for segment and chain end density distributions and bond orientation profiles

Computer simulations of thin polymer layers

AbstractMolecular dynamics calculations are used to explore the structure of dense monolayers of long‐chain molecules supported on a planar surface. As a model we consider ensembles of flexible chains consisting of N segments (N=32, 64 and 128) in a box with lateral (x, y) periodicity conditions. The effect of surface coverage on the conformational properties of chains is studied. At high coverages, the results of the simulations show that each chain is strongly stretched along the normal to the surface and the mean layer thickness is linear in N. The segment density distribution along the normal is found to be an universal function A2/3 f (zA1/3 N), where A is the surface area per chain. The high‐coverage distribution has a well defined broad plateau, in agreement with the so‐called blob model. In contrast to the predictions of this model, however, we observe that the chains are strongly stretched at all space scales. Differences between the results of simulations and those predicted by the mean‐field theory are also discussed.

Segment density distribution of symmetric diblock copolymers at the interface between two homopolymers as revealed by neutron reflectivity

A ternary system comprised of polystyrene (PS), poly(methyl methacrylate) (PMMA) and symmetric diblock copolymer styrene/methyl methacrylate (P(S-b-MMA)) was studied. It was found that the interface formed between the PS and PMMA segments could be described by a hyperbolic tangent function with an effective width of 75 A. This width is 50% broader than that found between the PS and PMMA homopolymers in the absence of the diblock copolymer and between the PS and PMMA lamellar microdomains of the pure P(S-b-MMA) in the bulk. A significant penetration of the PS and PMMA homopolymers into the interfacial region was also found

Monte Carlo simulations of partially ionized polyelectrolytes: Shape and distribution functions

A novel modification to the ‘‘slithering snake’’ algorithm is used to enable Monte Carlo simulations of partially ionized polyelectrolyte chains where the charged beads interact via screened Coulomb interactions. The use of ‘‘stroboscopic’’ averaging enables detailed shape characteristics of the chains to be calculated. The moment of inertia tensor, the distribution function of the end-to-end distance and the segment density distribution functions from the center of mass and both ends of the polyion are combined to give an overall characterization of the shape changes of a polyion as added salt concentration, chain length (up to 240 beads) and degree of ionization are varied. Some abrupt behavior seen for high degree of ionization may be smoothed once ionic degrees of freedom are included. The present work—by characterizing the shape of short chains—may also help to formulate models for very long polyions consisting of many segments, each of a few hundred beads.

Segment distribution about the center-of-mass in an isolated polymer coil. A renormalization group study

2014 We analyse the segment density distribution about the center of mass in an isolated selfinteracting polymer chain. We find that the center-of-mass operator is renormalizable without introducing new renormalisation factors. The segment density distribution is calculated to one loop order. The interaction reduces the density in the center of the chain. This effect, which was to be expected, is due to a somewhat surprising mechamism : the interaction suppresses fluctuations of individual segments away from their average position. J. Phys. France 49 (1988) 749-758 MAI 1988, Classification Physics Abstracts 36.20 61.40K 64.60

Statistical thermodynamics of molecular organization in mixed micelles and bilayers

The conformational and thermodynamic characteristics of molecular organization in mixed amphiphilic aggregates of different compositions and geometries are analyzed theoretically. Our mean-field theory of chain conformational statistics in micelles and bilayer membranes is extended from pure to mixed aggregates, without invoking any additional assumptions or adjustable parameters. We consider specifically binary aggregates comprised of long-chain and short-chain surfactants, packed in spherical micelles, cylindrical rods, and planar bilayers. Numerical results are presented for mixtures of 11- and 5-carbon chain amphiphiles. The probability distribution functions (pdfs) of the (different types of) chains are determined by minimizing the conformational free energy, subject to packing constraints which reflect the segment density distribution within the hydrophobic core. In order to analyze the relative thermodynamic stabilities of mixed aggregates of different compositions (long/short chain ratios) and different geometries, the aggregate’s free energy is expressed as a sum of conformational, surface, and mixing contributions. The conformational free energy is determined by the pdfs of the chains and the surface term is modeled in terms of the ‘‘opposing forces’’ operative at the hydrocarbon–water interface. An interesting coupling between these terms arises from the special geometric (surface/volume) limitations associated with packing short and long chains in a given ratio within a given aggregate. In particular, it is found that the minimal area per surfactant head group in a mixed spherical micelle is significantly lower than that in a pure micelle (similarly, though less drastically so, for cylindrical micelles). The most important qualitative conclusion of our thermodynamic analysis is that the preferred aggregation geometry may vary with composition. For example, we find that under certain conditions (areas per head group, chain lengths) the preferred micellar geometry of pure long or short-chain aggregates is that of a planar bilayer, whereas at intermediate compositions spherical micelles are more stable. Our analysis of chain conformational properties provides quantitative information on the extent of long (or short) chain distortion attendant upon chain mixing. For example, the results for bond order parameter profiles and segment density distributions reveal enhanced stretching of the long chain towards the central regions of the hydrophophic core as the fraction of short chains is increased.

Surfactant conformation and solvent penetration in sodium di-2-ethylhexyl phosphate reversed micelles. A multinuclear relaxation study

The conformation and dynamical behavior of sodium di-2-ethylhexyl phosphate (NaDEHP) in NaDEHP/H/sub 2/O/C/sub 6/H/sub 6/ and NaDEHP/H/sub 2/O/C/sub 6/H/sub 12/ reversed micelles have been investigated by /sup 1/H, /sup 2/H, /sup 13/C, and /sup 31/P relaxation over wide frequency ranges. In some experiments, the relaxation was enhanced by addition of small amounts of Mn/sup 2 +/, the geometry of binding being determined from the relaxation of /sup 31/P and /sup 13/C/sub 1/. The /sup 13/C paramagnetic relaxation in hydrocarbon chains was interpreted in terms of statistical weights of the conformers, providing in particular the density distribution of chain segments in the surfactant layer. Filling this layer to constant hydrocarbon density provides an estimate of the solvent nuclei. The order of which is ca. 3 A from the polar core. This is well confirmed by the paramagnetic relaxation of solvent nuclei. The order parameters of the C-H bonds in the alkyl chains were extracted from multifield /sup 13/C and /sup 2/H relaxation, using the two-step model. Consistent with the order parameters deduced from the paramagnetic relaxation was obtained for each chain having its own local director nearly oriented along the axis of the fully extended conformer. The approximation involved in themore » use of the two-step model and the significance of the dynamical parameters obtained are discussed on the basis of /sup 31/P and ..cap alpha.. proton relaxation experiments.« less

Density distribution of polymer chain segments near a nonadsorbing wall

Calcul du profil de densite des segments d'un polymere. Le resultat peut etre applique au cas de chaines courtes. La distribution theorique obtenue est en bon accord avec les donnees experimentales de D. Ausserre, Hervet et Roudelez

A Monte Carlo analysis of terminally attached self-avoiding polymer sequences in the vicinity of a rigid boundary

A Monte Carlo analysis of terminally attached hard sphere sequences of N<or=24 segments in the vicinity of a rigid plane is presented. The principal configurational properties of the system are determined, in particular the segment density distribution rho (z mod N) normal to the boundary, the mean square end-to-end length (R1N2), the mean square radius of gyration (SN2) and the mean thickness of the adsorbed layer (z1N). Comparisons with a previously presented iterative convolution analysis are made and the existence of a density discontinuity in rho (z mod N) is confirmed. Exponent representation of the data suggest (R1N2) approximately (N-1)gamma with gamma approximately 1.2, consistent with lattice-based analyses. The boundary configurations are resolved into loop, train and tail components and their dependence upon chain length determined. Good agreement with the convolution analysis is found, the results being consistent with earlier analyses by Roe (1965) and Chan et al. (1975), and the experimental investigations of Cosgrove et al. (1983).

Statistics of self-avoiding ring polymers

The iterative convolution (IC) technique previously reported for linear self-avoiding sequences is extended to the description of nonintersecting rings of hard-sphere segments. The principal geometrical features of rings of N=20, 40 and 62 segments are determined, including the intersegmental spatial distribution functions, the mean-square intersegmental separations, the radius of gyration, bond correlation function and segment density distribution function. These quantities are compared with independent Monte Carlo estimates, and the results are found to be generally in good quantitative agreement. A sum rule for the bond correlation function is proposed for rings, whilst the segment density distribution is found to exhibit serrations which are unresolved in the Monte Carlo data scatter. These serrations, moreover, occur at integral multiples of the segment diameter and are attributed to entropic processes associated with ring closure.

Method of calculating the average inertia radius of random branched polymers

An original analytical method is proposed for calculating the root-mean-square inertia radius of random branched macromolecules; this method takes into account the density distribution of segments inside the globule and enables the actual technology (history) of obtaining these branched macromolecules to be considered. The use of the Fourier transform considerably simplifies calculations, as a result of which a formula is derived for the average inertia radius of a random branched chain determined only by the lengths and average inertia moments of chain branches.

Pharmaceutical suspension studies II. The interaction between particles of diloxanide furoate B.P. coated with an adsorbed polymeric layer

The stability characteristics of a serie of diloxanide furoate suspensions stabilized with an adsorbed layer of polyvinylalcohol have been studied. The determination of the adsorbed layer thickness is attempted and this, in conjunction with data from the mass adsorption isotherms, has been used in correlating the suspension characteristics with potential energy diagrams based upon a mean polymer segment concentration within this layer. Such diagrams have also been constructed allowing for an exponential segment density distribution normal to the interface.

Statistical thermodynamics and configurational structure of chains confined between surfaces. Part 1.—Excluded-volume chains confined between a pair of non-adsorbing planes

The problem of the excluded-volume chain confined between a pair of parallel plates has been tackled using a Monte Carlo simulation approach. The configuration generation technique devised previously for tetrahedral chains on a single surface has been suitably modified to take account of the second surface. The calculations are directed to the evaluation (a) configurational free-energy changes with variation in interplate separation, which in turn lead to the determination of the force of steric repulsion and (b) configurational properties relating to the mean dimensions of the chain and structure of the interfacial region.Both terminally anchored and non-anchored chains (with no segment/surface interactions) are considered. It is found that although the two systems possess similar forces of steric repulsion, only the terminally anchored chain gives rise to the stabilisation of the plates at all separations. In the presence of the non-anchored, excluded-volume chain, the plates are stabilised at large interplate distances but destabilised at small separations. Terminal anchoring causes the chain to expand and produces significant asymmetry in the system with the result that the values of the configurational quantities with respect to the two surfaces are unequal and the segment density distributions are skewed.

The segment-cloud model of the second virial coefficient of polymer solutions: effects of chain length and branching

Abstract The segment-cloud model for polymer molecules has been used, and the second virial coefficient A 2 obtained as a function of the interaction parameter z for linear and branched chains having different values of n . It is observed that the chain length effect, though much smaller than in the perturbation theory, increases as the degree of branching increases. Also, the branching parameter g is found to be a better correlating parameter than the segment density distribution for A 2 . This is in contrast to earlier results for the perturbation theory of the excluded volume.

Steric stabilization in worse thanθ-solvents

The stabilization of colloidal particles by nonionic polymers that exhibit loopy adsorption is considered in terms of an exponentially decaying segment density distribution function. It is shown that the steric interaction, whether repulsive or attractive, in the interpenetrational domain is drastically reduced for an exponential function, compared with that for a constant or a Gaussian distribution function. This reduction originates in the small segment densities that occur in the outer regions of steric layers exhibiting loopy adsorption. The net effect is that incipient instability in such systems can only be generated by significant penetration into the worse than 8-solvent domain. Any correlation between the critical flocculation point and the θ-point is thus weakened and stable dispersions can be prepared in worse than θ-solvents for the stabilizing chains in free solution. Both phenomena have been observed experimentally. It is predicted that, in general, the penetration into the worse than B-solvent domain will be greater for nonaqueous than for aqueous dispersion media. The conformational effects are reinforced by any changes in the thermodynamic parameters due to loopy adsorption.

Statistical theory of the adsorption of interacting chain molecules. 1. Partition function, segment density distribution, and adsorption isotherms

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTStatistical theory of the adsorption of interacting chain molecules. 1. Partition function, segment density distribution, and adsorption isothermsJ. M. H. M. Scheutjens and G. J. FleerCite this: J. Phys. Chem. 1979, 83, 12, 1619–1635Publication Date (Print):June 1, 1979Publication History Published online1 May 2002Published inissue 1 June 1979https://doi.org/10.1021/j100475a012RIGHTS & PERMISSIONSArticle Views2525Altmetric-Citations1120LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (3 MB) Get e-Alerts

Chain length effects in the excluded volume of polymer chains having a generalized molecular architecture

Abstract A generalized treatment is presented for computing the coefficient of the first-order perturbation theory for the expansion factor, α S , in polymers of any chain length, n , and architecture. Results show substantial deviations from the longchain asymptote. Plots between the interpenetration factor, ψ, and α S 3 are different for different values of n , the spread decreasing with branching. It is found that the branching parameter g is insufficient to characterize the excluded volume effect and more detailed, unperturbed segment density distributions are necessary.

Cyclohexane‐polystyrene revisited

AbstractA semi‐empirical interaction function previously used in the quantitative description of critical miscibility data for the system cyclohexane/polystyrene is reconsidered in terms of molecular parameters. The empirical part of the function has approximately the same magnitude as correction terms which, owing to the dependence of the average randomness of orientation of molecules and polymer segments on the composition of the liquid, have to be applied to the combinatory entropy of mixing. Such a treatment largely ignores excess volume effects. These have been quantitatively dealt with by Flory et al., who had to bring in an empirical entropy correction whose order of magnitude may prove to be compatible with the orientational entropy contributions mentioned above. A full treatment in terms of molecular parameters seems within reach, but this will have to take the variation of the segment density distribution with concentration into account.

Hydrodynamic thickness of adsorbed polymers

Relationships between the molecular dimensions of polymers adsorbed on solid surfaces and the ’’hydrodynamic thickness’’ obtained by viscosimetry or flow rates through capillaries are derived by solving the corresponding Navier–Stokes equation. An exponential density distribution of polymer segments in the vicinity of the adsorbing interface was used. The theoretical results are discussed in connection with the experimental data of the literature.