Polymer Density Profile Research Articles

Monte Carlo density functional theory of nonuniform polymer melts

A theory for nonuniform polymer melts is presented, which combines density functional theory with Monte Carlo methods. The theory treats the ideal gas functional exactly via a single chain simulation and uses the weighted density approximation for the excess free energy functional. The bulk fluid properties required in the theory are obtained from a generalized Flory equation of state. The predictions of the theory are compared to Monte Carlo simulations for the density profiles of semiflexible polymer melts confined between flat plates. Good agreement between theory and simulation is found for 3mers and 20mers and for several densities and molecular stiffnesses.

The structure of a rotational isomeric state alkane melt near a hard wall: Comparison of density functional theory with related theories

Density functional theory is applied to inhomogeneous, rotational isomeric state polymer melts. In particular, a melt of tridecane near a hard wall is investigated, and the variation of polymer–wall correlation functions as a function of packing fraction is of primary interest. In addition to the evaluation of the wall–polymer density profile and the fractional distribution of sites, we use the relation between pressure and contact density to calculate the equation of state of the bulk. Agreement with the generalized Flory dimer equation of state is excellent, and this, in conjunction with our earlier comparison [Sen et al. J. Chem. Phys. 101, 9010 (1994)] with full, multichain simulation, indicates that the density functional theory gives an accurate description of inhomogeneous polymer melts.

Polymer melt near a solid wall

We develop a theory for the equilibrium concentration profile formed by a compressible polymer melt near a solid wall (or the mathematically equivalent incompressible polymer solution near a solid wall). The theory uses a Landau–Ginzburg free energy functional with a concentration dependent square gradient coefficient and an additional local contribution characterizing the influence of the wall. We introduce a mean-field algorithm for constructing the surface free energy contribution from the expression for the bulk free energy of lattice polymers. This algorithm automatically includes both energetic and entropic contributions with no adjustable parameters for lattice systems and can be applied for branched polymers as well. Approximate analytical solutions are provided for one-phase polymer density profiles at neutral, repulsive, and attractive walls. The approximate solutions reflect the behavior of the numerical solutions and display (only at lower polymer densities) a near wall linear variation of the polymer density which crosses over to an exponential approach to the bulk concentration. The numerically evaluated profiles for both athermal and nonathermal melts compare well with available Monte Carlo simulation data for a neutral wall. Physical arguments are presented which anticipate the existence of deviations between theory and simulations at higher densities. The use of lattice cluster theory free energy functions enables us for the first time to investigate the dependence of the density profile on the polymer architecture.

Segment density profiles of end-adsorbed polymers in chemically identical melts

The conformation of physically end-adsorbed polystyrene chains in polystyrene melt matrices was studied using neutron reflectivity. The results were compared with the predictions of numerical self-consistent field theory. The end-adsorbed chains formed weakly stretched brushes; the widths of the interface between free and brush chains were found to be slightly less than widths predicted by theory.

Neutron reflectivity study of adsorbed diblock copolymers

In this paper, we summarize our cumulative work on neutron reflectivity studies of polystyrene-poly(vinyl-2-pyridine) (PS-PVP) and polystyrene-polyethylene oxide (PS-PEO) adsorbed at a quartz-solvent interface. Deuterated toluene was chosen as the solvent since it is a good solvent for PS and a poor one for either of the other two blocks. In this case, the polystyrene dangles into the solvent while the other block acts as an anchor. The neutron reflectivity studies reveal that the form of the polymer density profile normal to the substrate may be varied from an extended «brush» to a condensed «mushroom» conformation by manipulating the ratio of the molecular weights of the two blocks. In addition, we present new data on the PS-PEO system in a poor solvent, deuterated cyclohexane, under conditions of shear flow in Poiseuille geometry. We find that when the PS-PEO diblock is absorbed from cyclohexane and is allowed to relax, the PS chain takes on a «mushroom» conformation. However, when the shear is applied, the layer shear thickens due to the PS chains extending to nearly twice their original lengths.

A theoretical model for copolymer–bilayer interactions

We develop a theory to model the interactions between an amphiphilic copolymer and a bilayer. The copolymer is represented as a Gaussian chain, which contains an alternating arrangement of hydrophobic and hydrophilic sites along the length of the chain. The bilayer is modeled as a hydrophobic layer embedded in a hydrophilic environment. We use the transfer matrix technique to determine the polymer density profiles and the phase diagram for this system. Two distinct phases are observed. In one phase, the copolymer is localized at the surface or within the bilayer. In the second phase, the polymer is unbound or ‘‘delocalized.’’ There is a continuous transition between the two phases. We also determine the scaling behavior for the density profiles. The scaling exponents agree with our analytical arguments. We discuss the implications of our findings on designing copolymers that can act as adhesives or macromolecular surfactants.

Free surfaces of polymer blends. I. Theoretical framework and application to symmetric polymer blends

In this paper we develop a general mean-field lattice model, in the spirit of the Scheutjens and Fleer theory of polymer solutions [J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979); Macromolecules 18, 1882 (1985)], of an N-component polymer blend in the vicinity of an impenetrable surface. We consider the special case of N=3, model one component as noninteracting holes and obtain the bulk density of this system by using the Sanchez–Lacombe equation of state. The free surface of a polymer blend is then modeled by considering the interphase which forms when this ternary mixture is phase separated. One sample case corresponding to the free surface of a symmetric isotopic polystyrenelike blend is probed and we find that the deuterated component is partitioned to the air surface in agreement with experiment. The application of the concept of the Gibbs dividing surface relative to the polymer density profile at the free surface is then examined, and we show that all comparisons to experiment must be conducted relative to this hypothetical plane. Finally, comparisons of the concentration profiles predicted by this theory to existing square gradient theories of binary polymer blends, as well as Monte Carlo simulations, are performed to highlight the usefulness of these calculations to realistic systems.

Neutron reflectivity study of end-adsorbed diblock copolymers : cross-over from nushrooms to brushes

We report neutron reflectivity data on polystyrene-poly(vinyl-2-pyridine) (PS-PVP) diblock copolymers adsorbed onto quartz from the selective solvent toluene (a good solvent for PS, but a poor one for PVP). The PVP > block adsorbs strongly to form a thin layer on the quartz substrate, while the PS chains dangle into the solvent. The grafting density of the non-adsorbing PS chains is varied by varying the size of the PVP block, while the PS molecular weight is kept constant. The PS adsorbance decreases systematically with increasing PVP molecular weight. The form of the polymer density profile normal to the substrate is found to change with the PS grafting density, and a transition from a > to a > conformation is observed as the PVP molecular weight is increased. For the copolymers with a high PVP content, the dependence of the maximum in the polymer density profile on the mean distance, s, between anchor points obeys the scaling law expected of mushrooms, while s increases with increasing molecular weight of the anchor block also in a manner consistent with a mushroom model.

Interfacial segment density profiles of end-anchored polymers in a melt

The segment density profile of end-functionalized deuterated polystyrene (EF-dPS) polymers anchored in a surrounding melt of hydrogenated polystyrene (hPS) to an interface with silicon was determined by neutron reflectometry. Thin films of mixtures with various volume fractions of the EF-dPS and hPS were spun cast from toluene solutions onto the silicon. These films as cast were uniform as a function of depth. After heating to 184 C for approximately 1 day to allow equilibrium segregation to be achieved in the films, neutron reflection measurements were performed. The EF-dPS segment density profiles ({phi})z needed to fit the reflectivity data showed a high {phi} at the silicon interface which increased to a maximum approximately 10 nm away from the interface and then fell monotonically to the bulk segment density [illegible]. The interface excess determined by integration of these profiles was in excellent agreement with that directly determined by forward recoil spectrometry on the same samples. The form of the profiles is consistent with the predictions of a self-consistent mean field theory if, in addition to a large attachment free energy of the end group to the silicon, there is a weak preferential attraction of the silicon for the more polarizable hPS segmentsmore » relative to the less polarizable dPS segments.« less

Determination of end-adsorbed polymer density profiles by neutron reflectometry

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTDetermination of end-adsorbed polymer density profiles by neutron reflectometryJ. B. Field, C. Toprakcioglu, R. C. Ball, H. B. Stanley, L. Dai, W. Barford, J. Penfold, G. Smith, and W. HamiltonCite this: Macromolecules 1992, 25, 1, 434–439Publication Date (Print):January 1, 1992Publication History Published online1 May 2002Published inissue 1 January 1992https://doi.org/10.1021/ma00027a067RIGHTS & PERMISSIONSArticle Views661Altmetric-Citations149LEARN 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 (2 MB) Get e-Alerts Get e-Alerts

Scaling theory for radial distributions of star polymers in dilute solution in the bulk and at a surface. II. ε expansion for monomer densities

The behavior of monomer density profiles of a star polymer in a d-dimensional good solvent, which was predicted in an earlier paper using scaling arguments, is now derived by using the renormalization group ε=4−d expansion method. Both the case of a free star in the bulk and of a center-adsorbed star at a free surface are considered. In the latter case of a semi-infinite problem, a distinction is made between repulsive walls, attractive walls—where for large arm length l, the configuration of the star is quasi-(d−1)-dimensional—and ‘‘marginal walls,’’ where for l→∞ the transition from d-dimensional to (d−1)-dimensional structure occurs. For free stars, ρ(r) behaves as r−d+1/ν for small r, where ν is the exponent describing the linear dimensions of the star, e.g., the gyration radius Rgyr∼lν. For center-adsorbed stars at repulsive or marginal walls, ρ(r∥,z) behaves as ρ(r∥,0)∼r−d+λ( f )∥ and ρ(0,z)∼z−d+1/ν, where r∥ and z denote the distances parallel and perpendicular to the surface, respectively; the new exponent λ( f ) depends explicitly on the number of arms f in general. We calculate this exponent λ( f ) to first order in ε=4−d; then λ( f ) is obtained to be (f−1)ε/4+𝒪(ε2) for repulsive walls and 2−ε/4+𝒪(ε2) for marginal walls.