Configuration of terminally attached chains at the solid/solvent interface: self-consistent field theory and a Monte Carlo model

Cosgrove, Terence; Heath, Tahirah K; Lent, B.; Leermakers, F.A.M.; Scheutjens, J.M.H.M.

doi:10.1021/ma00173a041

Cited by 271 publications

(213 citation statements)

References 6 publications

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“…The simple scaling calculation predicts the brush height D correctly in the asymptotic limit of long chains and strong overlap. It has been confirmed by experiments [189,277,278] and computer simulations [285,286]. The above scaling result assumes that all chains are stretched to exactly the same height, leading to a step-like shape of the density profile.…”

Section: Neutral Grafted Polymerssupporting

confidence: 59%

Neutral and charged polymers at interfaces

2003

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Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a summary of recent progress in this rapidly evolving field. Because many experimental studies are performed with rather stiff biopolymers, we discuss in detail the case of semi-flexible polymers in addition to flexible ones. We first review the behavior of neutral and charged chains in solution. Then, the adsorption of a single polymer chain is considered. Next, the adsorption and depletion processes in the many-chain case are reviewed. Profiles, changes in the surface tension and polymer surface excess are presented. Mean-field and corrections due to fluctuations and lateral correlations are discussed. The force of interaction between two adsorbed layers, which is important in understanding colloidal stability, is characterized. The behavior of grafted polymers is also reviewed, both for neutral and charged polymer brushes.

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Section: Neutral Grafted Polymerssupporting

confidence: 59%

Neutral and charged polymers at interfaces

2003

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“…From the given densities ͑ex-pressing the local specimen volume fraction͒, the surfacegrafted amount for each species can be determined by i ϭN i ϫ i . 37 Within the first z layer, the grafting densities for the intercalant and the grafted polymer represent the number of molecules attached to the clay surface ͑per unit area͒. Unlike other constituents, the host polymer does not chemically bond to the solid platelet thus, the density of the host polymer in the vicinity of the solid wall is calculated as h ϭ1Ϫ ( o ϩ g ϩ v ).…”

Section: Formulationmentioning

confidence: 99%

“…The advantages of the self-consistent mean-field ͑SCF͒ model [33][34][35][36][37][38][39][40][41][42] over the classical lattice approach are well described in a series of publications by Balazs and co-workers. [6][7][8][9] The model used in the SCF calculations consists of two infinite parallel platelets immersed in a bath of molten polymer.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of polymer nanocomposites using self-consistent mean-field model

Kim

Utracki

Kamal

2004

The Journal of Chemical Physics

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Clay-containing polymeric nanocomposites (PNC) are mixtures of dispersed clay platelets in a polymeric matrix. These materials show enhancement of physical properties, such as modulus, strength, and dimensional stability, as well as a reduction of gas permeability and flammability. The performance is related to the degree of clay dispersion (i.e., intercalation or exfoliation) and the bonding between the clay and the matrix. The main goal of this work has been to map the degree of dispersion as a function of independent variables (viz., magnitude of the interaction parameters, molecular weights, composition, etc.). In this paper, we present the results of the numerical analysis of the equilibrium thermodynamic miscibility using one- and two-dimensional (1D and 2D) models based on the self-consistent mean-field theory. In the limit, the 2D model reproduced the 1D model published results. The adopted 2D model considers the presence of four PNC components: solid clay platelets, low molecular weight intercalant, polymeric matrix, and end-functionalized compatibilizer. The simulations, with realistic values of the binary interaction parameters, were analyzed for potential exfoliation of PNC with a polyolefin as the matrix. The simulation results show that intercalation and exfoliation is expected within limited ranges of the independent variables. The presence of a bare clay surface (e.g., generated by thermal decomposition of intercalant or extraction by molten polymer) has a strong negative effect on the dispersion process. The simulation successfully identified the most influential factors, e.g., optimum ranges of the compatibilizer and the intercalant concentration.

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“…These include scaling approaches [59][60][61][62] , analytical 2,[63][64][65][66] and numerical [67][68][69][70][71][72][73][74][75][76][77] self-consistent field (SCF) calculations, a single-chain mean field statistical mechanical approach (SCMF) 31) , renormalization group theory 33) , and Monte Carlo (MC) and Molecular Dynamics (MD) simulations 32,[78][79][80] . In the limit of high molecular weight and sufficiently high surface density such that fluctuations of a chain about its lowest free energy configuration can be neglected, SCF theory has provided analytical forms for the segment density profiles and free energy, as well as scaling relations of the profile characteristics with the molecular parameters in various geometries.…”

Section: Introductionmentioning

confidence: 99%

A quantitative study of tethered chains in various solution conditions using Langmuir diblock copolymer monolayers

Kent¹

2000

Macromol. Rapid Commun.

111

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This article summarizes our investigations of tethered chain systems using Langmuir monolayer of polydimethysiloxane-poly styrene (PDMS-PS) diblock copolymers on organic liquids. In this system, the PDMS block adsorbs to the air surface while the PS block dangles into the subphase liquid. The air surface can be made either repulsive or attractive for the tethered PS chain segments by choosing a subphase liquid which has a surface tension lower or greater than that of PS, respectively. The segment profile of the PS block is determined by neutron reflection as a function of the surface density, the molecular weights of the PS and PDMS blocks, and the solution conditions. We cover the range of reduced surface density (Z) characteristic of the large body of data in the literature for systems of chains tethered onto solid surfaces from dilute solution in good or theta solvent conditions (Z< 12). We emphasize quantitative comparisons with analytical profile forms and scaling predictions. We find that the strong-stretching limit invoked in analytical SCF and scaling theories is not valid over this Z range. On the other hand, over a large portion of this range (X e 5) tethered layers are well described by a renormalization group theory addressing weakly interacting or noninteracting chains. Simultaneous with the study of the profile form, the free energy of the chains is examined through the surface tension. A strong increase in the surface pressure is observed with increasing surface density which determines the maximum surface density which can be achieved. This apparently nonequilibrium effect is attributed to steric interactions and limited lateral interpenetration.This effect may explain several outstanding discrepancies regarding the adsorption of end-functionalized chains and diblock copolymers onto solid surfaces.

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Configuration of terminally attached chains at the solid/solvent interface: self-consistent field theory and a Monte Carlo model

Cited by 271 publications

References 6 publications

Neutral and charged polymers at interfaces

Neutral and charged polymers at interfaces

Numerical simulation of polymer nanocomposites using self-consistent mean-field model

A quantitative study of tethered chains in various solution conditions using Langmuir diblock copolymer monolayers

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