Analysis of compression of polymer mushrooms using self-consistent field theory

Steels, Bradley M; Leermakers, F.A.M.; Haynes, Charles A.

doi:10.1016/s0378-4347(00)00199-7

Cited by 23 publications

(38 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The resistance force decreases abruptly, indicating a first-order transition. The escape transition was studied rather extensively both by analytical [22][23][24][25][26] and numerical [27][28][29][30][31][32][33][34][35][36] methods.…”

Section: Introductionmentioning

confidence: 99%

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Skvortsov

Klushin

Leermakers

2007

The Journal of Chemical Physics

View full text Add to dashboard Cite

An end-tethered polymer chain compressed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flowerlike conformation partially escaped from the gap. This phase transition is first order in the thermodynamic limit of infinitely long chains. A rigorous analytical theory is presented for a Gaussian chain in two ensembles: ͑a͒ the H-ensemble, in which the distance H between the pistons plays the role of the independent control parameter, and ͑b͒ the conjugate f-ensemble, in which the external compression force f is the independent parameter. Details about the metastable chain configurations are analyzed by introducing the Landau free energy as a function of the chain stretching order parameter. The binodal and spinodal lines, as well as the barrier heights between the stable and metastable states in the free energy landscape, are presented in both ensembles. In the loop region for the average force with dependence on the distance H ͑i.e., in the H-ensemble͒ a negative compressibility exists, whereas in the f-ensemble the average distance as a function of the force is strictly monotonic. The average fraction of imprisoned segments and the lateral force, taken as functions of the distance H or the average H, respectively, have different behaviors in the two ensembles. These results demonstrate a clear counterexample of a main principle of statistical mechanics, stating that all ensembles are equivalent in the thermodynamic limit. The authors show that the negative compressibility in the escape transition is a purely equilibrium result and analyze in detail the origin of the nonequivalence of the ensembles. It is argued that it should be possible to employ the escape transition and its anomalous behavior in macroscopically homogeneous, but microscopically inhomogeneous, materials.

show abstract

Section: Introductionmentioning

confidence: 99%

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Skvortsov

Klushin

Leermakers

2007

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…[17][18][19] The lattice layers along the axis of the cylinder are numbered according to z = 1, 2, · · · , N z , while circular arrangements of the lattice sites within each z-layer are numbered as r = 1, 2, · · · , N r . Due to the azimuthal symmetry of the problem, there are L(r) = π[r 2 − (r − 1) 2 ] indistinguishable sites at each coordinate (z, r).…”

Section: Microscopic Model and Theorymentioning

confidence: 99%

“…The SCF equation for the volume fraction of grafted chains is written in terms of propagators as follows: [10,[17][18][19] …”

Section: Microscopic Model and Theorymentioning

confidence: 99%

Sterically stabilized lock and key colloids: A self-consistent field theory study

Егоров

2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

A self-consistent field theory study of lock and key type interactions between sterically stabilized colloids in polymer solution is performed. Both the key particle and the lock cavity are assumed to have cylindrical shape, and their surfaces are uniformly grafted with polymer chains. The lockkey potential of mean force is computed for various model parameters, such as length of free and grafted chains, lock and key size matching, free chain volume fraction, grafting density, and various enthalpic interactions present in the system. The lock-key interaction is found to be highly tunable, which is important in the rapidly developing field of particle self-assembly.

show abstract

“…The goal of this paper is to present a rigorous analytical theory for a phase transition in a single macromolecule that has received much attention recently, namely the escape transition observed for an end-tethered chain compressed between two pistons [8][9][10][11][12][13][14][15][16][17][18]. At weak compressions, the chain is deformed uniformly to make a relatively thick pancake; the resistance force due to the compressed chain increases monotonously as the distance between two pistons, H, decreases.…”

Section: Introductionmentioning

confidence: 99%

“…The equilibrium properties of the escape transition were investigated thoroughly by scaling theory [8,9], numerical calculations [10,15], and computer modeling [13,14,18]. The main result relates the critical compression distance H * to the piston radius, L, and the chain length, Na.…”

Section: Introductionmentioning

confidence: 99%

Partition function, metastability, and kinetics of the escape transition for an ideal chain

2004

View full text Add to dashboard Cite

An end-tethered polymer chain squeezed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flower-like conformation partially escaped from the gap. We present a rigorous analytical theory for the equilibrium and kinetic aspects of this phenomenon for a Gaussian chain. Applying the analogy with the problem of the adsorption of an ideal chain constrained by one of its ends, we obtain a closed analytical expression for the exact partition function. Various equilibrium thermodynamic characteristics (the fraction of imprisoned segments, the average compression, and lateral forces) are calculated as a function of the piston separation. The force versus separation curve is studied in two complementary statistical ensembles, the constant force and the constant confinement width ones. The differences in these force curves are significant in the transition region for large systems, but disappear for small systems. The effects of metastability are analyzed by introducing the Landau free energy as a function of the chain stretching, which serves as the order parameter. The phase diagram showing the binodal and two spinodal lines is presented. We obtain the barrier heights between the stable and metastable states in the free energy landscape. The mean first passage time, i.e., the lifetime of the metastable coil and flower states, is estimated on the basis of the Fokker-Planck formalism. Equilibrium analytical theory for a Gaussian chain is complemented by numerical calculations for a lattice freely jointed chain model.

show abstract

Analysis of compression of polymer mushrooms using self-consistent field theory

Cited by 23 publications

References 17 publications

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Sterically stabilized lock and key colloids: A self-consistent field theory study

Partition function, metastability, and kinetics of the escape transition for an ideal chain

Contact Info

Product

Resources

About