Compression of a polymer chain by a small obstacle: The effect of fluctuations on the escape transition

Ennis, Jonathan; Sevick, Edith M; Williams, D. R. M.

doi:10.1103/physreve.60.6906

Cited by 26 publications

(56 citation statements)

References 12 publications

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“…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

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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.

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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

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“…The region of extreme compression H Ͻ 1 (not shown in the diagram) was studied extensively by Ennis et al [10]. Of course, under these conditions the compression entropy and the stem elasticity become strongly dependent on the details of the model used (lattice vs off-lattice, persistent vs freely jointed, etc., including the particulars of the single-segment bond potential).…”

Section: Barrier Heights Separating the Stable And The Metastable mentioning

confidence: 99%

“…It serves as a good starting point for understanding more general situations and the escape transition for ideal chains was investigated very thoroughly by Ennis et al using numerical methods [10]. We start from an analogy between an escape transition and a coil-to-flower transition for a chain near a solid adsorbing surface to construct a closed-form analytical expression for the partition function.…”

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%

“…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%

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

2004

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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.

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On the Escape Transition of a Tethered Gaussian Chain; Exact Results in Two Conjugate Ensembles

Skvortsov

Klushin

Leermakers

2006

Macromolecular Symposia

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Summary: Upon compression between two pistons an end‐tethered polymer chain undergoes an abrupt transition from a confined coil state to an inhomogeneous flower‐like conformation that is partially escaped from the gap. In the thermodynamic limit the system demonstrates a first‐order phase transition. A rigorous analytical theory of this phenomenon for a Gaussian chain is presented in two ensembles: a) the H‐ensemble, in which the distance H between pistons plays the role of the control parameter, and b) the conjugate f‐ensemble in which the external compression force f is the independent parameter. A loop region for 〈f(H)〉 with negative compressibility exists in the H‐ensemble, while in the f‐ensemble 〈H(f)〉 is strictly monotonic. The average lateral forces taken as functions of H (or 〈H〉, respectively) have distinctly different behavior in the two ensembles. This result is a clear counterexample of the main principles of statistical mechanics stating that all ensembles are equivalent in the thermodynamic limit. Another theorem states that the thermodynamic potential as a function of volume must be concave everywhere. We demonstrated that the exact free energy in the H‐ensemble contradicts this statement. Inapplicability of these fundamental theorems to a macromolecule undergoing the escape transition is clearly related to the fact that phase coexistence in the present system is strictly impossible. This is a direct consequence of the tethering and the absence of global translational degrees of freedom of the polymer chain.

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Compression of a polymer chain by a small obstacle: The effect of fluctuations on the escape transition

Cited by 26 publications

References 12 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

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

On the Escape Transition of a Tethered Gaussian Chain; Exact Results in Two Conjugate Ensembles

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