Fracture in one dimension

Welland, R. W.; Shin, Mincheol; Allen, Douglas R.; Ketterson, J. B.

doi:10.1103/physrevb.46.503

Cited by 13 publications

(8 citation statements)

References 3 publications

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“…At non-zero temperature, any finite-length loosely bound chain cannot be in equilibium when it is under tension. So, for a chain pulled from its ends at non-zero temperature, if the chain starts unbroken it will always break given time [41,46]. Under periodic boundary conditions or fixed boundary conditions a chain at nonzero temperature will repeatedly break and "heal", even if the chain is under pressure, so that the number of breaks in the chain will fluctuate with time.…”

Section: Clusters and Breaks In Loosely Bound Chainsmentioning

confidence: 99%

Cluster sizes in a classical Lennard-Jones chain

Lee-Dadswell¹,

Barrett²,

Power³

2017

Phys. Rev. E

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The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed.Analytical expressions are obtained for the expected cluster length, K , as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that K increases exponentially with β = 1/k B T and with pressure, P in agreement with previous results in the literature. A method is illustrated for using K (β, P ) to generate a "phase diagram" for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.

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Section: Clusters and Breaks In Loosely Bound Chainsmentioning

confidence: 99%

Cluster sizes in a classical Lennard-Jones chain

Lee-Dadswell¹,

Barrett²,

Power³

2017

Phys. Rev. E

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“…1). This problem has been studied previously by numerical simulations [5,6,7] and theoretically with phenomenological assumptions on the effect of friction on the collective modes [8,9]. Multidimensional Kramers escape theory has also been applied to the study of breakage in a one-dimensional ring [10].…”

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confidence: 99%

Thermal breakage of a discrete one-dimensional string

Lee

2009

Phys. Rev. E

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We study the thermal breakage of a discrete one-dimensional string, with open and fixed ends, in the heavily damped regime. Basing our analysis on the multidimensional Kramers escape theory, we are able to make analytical predictions on the mean breakage rate, and on the breakage propensity with respect to the breakage location on the string. We then support our predictions with numerical simulations.PACS numbers: 82.20.Uv, 02.50.Ey Recently, there is much discussion on the possibility of exploiting biopolymers as functional materials [1,2,3,4]. To achieve this goal, the stabilities of such materials have to be thoroughly investigated. Furthermore, the facts that the biopolymers are necessarily finite and consist of discrete parts, such as individual peptides in an amyloid fibril [2], have to be taken into consideration. As a step towards this direction, we study here a toy model for the breakage of a discrete one-dimensional string under thermal fluctuations, in both fixed-ended and openended configurations (c.f. Fig. 1). This problem has been studied previously by numerical simulations [5,6,7] and theoretically with phenomenological assumptions on the effect of friction on the collective modes [8,9]. Multidimensional Kramers escape theory has also been applied to the study of breakage in a one-dimensional ring [10]. The energy profile for the bonds in the string is usually modeled by a quadratic potential at the minimum energy region, and by an inverted quadratic potential at the breakage point. Here, we employ a simplified model where all bonds are assumed to be Hookian up to the breakage point. This model has the virtue of rendering the theoretical analysis asymptotically exact as temperature goes to zero. By studying in detail the energy dependency on the collective modes, we are able to employ the multidimensional Kramers escape theory to predict the breakage rate and the breakage propensity with respect to the breakage location. These predictions are then verified by numerical simulations.A. String with fixed ends

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“…Consequently, it is not possible by any means for the activation energy E S to be smaller than E b . Finally, we notice an unexpected large variation on S and E S with N. Before we discuss those results, we note that Welland et al 9 plotted as a function of T. From their results we got ln͑͒ as a function of ␤, which suggested a straight line. However, their four points were not enough to obtain a good activation energy.…”

Section: ͑3͒mentioning

confidence: 70%

“…In this way, both computer simulations and analytical results have been obtained for harmonic 8 and anharmonic chains. 9,10 Welland et al 9 performed computer simulations on 1D systems. They used the Lennard-Jones potential and fixed boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Transition-state analysis for fracture nucleation in polymers: The Lennard-Jones chain

Oliveira

1998

Phys. Rev. B

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We present here a microscopic theory for fracture nucleation in finite chains, which may account for results found in simulations and in some experimental situations. We obtain the characteristic breaking time for an ensemble of one-dimensional Lennard-Jones chains, which is mainly a large prefactor times an Arrhenius rate. We show that the expression scales well and that the activation energy agrees with the analytical results. We show that the delay in the fragmentation is a consequence of the long-range time correlation in the relative motion of two adjacent particles. This correlation is responsible for the origin of a self-organized memory as well as the large elongation necessary for irreversible break to occur. We discuss the possibility of using this simple theory to understand the main characteristic of fragmentation in more complex and realistic systems.

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Fracture in one dimension

Cited by 13 publications

References 3 publications

Cluster sizes in a classical Lennard-Jones chain

Cluster sizes in a classical Lennard-Jones chain

Thermal breakage of a discrete one-dimensional string

Transition-state analysis for fracture nucleation in polymers: The Lennard-Jones chain

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