Shear creep and recovery of a technical polystyrene

Link, G.; Schwarzl, Friedrich Rudolf

doi:10.1007/bf01332257

Cited by 14 publications

(7 citation statements)

References 17 publications

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“…The retardation times of the sample used in the simulation are (in s):

3.0 \times 10^{- 6}

5.0 \times 10^{- 5}, 3.0 \times 10^{- 4}, 4.0 \times 10^{- 3}, 3.0 \times 10^{- 3}, 7.0

, and their respective compliances (Pa −1 ) are

5.0 \times 10^{- 9}, 2.0 \times 10^{- 8}, 5.0 \times 10^{- 9}, 3.0 \times 10^{- 6}, 4.0 \times 10^{- 6}, 7.0 \times 10^{- 8},

and J g =

3.0 \times 10^{- 10}

Pa −1 . This artificial sample does not reproduce the behavior of any real material, although its compliance coincides in orders of magnitude with the compliance of polystyrene at 160 °C (in the timescale shown by Link and Schwarzl). The cantilever parameters for the AFM simulation are the same as those shown in the caption of Figure 2.…”

Section: Resultsmentioning

confidence: 77%

“…(d) Percentage error in the fitted model's

θ (|, ω)

with respect to the Original Model. The Original Model parameters are

J_{g} = 2.0 \times 10^{- 10} {P a}^{- 1}, J_{1} = 5.0 \times 10^{- 9} {P a}^{- 1}, J_{2} = 7.0 \times 10^{- 9} {P a}^{- 1}, J_{3} = 1.0 \times 10^{- 10} {P a}^{- 1}, J_{4} = 3.0 \times 10^{- 6} {P a}^{- 1}, J_{5} = 4.0 \times 10^{- 6} {P a}^{- 1}, τ_{1} = 5.0 \times 10^{- 5} s, τ_{2} = 5.0 \times 10^{- 4} s, τ_{3} = 5.0 \times 10^{- 3} s, τ_{4} = 5.0 \times 10^{- 2} s, τ_{5} = 5.0 \times 10^{- 1} s, ϕ_{f} = 3.7 \times 10^{- 16} {P a}^{- 1} s^{- 1} .

This fictitious sample does not reproduce the behavior of any real material, although for the reader's perspective, its compliance coincides in orders of magnitude with the compliance of polystyrene at 160 °C (in the timescale shown by Link and Schwarzl). The cantilever parameters of the AFM simulation are:

…”

Section: Resultsmentioning

confidence: 99%

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Calculation of standard viscoelastic responses with multiple retardation times through analysis of static force spectroscopy AFM data

López-Guerra

Eslami

Solares

2017

J Polym Sci B Polym Phys

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We explore the physics of an atomic force microscopy (AFM) cantilever tip interacting with a generalized viscoelastic sample containing an arbitrary number of characteristic times, when the cantilever's base is driven with constant velocity toward the sample. This mode of operation, often called static force spectroscopy (SFS), can be harnessed to thoroughly analyze time-dependent viscoelastic information frequently overlooked in experiments. We generalize the solution of previous authors who have studied the standard linear solid model, and offer a solution applicable to any linear viscoelastic model. This generalization is crucial for the prediction of the model's response over wide ranges of time-scale. As a demonstration, successful predictions of harmonic functions (e.g., loss tangent) over a wide frequency range are obtained through analysis of simulated SFS results. In addition, we show that analysis through the generalized solution and previous expressions is no longer valid when the force does not grow linearly in time, so we also deliver an alternate route for extracting the viscoelastic information, which does not rely on the force linearity assumption. Despite the large amount of theoretical content (included for theoretical rigor's sake), the practical user can also benefit from the new procedures offered and the corresponding explanations.

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“…The retardation times of the sample used in the simulation are (in s):

3.0 \times 10^{- 6}

5.0 \times 10^{- 5}, 3.0 \times 10^{- 4}, 4.0 \times 10^{- 3}, 3.0 \times 10^{- 3}, 7.0

, and their respective compliances (Pa −1 ) are

5.0 \times 10^{- 9}, 2.0 \times 10^{- 8}, 5.0 \times 10^{- 9}, 3.0 \times 10^{- 6}, 4.0 \times 10^{- 6}, 7.0 \times 10^{- 8},

and J g =

3.0 \times 10^{- 10}

Section: Resultsmentioning

confidence: 77%

“…(d) Percentage error in the fitted model's

θ (|, ω)

with respect to the Original Model. The Original Model parameters are

J_{g} = 2.0 \times 10^{- 10} {P a}^{- 1}, J_{1} = 5.0 \times 10^{- 9} {P a}^{- 1}, J_{2} = 7.0 \times 10^{- 9} {P a}^{- 1}, J_{3} = 1.0 \times 10^{- 10} {P a}^{- 1}, J_{4} = 3.0 \times 10^{- 6} {P a}^{- 1}, J_{5} = 4.0 \times 10^{- 6} {P a}^{- 1}, τ_{1} = 5.0 \times 10^{- 5} s, τ_{2} = 5.0 \times 10^{- 4} s, τ_{3} = 5.0 \times 10^{- 3} s, τ_{4} = 5.0 \times 10^{- 2} s, τ_{5} = 5.0 \times 10^{- 1} s, ϕ_{f} = 3.7 \times 10^{- 16} {P a}^{- 1} s^{- 1} .

…”

Section: Resultsmentioning

confidence: 99%

Calculation of standard viscoelastic responses with multiple retardation times through analysis of static force spectroscopy AFM data

López-Guerra

Eslami

Solares

2017

J Polym Sci B Polym Phys

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“…The creep compliance strongly increases in the vicinity of the glass transition up to values of the order of 10 −6 Pa −1 . The data indicate that the time scale of glass transition (see also the work of Link and Schwarzl for experimental data) strongly influences compaction of polymer membranes. The Burgers model phenomenologically describes the real behaviour of polymers, and hence is a well‐established model for the creep behaviour of polymers.…”

Section: Creep and Diffusion In Polymersmentioning

confidence: 72%

“…Then a compressive strain of ϵ xx = 0.30 for a membrane with porosity ϵ 0 = 30% is attained, if the tensile creep compliance D membrane ( t ) attains the value 1 × 10 −7 Pa −1 . At a temperature of 70 °C, such a value is attained at time t life = 16/10 −5.49 s = 57 days for bulk polystyrene . In particular in the region around the glass transition temperature, a strong temperature dependence of the life‐time of a membrane can be expected; see, for example, the data of Link and Schwarzl for a technical polystyrene.…”

Section: Estimation Of Time Scalesmentioning

confidence: 97%

“…At a temperature of 70 °C, such a value is attained at time t life = 16/10 −5.49 s = 57 days for bulk polystyrene . In particular in the region around the glass transition temperature, a strong temperature dependence of the life‐time of a membrane can be expected; see, for example, the data of Link and Schwarzl for a technical polystyrene. If a gas is dissolved in a porous support structure of a composite membrane, then the time scale of creep is strongly reduced …”

Section: Estimation Of Time Scalesmentioning

confidence: 99%

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Analysis of compaction and life‐time prediction of porous polymer membranes: influence of morphology, diffusion and creep behaviour

Handge

2016

Polymer International

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In membrane applications, large values of permeability and selectivity are generally desired during the whole period of application. The permeability of porous polymer membranes often is reduced by the effect of compaction. Compaction of polymer membranes is a time‐dependent process which is strongly determined by the viscoelastic properties of the polymer and its plasticisation caused by the feed medium (e.g. a liquid medium or a process gas in the case of porous support structures). In this study, the time‐dependent compaction of porous polymer membranes under pressure is modelled. The influence of viscoelastic and diffusion properties of the polymer material on the permeability of the membrane is analysed for different types of membrane morphologies. The life‐time of a porous polymer membrane is associated with the time at which the glass transition is achieved in a creep experiment. Equations are derived in order to estimate the maximum life‐time of polymer membranes based on compaction. The analysis reveals that the diffusion coefficient, the average retardation time in creep, the magnitude of creep compliance and the time–temperature–pressure shift factor strongly influence compaction of microporous membranes. Generally, a larger tortuosity at constant porosity yields a lower life‐time of the membrane. Buckling of cell struts is the dominant failure mechanism in porous membranes with a very high porosity and allows an estimation of life‐time. © 2016 Society of Chemical Industry

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Compression creep of molten polystyrene

Alemán

1990

Angew. Makromol. Chem.

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Viscoelastic parameters of polystyrene (PS) melt in compression creep have been measured in an lnstron capillary‐rheometer. Bulk compression creep compliance B(t) shows plateau regions in the molten state (B1) and the glassy state (Bg), both decreasing with increasing stress. Shifting of B(t) curves provides master curves suitable to analysing the total (superposed elastic and viscous deformations) bulk compression behaviour. The steady‐state creep compliance (Bs) allows to describe the recoverable elastic energy (Be) and seems to be related to the extrusion die swell (B cs/B ds). Volume viscosity (ηk) decreases with decreasing stress (P), increasing compression rates (k) and decreasing temperature (T).

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Shear creep and recovery of a technical polystyrene

Cited by 14 publications

References 17 publications

Calculation of standard viscoelastic responses with multiple retardation times through analysis of static force spectroscopy AFM data

Calculation of standard viscoelastic responses with multiple retardation times through analysis of static force spectroscopy AFM data

Analysis of compaction and life‐time prediction of porous polymer membranes: influence of morphology, diffusion and creep behaviour

Compression creep of molten polystyrene

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