Elastic Entropic Forces in Polymer Deformation
"> Figure 1
<p>(<b>a</b>) The hysteresis curves for a PMVS rubber specimen subjected to repeated forced extension, and compression at 250 mm/min at room temperature, with the relative strain <math display="inline"><semantics> <mi>ε</mi> </semantics></math>. (<b>b</b>) The <span class="html-italic">standard linear solid</span> (SLS) mechanical model.</p> "> Figure 2
<p>(<b>a</b>) The strain dynamics in the case of constant strain rate <math display="inline"><semantics> <mrow> <mo>±</mo> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> over the stretching and retracting deformations. (<b>b</b>) The model stress–strain curves for the constant strain rate <math display="inline"><semantics> <mrow> <mo>±</mo> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> over the stretching and retracting deformations.</p> "> Figure 3
<p>(<b>a</b>) A particular solution (<a href="#FD24-entropy-24-01260" class="html-disp-formula">24</a>) of the KVDE (<a href="#FD22-entropy-24-01260" class="html-disp-formula">22</a>) for <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. (<b>b</b>) The experimental creep curves for silicon rubber under the initial stress <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>6.4947</mn> </mrow> </semantics></math> MPa, at the temperatures <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>80.3</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math>C (solid curve 1), <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>80.6</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math>C (triangles, curve 2), and another time at <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>80.6</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math>C (crosses, curve 3) for reproducibility.</p> "> Figure 4
<p>(<b>a</b>) The recovery of reversible deformation, <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>e</mi> </msub> </semantics></math>, over time after rotation shut down in polystyrene melts at <math display="inline"><semantics> <mrow> <mn>190</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>, with shear rate <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>γ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>0.012</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, shear stress <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>114.3</mn> </mrow> </semantics></math> Pa, and the total value of reversible deformation <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>1.135</mn> </mrow> </semantics></math>. (<b>b</b>) The value of <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mfenced separators="" open="(" close=")"> <mi>η</mi> <mo>/</mo> <mi>τ</mi> </mfenced> </mrow> </semantics></math> as a function of share stress <math display="inline"><semantics> <mi>τ</mi> </semantics></math> for polystyrene melts at <math display="inline"><semantics> <mrow> <mn>180</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>, for the stretching rates ranging from <math display="inline"><semantics> <mrow> <mn>0.0648</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> to 2 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 5
<p>(<b>a</b>) The linear relationship between the value of reversible deformation, <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>e</mi> </msub> </semantics></math>, and the logarithm of shear rate, <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mover accent="true"> <mi>γ</mi> <mo>˙</mo> </mover> </mrow> </semantics></math>, for polystyrene melts at <math display="inline"><semantics> <mrow> <mn>190</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>, measured sequentially at the following shear rates: <math display="inline"><semantics> <mrow> <mn>0.100</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.113</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.150</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.150</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.201</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.201</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.299</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.300</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.500</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.500</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>1.00</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>2.00</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. (<b>b</b>) The linear relationship between the reversible deformation, <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>e</mi> </msub> </semantics></math>, and logarithm of shear stress <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mi>τ</mi> </mrow> </semantics></math> for polystyrene melts at <math display="inline"><semantics> <mrow> <mn>190</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> <mi mathvariant="normal">C</mi> </mrow> </semantics></math> measured at the constant shear rates, as specified in (<b>a</b>). (<b>c</b>) The value of <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mfenced separators="" open="(" close=")"> <mi>η</mi> <mo>/</mo> <mi>τ</mi> </mfenced> </mrow> </semantics></math> plotted against the volume of reversible deformation, <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>e</mi> </msub> </semantics></math>, measured in polystyrene melts at <math display="inline"><semantics> <mrow> <mn>180</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>, for the stretching rates ranging from <math display="inline"><semantics> <mrow> <mn>0.0648</mn> </mrow> </semantics></math> s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> to 2 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 6
<p>(<b>a</b>) True stress vs. strain dependence for silicone rubber at room temperature at a tensile rate of 250 mm/min for the first (dashed line 1) and second (solid line 2) hysteresis cycles. (<b>b</b>) Dependence of the value −<math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mfenced separators="" open="(" close=")"> <mrow> <mrow> <mo>(</mo> <mi>H</mi> <mo>+</mo> <mi>E</mi> <mo>)</mo> </mrow> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> <mo>−</mo> <mover accent="true"> <mi>σ</mi> <mo>˙</mo> </mover> </mrow> </mfenced> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>η</mi> </msub> <mo>≡</mo> <mrow> <mo>(</mo> <mi>σ</mi> <mo>−</mo> <mi>E</mi> <mi>ε</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for the ascending strain curve shoulder of the first hysteresis cycle (dashed line 1) and the second hysteresis cycle (solid line 2).</p> "> Figure 7
<p>Approximation of the second hysteresis loop in the framework of linear relations (<a href="#FD16-entropy-24-01260" class="html-disp-formula">16</a>) in the framework of the modified SLS model requires three linear segments: the initial (<b>a</b>), main (<b>b</b>), and final (<b>c</b>) segments of the ascending tensile curves.</p> "> Figure 8
<p>(<b>a</b>) The creep curves (PMVS) and their approximation according to the KV model (<a href="#FD22-entropy-24-01260" class="html-disp-formula">22</a>) taken for an initial stress of <math display="inline"><semantics> <mrow> <mn>6.4947</mn> </mrow> </semantics></math> MPa. (<b>b</b>) The creep curves (PMVS) observed at the value of initial stress <math display="inline"><semantics> <mrow> <mn>8.1633</mn> </mrow> </semantics></math> MPa, at temperatures of <math display="inline"><semantics> <mrow> <mn>26.2</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (curve 1) and <math display="inline"><semantics> <mrow> <mn>54.8</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (curve 2), as well as at the initial stress value of <math display="inline"><semantics> <mrow> <mn>6.495</mn> </mrow> </semantics></math> MPa at temperatures of <math display="inline"><semantics> <mrow> <mn>80.3</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (curve 3) and <math display="inline"><semantics> <mrow> <mn>106.5</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (curve 4).</p> "> Figure 9
<p>(<b>a</b>) Approximation of the creep curves shown in <a href="#entropy-24-01260-f008" class="html-fig">Figure 8</a>b in the framework of the KV model (<a href="#FD22-entropy-24-01260" class="html-disp-formula">22</a>). The descriptions of the lines are the same as in <a href="#entropy-24-01260-f008" class="html-fig">Figure 8</a>b. (<b>b</b>) Linearity of the <math display="inline"><semantics> <mrow> <mo>−</mo> <mo form="prefix">ln</mo> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> value against <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>σ</mi> <mo>−</mo> <mi>E</mi> <mi>ε</mi> <mo>)</mo> </mrow> </semantics></math> as predicted by the KV model (<a href="#FD22-entropy-24-01260" class="html-disp-formula">22</a>) has been verified for PMVS rubber, for a variety of initial stresses and at various temperatures: at <math display="inline"><semantics> <mrow> <mn>25</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (shown by solid lines), for the following initial stress values—<math display="inline"><semantics> <mrow> <mn>8.835</mn> </mrow> </semantics></math> MPa (curve 1), <math display="inline"><semantics> <mrow> <mn>8.163</mn> </mrow> </semantics></math> MPa (curve 2), <math display="inline"><semantics> <mrow> <mn>3.365</mn> </mrow> </semantics></math> MPa (curve 3), <math display="inline"><semantics> <mrow> <mn>2.428</mn> </mrow> </semantics></math> MPa (curve 4), and <math display="inline"><semantics> <mrow> <mn>1.722</mn> </mrow> </semantics></math> MPa (curve 5); at <math display="inline"><semantics> <mrow> <mn>55</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (shown by crosses), for the following initial stress values—<math display="inline"><semantics> <mrow> <mn>8.163</mn> </mrow> </semantics></math> MPa (curve 6) and <math display="inline"><semantics> <mrow> <mn>7.228</mn> </mrow> </semantics></math> MPa (curve 7); at <math display="inline"><semantics> <mrow> <mn>55</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (shown by dashed lines): <math display="inline"><semantics> <mrow> <mn>7.037</mn> </mrow> </semantics></math> MPa (curve 8) and <math display="inline"><semantics> <mrow> <mn>6.495</mn> </mrow> </semantics></math> MPa (curve 9); at <math display="inline"><semantics> <mrow> <mn>100</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math> (shown by points)—<math display="inline"><semantics> <mrow> <mn>5.679</mn> </mrow> </semantics></math> MPa (curve 10) and <math display="inline"><semantics> <mrow> <mn>6.909</mn> </mrow> </semantics></math> MPa (curve 11).</p> "> Figure 10
<p>(<b>a</b>) The slopes of creep curves, <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <msub> <mi>η</mi> <mn>0</mn> </msub> <mo>=</mo> <mo form="prefix">ln</mo> <mi>A</mi> <mo>+</mo> <msub> <mi mathvariant="script">E</mi> <mn>0</mn> </msub> <mo>/</mo> <msub> <mi>k</mi> <mi>B</mi> </msub> <mi>T</mi> <mo>,</mo> </mrow> </semantics></math> shown in <a href="#entropy-24-01260-f009" class="html-fig">Figure 9</a>b against the values of initial stress. (<b>b</b>) The viscous volume coefficient <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>/</mo> <msub> <mi>k</mi> <mi>B</mi> </msub> <mi>T</mi> </mrow> </semantics></math> shown against the values of initial stress <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>0</mn> </msub> <mo>,</mo> </mrow> </semantics></math> with the stress and temperature data specified in <a href="#entropy-24-01260-f009" class="html-fig">Figure 9</a>b.</p> "> Figure 11
<p>(<b>a</b>) Values of Flory’s correction factor <span class="html-italic">g</span> against the initial stress values <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> in the measurements with stress and temperature specified in <a href="#entropy-24-01260-f009" class="html-fig">Figure 9</a>b. (<b>b</b>) The values of <math display="inline"><semantics> <mrow> <mo>−</mo> <mo form="prefix">ln</mo> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> against strain <math display="inline"><semantics> <mi>ε</mi> </semantics></math> measured at a variety of initial stress values and at various temperatures. Solid lines are for measurements taken at <math display="inline"><semantics> <mrow> <mn>25</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math>, for the following stress values: <math display="inline"><semantics> <mrow> <mn>8.835</mn> </mrow> </semantics></math> MPa (curve 1), <math display="inline"><semantics> <mrow> <mn>8.163</mn> </mrow> </semantics></math> MPa (curve 2), <math display="inline"><semantics> <mrow> <mn>3.365</mn> </mrow> </semantics></math> MPa (curve 3), <math display="inline"><semantics> <mrow> <mn>2.428</mn> </mrow> </semantics></math> MPa (curve 4), and <math display="inline"><semantics> <mrow> <mn>1.722</mn> </mrow> </semantics></math> MPa (curve 5). Crosses show the measurements taken at <math display="inline"><semantics> <mrow> <mn>55</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math>, for the following stress values: <math display="inline"><semantics> <mrow> <mn>8.163</mn> </mrow> </semantics></math> MPa (curve 6) and <math display="inline"><semantics> <mrow> <mn>7.228</mn> </mrow> </semantics></math> MPa (curve 7). Dashed lines show the measurements taken at <math display="inline"><semantics> <mrow> <mn>80</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math>, for the following stress values: <math display="inline"><semantics> <mrow> <mn>7.037</mn> </mrow> </semantics></math> MPa (curve 8) and <math display="inline"><semantics> <mrow> <mn>6.495</mn> </mrow> </semantics></math> MPa (curve 9). Points stay for the measurements taken at <math display="inline"><semantics> <mrow> <mn>100</mn> <msup> <mspace width="0.166667em"/> <mo>°</mo> </msup> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">C</mi> </semantics></math>, for the following stress values: <math display="inline"><semantics> <mrow> <mn>5.679</mn> </mrow> </semantics></math> MPa (curve 10) and <math display="inline"><semantics> <mrow> <mn>6.909</mn> </mrow> </semantics></math> MPa (curve 11).</p> "> Figure 12
<p>A schematic representation of a possible tensile curve for stretching branched polymers.</p> ">
Abstract
:1. Introduction
2. Methods: Accounting for Entropic Elastic Forces in Polymer Deformation Processes
2.1. Viscosity Anomalies in Polymer Flows
2.2. Dependence of Elastomer Tensile Curves on Elastic Entropic Forces
- (1)
- With increasing deformation over the stretching phase, the EEF reinforces the resistance of molecular network against the tensile stress fostering an increase of the jump activation energy in Eyring’s formula (3) by an amount where is a viscous volume coefficient related to the stretching deformation [5,14,30], viz.,
- (2)
- In a retraction phase of deformation, the EEF decreases the jump activation energy by an amount , as the action of EEF coincides with the retraction direction of the specimen deformation, and, therefore,
2.3. Entropic Elastic Forces for Creeping Prediction
3. Results: Experimental Verification of Entropic Elastic Forces
3.1. Experimental Verification of the Entropic Nature of Viscosity Anomaly
3.2. Experimental Verification of the Effect of Elastic Entropic Forces on Elastomer Tensile Curves
3.3. Experimental Study of Creeping Behavior in Silicon Rubber
4. Discussion
- The experimentally recorded values of the Flory correction coefficient g depend on neither temperature nor stretching rate. We, therefore, assume that the value of g may characterize the tendency of polymers to maintain a stable structure in mechanical deformation.
- Flory’s corrections measured for the repeated hysteresis loops were close to each other. Only the first hysteresis round seems to differ substantially from the others, as also predicted by the analytic solutions of the model Equations (18)–(20). The prominent distinction between the first stretching of the specimen and the subsequent rounds indicates an irreversible change that occurs in the polymer structure due to the rupture of weak structural constituents, after which the system acquires a more deformation resistible structure, as manifested by the Mullins effect. The specimen acquires a slight residual deformation, which changes a little during subsequent hysteresis cycles (see Figure 1a)
- Up to five stable segments can be identified visually on the experimental hysteresis curves. In particular, there are three regions of increasing deformation and two regions of reversible deformation. The measured values of Flory corrections exhibited sufficient reproducibility for all tested samples. For the tested PMVA specimen, the recorded Flory correction factor was 5–7 units.
- A quantitative description of elastomer deformation can be obtained, using the basic equations of the statistical theory of rubber elasticity and Eyring’s equation modified to take into account the entropic nature of deformation in polymers. For the stretching phase of rubber deformation, the elastic forces increase the activation energy, while they decrease during the retraction deformation.
- The small segments at the beginning and at the end of tensile curves (denoted as the initial and final segments of hysteresis cycles) show a stress growth slowdown, which may be associated with a decrease in the activation energy. There was a significant change in the values of Flory corrections in these segments at the same time. The final section of the return hysteresis curve has a particularly sharp increase in the Flory correction factor. This can be interpreted as a result of a strong increase in the number of physical cross-links at the final stage of the elastomer chain folding process.
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
EEF | Elastic Entropic Force |
IEP | Irreversible Entropy Production |
KVDE | Kelvin–Voigt Differential Equation |
KVM | Kelvin–Voigt Model |
MFI | Melt Flow Index |
MKU | Molecular Kinetic Units |
PMVS | Polymethylvinylsiloxane (rubber) |
RUL | Remaining Useful Life |
SLS | Standard Linear Solid |
Appendix A. Entropic Force of Elasticity
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Hysteresis Cycle | Ascending Strain Interval | g | Determination, | Tensile Slope, |
---|---|---|---|---|
1 | [1.8–20%] | 24 | ||
1 | [21–170%] | |||
2 | [21–56%] | 10 | ||
2 | [65–164%] | |||
2 | [166–179%] |
Hysteresis Cycle | Ascending Strain Interval | g | Determination, | Tensile Slope, |
---|---|---|---|---|
1 | [173–103%] | 7 | ||
1 | [65–25%] | 70 | ||
2 | [178–81%] | |||
2 | [70–29%] | 81 |
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Kartsovnik, V.I.; Volchenkov, D. Elastic Entropic Forces in Polymer Deformation. Entropy 2022, 24, 1260. https://doi.org/10.3390/e24091260
Kartsovnik VI, Volchenkov D. Elastic Entropic Forces in Polymer Deformation. Entropy. 2022; 24(9):1260. https://doi.org/10.3390/e24091260
Chicago/Turabian StyleKartsovnik, Vladimir I., and Dimitri Volchenkov. 2022. "Elastic Entropic Forces in Polymer Deformation" Entropy 24, no. 9: 1260. https://doi.org/10.3390/e24091260