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Research Papers

Variable Chain Confinement in Polymers With Nanosized Pores and Its Impact on Instability

[+] Author and Article Information
Shan Tang

College of Aerospace Engineering,
Chongqing University,
Chongqing 400017, China
e-mail: stang@cqu.edu.cn

Steven M. Greene, Wing Kam Liu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Xiang He Peng

College of Aerospace Engineering,
Chongqing University,
Chongqing 400017, China

Zaoyang Guo

Institute of Solid Mechanics,
Beihang University,
Beijing 100191, China

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 6, 2015; final manuscript received June 15, 2015; published online July 9, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(10), 101001 (Oct 01, 2015) (10 pages) Paper No: JAM-15-1228; doi: 10.1115/1.4030864 History: Received May 06, 2015; Revised June 15, 2015; Online July 09, 2015

Recent experiments and molecular dynamics simulations have proven that polymer chains are less confined in layers near the free surfaces of submicron-nanosized pores. A recent model has incorporated this observed variable chain confinement at void surfaces in a mechanism-based hyperelastic model. This work employs that model to do two things: explain the large discrepancy between classical homogenization theories and physical experiments measuring the modulus of nanoporous polymers, and describe the instability behavior (onset and postinstability deformation) of this class of materials. The analysis demonstrates that less confinement of polymer chains near free surfaces of voids inhibits tilting buckling while promoting pattern transformation. The sensitivity of geometric instability modes to void size is also studied in depth, helping lay the foundation for fabricating solids with tunable acoustic and optical properties. The simulation approach outlined provides experimentalists with a practical route to estimate the thickness of the interfacial layer in nanoporous polymers.

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Figures

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Fig. 1

(a) Three typical submicron-nanopolymer systems. (b) On the left: polymer chains close to a free surface easily orient along the free surface, resulting in small radius of gyration and larger fictitious tube confinement. On the right: polymer chains in the bulk are more randomly intertwined and have a large radius of gyration leading to a smaller confining tube.

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Fig. 2

(a) Schematic of a unit cell with uniform distributed voids with the same void size subjected to compressive loadings in the simulation. (b) The initial tube diameter decreases exponentially from the void surface to the bulk in the interfacial layer.

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Fig. 3

Comparison of three homogenization theories and the chain confinement model employed here with experiments [17]

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Fig. 4

The strain at the onset of instability versus void volume fraction under three levels of confinement difference between the interfacial layer and the bulk. The solid line with symbol represents the dsurf/dbulk = 1 and the dotted line with symbol represents the dsurf/dbulk = 4. Three instability regions are delineated, marked by I, II, and III.

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Fig. 5

Eigenmode transition from tilting pattern to pattern transformation for (a) dsurf/dbulk = 1 corresponding to points A' and A and (b) dsurf/dbulk = 4 corresponding to points B' to B shown in Fig. 4

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Fig. 6

Eigenmode transition from localization to tilting pattern for (a) dsurf/dbulk = 1 corresponding to points C' and C and (b) dsurf/dbulk = 4 corresponding to points D' to D shown in Fig. 4

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Fig. 7

Nominal stress versus nominal strain curves under three levels of chain confinement between the interfacial layer and the bulk in the postbuckling analysis. A series of deformed shapes at various levels of compression are displayed, showing the process of pattern transformation with dsurf/dbulk = 4.

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Fig. 8

Eigenmodes 1 and 3 of finite-sized specimen under compression for four different levels of void size with the same void volume fraction 0.47

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Fig. 9

The strain at the onset of instability versus void size with void volume fraction 0.47 and dsurf/dbulk = 4

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Fig. 10

Nominal stress versus nominal strain curves under four levels of void size and the same void volume fraction 0.47. A series of deformed shapes at various levels of compression are displayed with a large void size, showing more homogeneous pattern transformation.

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Fig. 11

(a) The strain at the onset of instability versus void size with void volume fraction 0.24 and dsurf/dbulk = 4. (b) Nominal stress versus nominal strain curves under four levels of void size and the same void volume fraction 0.24.

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