GLYPH<s49>GLYPH<s46> GLYPH<s48> GLYPH<s50>GLYPH<s46> GLYPH<s48> GLYPH<s51>GLYPH<s46> GLYPH<s48> GLYPH<s52>GLYPH<s46> GLYPH<s48> GLYPH<s49> GLYPH<s53> GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s53> GLYPH<s50> GLYPH<s48> GLYPH<s52>GLYPH<s71>GLYPH<s80>GLYPH<s97> GLYPH<s49>GLYPH<s48>GLYPH<s71>GLYPH<s80>GLYPH<s97> GLYPH<s56>GLYPH<s71>GLYPH<s80>GLYPH<s97> GLYPH<s40> GLYPH<s98>GLYPH<s41> GLYPH<s73>GLYPH<s110>GLYPH<s110>GLYPH<s101>GLYPH<s114>GLYPH<s109>GLYPH<s111>GLYPH<s115>GLYPH<s116>GLYPH<s32>GLYPH<s116>GLYPH<s117>GLYPH<s98>GLYPH<s101>GLYPH<s32>GLYPH<s114>GLYPH<s97>GLYPH<s100>GLYPH<s105>GLYPH<s117>GLYPH<s115>GLYPH<s32> GLYPH<s82> GLYPH<s32>GLYPH<s91>GLYPH<s110>GLYPH<s109>GLYPH<s93> GLYPH<s78>GLYPH<s117>GLYPH<s109>GLYPH<s98>GLYPH<s101>GLYPH<s114>GLYPH<s32>GLYPH<s111>GLYPH<s102>GLYPH<s32>GLYPH<s119>GLYPH<s97>GLYPH<s108>GLYPH<s108>GLYPH<s115>GLYPH<s32>GLYPH<s32> GLYPH<s78> GLYPH<s82>GLYPH<s105>GLYPH<s100>GLYPH<s103>GLYPH<s101>GLYPH<s32> GLYPH<s99> GLYPH<s117>GLYPH<s114>GLYPH<s118>GLYPH<s101>GLYPH<s32> GLYPH<s111>GLYPH<s102> GLYPH<s32> GLYPH<s116> GLYPH<s104>GLYPH<s101>GLYPH<s32> GLYPH<s112> GLYPH<s67> GLYPH<s45>GLYPH<s115> GLYPH<s117>GLYPH<s114>GLYPH<s102> GLYPH<s97>GLYPH<s99> GLYPH<s101> GLYPH<s54>GLYPH<s71>GLYPH<s80>GLYPH<s97> GLYPH<s49>GLYPH<s46> GLYPH<s48> GLYPH<s50>GLYPH<s46> GLYPH<s48> GLYPH<s51>GLYPH<s46> GLYPH<s48> GLYPH<s52>GLYPH<s46> GLYPH<s48> GLYPH<s49> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s53> GLYPH<s50>GLYPH<s48> GLYPH<s49>GLYPH<s54> GLYPH<s49>GLYPH<s55> GLYPH<s40> GLYPH<s97>GLYPH<s41> GLYPH<s55> GLYPH<s49>GLYPH<s53> GLYPH<s49>GLYPH<s52> GLYPH<s49>GLYPH<s51> GLYPH<s49>GLYPH<s50> GLYPH<s49>GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s57> GLYPH<s56> GLYPH<s52> GLYPH<s53> GLYPH<s54> GLYPH<s56> GLYPH<s55> GLYPH<s78>GLYPH<s117>GLYPH<s109>GLYPH<s98>GLYPH<s101>GLYPH<s114>GLYPH<s32>GLYPH<s111>GLYPH<s102>GLYPH<s32>GLYPH<s119>GLYPH<s97>GLYPH<s108>GLYPH<s108>GLYPH<s115>GLYPH<s32>GLYPH<s32> GLYPH<s78> GLYPH<s73>GLYPH<s110>GLYPH<s110>GLYPH<s101>GLYPH<s114>GLYPH<s109>GLYPH<s111>GLYPH<s115>GLYPH<s116>GLYPH<s32>GLYPH<s116>GLYPH<s117>GLYPH<s98>GLYPH<s101>GLYPH<s32>GLYPH<s114>GLYPH<s97>GLYPH<s100>GLYPH<s105>GLYPH<s117>GLYPH<s115>GLYPH<s32> GLYPH<s82> GLYPH<s32>GLYPH<s91>GLYPH<s110>GLYPH<s109>GLYPH<s93> GLYPH<s32> GLYPH<s79>GLYPH<s117>GLYPH<s116> GLYPH<s119>GLYPH<s97>GLYPH<s114>GLYPH<s100> GLYPH<s73> GLYPH<s110>GLYPH<s119>GLYPH<s97>GLYPH<s114>GLYPH<s100> GLYPH<s110>GLYPH<s61>GLYPH<s57> FIG. 3: (color online) (a) Phase diagram of the radial corrugation for embedded MWNTs. A slanted solid line represents the phase boundary between the inward-deformation phase (below the line) and the outward phase (above). (b) Contour plot of the critical pressure p c ( R,N ) on the R - N plane. A solid line represents the ridge line appearing in the three-dimensional p c -surface (see Fig. 2(b)). D. Corrugation amplitudes lowing two effects of irradiation on the mechanical stiff- ness of MWNTs: irradiation reduces the axial stiffness because it creates vacancies, 46,47 and simultaneously, it enhances the radial stiffness owing to the production of covalent bonding between adjacent walls. 32 A quantita- tive examination of the degree to which this hypothe- sis holds requires elaborated measurements or large-scale atomistic simulations, and therefore, we have no avail- able data for the proof. Instead, it is possible to gener- alize the theoretical method by considering the possible anisotropic elasticity in the medium. Our preliminary calculations showed that moderate anisotropy causes lit- tle modification in the phase diagram. More detailed results will be shown elsewhere. The contrasting difference in corrugation amplitude distributions between the inward and outward phases is quantified by plotting the deformation amplitudes δ ¯ µ$_{i}$ introduced in Eq. (7). Figure 4 shows the normalized deformation amplitudes, ξ$_{i}$ ≡ | δ ¯ µ$_{i}$/δ ¯ µ$_{N}$ | , of individual concentric walls for N -walled nanotubes with different N and R = 6 . 0 nm be fixed. It follows from the figure that the value of ξ$_{1}$ suddenly drops off from ξ$_{1}$ > 1 . 0 to ξ$_{1}$ < 1 . 0 across the phase boundary ( i.e. , from N = 8 to 9 with R = 6 . 0 nm being fixed). To understand this visually, we show in Fig. 5 the sequential variation of the corrugation amplitude distribution in the cross section near the phase boundary, In the inward mode ( N ≤ 8), the restoring force exerted by the surrounding medium is relatively strong so that it tends to prevent radial de- formation of outer walls; this is why inner walls exhibit significant corrugation amplitudes to lower the energy U of the system. By increasing N , such restoring force ef- fects become ineffective to support the radial instability of outer walls, as a result of which the system falls into the outward phase for N ≥ 9. A similar scenario applies if we fix N and modulate R in the vicinity of the phase boundary. We have also performed corrugation analyses by im- posing other values of E$_{M}$ than E$_{M}$ = 100 GPa. It was found that larger (smaller) values of E$_{M}$ result in more (less) number of corrugation modes observed in the phase diagram with fixed ranges of R and N set in Fig. 3(a). With decreasing E$_{M}$ , the phase boundary shifts down- ward until E$_{M}$ = 0 . 1 GPa, below which the boundary disappears leaving the outward phase as the only possi- bility. Therefore, our predictions of diverse corrugation patterns and the two corrugation phases are possible for any choice of E$_{M}$ as far as E$_{M}$ > 0 . 1 GPa. From an engineering perspective, the selectivity of the innermost wall geometry by tuning the material param- eters R , N and p may be useful in developing nanotube- based nanofluidic 24–26 or nanoelectrochemical devices $^{27}$, because both utilize the hollow cavity within the in- nermost tube. A very interesting issue from the aca- demic viewpoint is the effect of the core tube defor- mation on the physical and chemical properties of in- tercalated molecules confined in the hollow cavity. It has thus far been known that various types of interca- lated molecules (diatomic gas, water, organic, and tran- The present results are based on the approximation that the radially shrinking part of an MWNT under electron-beam irradiation is mapped onto a continuum elastic medium with homogeneous and isotropic elastic- ity of the modulus E$_{M}$ = 100 GPa. The validity of the homogeneity and isotropy hypothesis depends on the fol- IV. DISCUSSIONS 5