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stick-ing ratio.It is a daunting challenge to grow 1D nanomate-rials with diameters in a quantum confined regime.According to thermodynamics, the minimum radiusfor a liquid metal droplet of a single component isgiven by[65]rmin = 2Ωl¾lkBTlnS(2)where Ωl, kB, and T denote average atomic volumein liquid, Boltzmann0s constant, and absolute tem-perature, respectively. ¾l, has the same meaning asdefined before. S is the supersaturation ratio in thevapor phase, defined asS = p ¡ p0p0(3)where p and p0 are real gas phase pressure andthe equilibrium pressure with an infinite flat surface,respectively.Equation (2) gives the rmin value in submicrom-eter range. The actual value that can be reached inan experiment is smaller since alloy droplet of two orthree components exists instead of a single componentof a pure metal droplet, where ¾l is much smaller forthe former system than the latter one.Owing to the difficulty in obtaining catalystdroplets in nanometer scale, it is rather challengingto synthesize 1D nanomaterials with small diametersby VLS mechanism. To overcome this difficulty, con-fined synthesis in a nanoscale channels or pores for 1Dnanomaterials has been explored using mesoporoussilica[66–69]and zeolites[70–72].2.2 VS Growth mechanismThe metal alloy droplets are not always needed togrow 1D nanomaterials. When no foreign metal par-ticles are introduced, the growth follows a VS mecha-nism. In this mechanism, the growth proceeds with-out the guidance of metal alloy droplets; instead, thematerial grows with the help of defects, includingscrew dislocations, stacking faults, steps and kinks,and so on. As the name indicates, a vapor phaseand a solid phase are involved in the growth of 1Dnanomaterials. Since the growth usually proceedsvia the evaporation of a solid precursor and conse-quent condensation of the vapor phase again into asolid phase, this mechanism is also called evaporation-condensation mechanism. Similar to VLS mecha-nism, the defects also act as effective collecting sitesfor incoming atoms and growth proceeds preferablywherein. The defects cannot be as effective as thealloy droplets in guiding the growth of 1D nanoma-terials since the capturing efficiency for the defects issmaller than 1. It is not surprising that the growthrate by a VLS mechanism is much larger than thatby a VS one. Consistently, VLS growth is less influ-enced by thermodynamics than VS growth. In a freemode VLS growth, the 1D structure will grow mostlyin a favorable crystallographic orientation that is notnecessary the thermodynamically most stable config-uration, while for a VS growth the crystallographicorientation will be averaged according to statisticaldistribution, which means that under the VS growthmechanism, equilibrium thermodynamics plays a cer-tain role in determining the growth rate and final mor-phology of the nanomaterials.VS mechanism was first proposed and theoreti-cally modeled by Burton, Cabrera, and Frank (BCFtheorem)[73;74], and later elaborated by Sears[75–77].Since then, many materials, including metals andsemiconductors, have been synthesized via this mech-anism in a whisker form[78–81]. Theoretical investiga-tions of the growth processes have also been exten-sively carried out and growth phenomena have beenexplained by using these models[82–88].The theories for VS mechanism were based onthe operation of a screw dislocations at the tip of the growing whiskers as the source of growth steps,however, many experimental results showed that thescrew dislocations had not been confirmed univer-sally, and other defects such as dislocations, stack-ing faults, and twin crystals could also provide thegrowth steps[89;90]. It has been well-known that thefinal shape of a crystal which grows under thermalequilibrium conditions was determined by Wulff the-orem, namely that, the crystals are bound with sur-face planes of minimum total surface free energy[91;92].However, the growth of whiskers in reality takes placeunder nonequilibrium conditions, and thus, the finalmorphology of the crystals may deviate greatly fromwhat Wulff theorem predicts, which means that thegrowth behavior of various planes is manifested kinet-ically. This case is especially true for VS mechanism.As we have discussed earlier,
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