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Water Collection Behavior and Hanging Ability of Bioinspired Fiber Yongping Hou,‡ Yuan Chen,‡ Yan Xue,‡ Yongmei Zheng,*,‡ and Lei Jiang*,‡,§ ‡

Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry and Environment, Beihang University, Beijing 100191, P. R. China § Beijing National Laboratory for Molecular Sciences, Key Laboratory of Organic Solids, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China S Supporting Information *

ABSTRACT: Since the water-collecting ability of the wetted cribellate spider capture silk is the result of a unique fiber structure, bioinspired fibers have been researched significantly so as to expose a new water-acquiring route in fogging-collection projects. However, the design of the geometry of bioinspired fiber is related to the ability of hanging drops, which has not been investigated in depth so far. Here, we fabricate bioinspired fibers to investigate the water collection behavior and the influence of geometry (i.e., periodicity of spindle knot) on the hanging-drop ability. We especially discuss water collection related to the periodicity of geometry on the bioinspired fiber. We reveal the length of the three phase contact line (TCL) at threshold conditions in conjunction with the maximal volume of a hanging drop at different modes. The study demonstrates that the geometrical structure of bioinspired fiber induces much stronger water hanging ability than that of uniform fiber, attributed to such special geometry that offers effectively an increasing TCL length or limits the contact length to be shorted. In addition, the geometry also improves the fog-collection efficiency by controlling tiny water drops to be collected in the large water drops at a given location.

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INTRODUCTION The issue of water shortage has become one of the major global concerns.1−3 Approximately one billion people live without access to clean water sources in rural areas of African, Asian, and Latin American countries. Interestingly, some indigenous animals and plants in many of these regions could readily cope with insufficient access to fresh water or lack of precipitation through dew and fog collection as well as water-vapor absorption.4−6 For example, desert beetles are able to use micrometer-sized patterns of hydrophobic and hydrophilic regions on their backs to capture water from humid air.7 Fog precipitation is a more reliable source of water than rainfall for the desert fauna and flora, and it could also be used as a supplementary source of water for human settlements in this area.8,9 Biomimetic replication of natural fog harvesting systems is becoming a topic of interest to the scientific community with the aim being to help maximize fog-collection efficiency.10,11 Recently, our team has found that the water-collecting ability of the capture silk of the cribellate spider (Uloborus walckenaerius) is the result of a unique fiber structure that forms after wetting. These structural features result in a surface energy gradient between the spindle knots and the joints and also in a difference in Laplace pressure, with both factors acting together © 2012 American Chemical Society

to achieve continuous condensation and directional collection of water drops around spindle knots.12 This finding may open new routes to design a fog-collection project. It is well-known that the fogwater drops are much finer (1−40 μm) than raindrops. If these tiny water drops cannot be collected effectively, they would quickly be lost due to the heat and winds in the environment.7 How to control the collection behavior of water drops and modulate the ability of water collection on fiber by mimicking the biological structures is an important issue for improving the fog-collection efficiency on fiber-based devices. Here, we fabricate a series of the bioinspired fibers to investigate the water collection behavior and the influence of geometry on hanging-drop ability. Related to the periodicity of geometry on bioinspired fiber, two modes of directional water collection are discussed, which reveal the length of the three phase contact line (TCL) at threshold conditions in conjunction with the maximal volume of a hanging drop. The study demonstrates that the geometry of bioinspired fiber induces a much stronger water-hanging ability than that of Received: November 29, 2011 Revised: February 8, 2012 Published: February 15, 2012 4737

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Figure 1. Structural features of bioinspired fiber. Optical and SEM images of spindle knot on fiber surface at different drawing out velocities: (a) 50, (b) 100, (c) 150, (d−h) 200 mm s−1. Optical images a−d indicate the drawing velocity has a significant influence on the size of the spindle knot. With the increasing drawing velocity, the height, length, and periodicity of the spindle knot increase obviously. SEM images show (e) a single rough geometric spindle knot, (f) the connecting part between spindle knots composed of porous rough structure, and (g−h) the roughness gradient that forms from the center region (g) to the side region of a spindle knot (near the connecting part), accompanying the anisotropic distribution due to the structure extension (h). completely in the ambient environment, periodic polymer spindle knots formed, similar to the geometry of wetted spider silk. Volume of Hanging Water Drops. During the process of water collection, it was found that the water drop changed to ellipsoid because of the influence of gravity. Thus we calculated the volume of water drop V = 4πra2rb/3 (ra and rb are the horizontal radius and vertical radius of a water drop, respectively, Figure S1, Supporting Information). Vm is taken as the maximal volume before a drop detaches. The maximal volume (Vm) of a water drop and the length (L) of TCL were correlated by linear fitting of the OriginPro8 software. Characterization of Microstructure. The structures of fiber and spindle knot were observed by scanning electron microscope (SEM, Quanta FEG 250, FEI) at 25 kV with gold plating. Water Collection and Observation. In order to clearly observe the behavior of water drops, the fibers and bioinspired fibers placed on a small U-shaped holder were put in a chamber of sample. Numerous tiny water drops generated by an YC-E350 ultrasonic humidifier (Beijing YADU Science and Technology Co., Ltd.) were introduced into the sample chamber and collected on the fiber. The behavior of water drop was recorded by the optical contact angle meter system (OCA 40, Dataphysics Instruments GmbH, Germany) with time scale. Time zero was chosen to be the frame in which collected drops began to visually appear.

uniform fiber, attributed to such special structure that offers effectively an increasing TCL length or limits the contact length between the water drop and fiber to be shorted. In addition, the geometry also improves the fog-collection efficiency by controlling the movement of tiny water drops to form large water drops at a given location and free the original place for a new cycle of collection. This study is significant to design materials for developing the application on a large scale into the fogwater collection tents and web filtering projects such as for the noxious emission of aerosol and dust pollution from chemical plants.2,13−17

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EXPERIMENTAL SECTION

Fabrication of Nylon Fiber Specimens and Bioinspired Fibers. The nylon fiber specimens were made by using an adhesive tape to fix a single nylon fiber with a diameter of ∼17 μm (obtained from TaiZhou Feite Nylon Rope & Net & Belt CO., LTD, China) on a U-shaped holder with a certain amount of tension, and the length of the fiber was about 2.5 cm. Bioinspired fibers with a poly(vinylidene fluoride) (PVDF) (Mw = 300 000, Aldrich) spindle knot were prepared by immersing nylon fiber specimens in the PVDF/DMF solution (DMF: N,N-dimethylformamide) (7:100, PVDF:DMF, by weight) and drawing it out horizontally at different velocities (50−200 mm/s). A cylindrical film of polymer solution was then formed on the fiber surface and spontaneously broken up into polymer drops along the fiber owing to the Rayleigh instability. After the fiber was dried

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RESULTS AND DISCUSSION By understanding the surface structure feature on wetted spider silk, we fabricate a series of bioinspired fibers by using original 4738

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Figure 2. Observation and illustration of water collection on two spindle knots of bioinspired fiber. (a) Optical image of directional water collection that was observed on two spindle knots of bioinspired fiber. Water is collected (Frame 1), coalesced (Frame 2), and grown (Frame 3). The distance between the spindle knots is short, and the water drop is rooted on the two spindle knots during coalescence of water drops (Frame 4−6). Finally, the water drop detaches from two spindle knots. The zoomed pictures show that first some tiny drops appear on both sides of the contact region between the water drop and fiber and then appear on the whole region before falling off (Frame 4−6, the tops). (b) Model illustration of water collection above (Frames 1−6 are the side view; Frames 1′−6′ are the top view; gray and blue parts denote bioinspired fiber and water drops, respectively, and the red dashed line denotes the three phase contact line). Compared to a common fiber, a water drop is rooted on the spindle knot and the contact length is almost constant. As the water drop grows, the liquid film on the surface of the spindle knot and fiber breaks up gradually and the length of TCL also increases slowly. At threshold conditions, the TCL is composed of two half-ellipses and two lines and the length (L) of TCL can be written as L ≈ 2m + π(bl + b2) (m being the contact length between fiber and water drop; 2b1, 2b2 being the height of the spindle knot).

structure similar to that of natural spider silk which can be related to the ability of directional water collection. Furthermore, the behavior of water drops on different bioinspired fibers was observed by a charge coupled device (CCD) camera. It is found that water drops are collected on the spindle knots of bioinspired fiber as expected. There seem to be two modes of directional water collection on bioinspired fiber due to the periodicity of spindle knots: i.e., two spindle knots collect together and a single spindle knot collects individually. In the mode of water collection by two spindle knots, in general, the periodicity of the spindle knot is relatively short (Figure 2a; ∼39.5 μm in height, ∼127.5 μm in length, and ∼426.7 μm in periodicity). Initially, it is observed that water drops are collected on every spindle knot of bioinspired fiber (Figure 2a, Frame 1) and grow gradually (Figure 2a, Frame 2). Then the water drop is rooted on the two spindle knots during coalescence of two water drops (Figure 2a, Frame 3) and the contact length (m) between the fiber and water drop (see Supporting Information Figure S1 for the definition of m) is almost constant during the whole process. The reason for this is that both the surface energy gradient and difference in Laplace pressure drive drops to move from joints to the center of the spindle knots (the curvature and water contact angle are the smallest). As the drop grows in size, the drop changes into a downward clam-shell conformation and some tiny water drops appear on the top surface of the spindle knot and fiber (Figure 2a, Frame 4−6), which indicates that the liquid film on the surface of the spindle knots and fiber begins to break up. Finally, the gravity overcomes the surface force and a water

nylon fiber and PVDF polymer via the Rayleigh instability method. Figure 1 shows optical microscopy images and scanning electron microscope (SEM) images of spindle knots on bioinspired fibers via different drawing velocities. It is clear that periodic spindle knots are formed on the fiber surface (Figure 1a−d). With the increasing of drawing velocity, the size of spindle knot increases from ∼38.3 to ∼93.5 μm in height, from ∼125.3 to ∼235.5 μm in length, and from ∼362.4 to ∼1057.1 μm in periodicity. The statistical data about the height, length, and periodicity of the spindle knots are shown in Table S1 in detail (Supporting Information), which indicates that drawing velocity has a significant influence on the size of the spindle knot. In addition, it is observed that there are some small spindle knots between larger spindle knots, which may be attributed to the second Rayleigh instability.18 As for the microscale structure feature, the SEM observation shows the rough geometric feature of a spindle knot (Figure 1e) and the connecting part composed of porous structure between spindle knots (Figure 1f). And, the gradient roughness is formed along a spindle knot from the center region (Figure 1g) to the side region (near the connecting part, Figure 1h), accompanied with anisotropic distribution due to the structure extending. Thus, water drops can be driven by the surface energy gradient arising from differences in roughness.19 In addition, the spindle-shaped geometry will generate a difference in Laplace pressure,20,21 which will cooperatively favor this directional movement of drops toward the spindle knots. This fabrication and observation above indicate that the bioinspired fiber has a 4739

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Figure 3. Observation and illustration of water collection on one spindle knot of bioinspired fiber. (a) Optical images of directional water collection that were observed on one spindle knot of bioinspired fiber. Water is collected (Frame 1), coalesced (Frame 2), and grown (Frame 3). The distance between the spindle knots is long, and every spindle knot collects water, respectively (Frames 4−6). Finally, a water drop detaches from a single spindle knot. The zoomed pictures show that more and more tiny drops appear on the fiber and spindle knot surface as the water drop grows (Frame 4−6, the tops). Finally, a water drop detaches from one spindle knot. (b) Illustration of water collection above (Frames 1−6 are the side view; Frames 1′−6′ are the top view; gray and blue parts denote bioinspired fiber and water drops, respectively, and red dashed line denotes the three phase contact line). Under this circumstance, a water drop on bioinspired fiber cannot move easily and one side is rooted on the spindle knot. The length of TCL also increases slowly during the water collection process, and when the volume reaches maximal volume, the TCL is composed of one-half-ellipse and two lines and the length (L) of the TCL can be written as L ≈ 2m + πb (m being the contact length between the fiber and water drop; 2b being the height of the spindle knot).

Supporting Information Figure S2a, with the increase in the volume of a drop, the drop changes from asymmetric clamshell, downward barrel to downward clam-shell conformation. The zoomed pictures in Figure S2a also show that at first some tiny drops appear on both sides of the contact region between the water drop and fiber, and then appear on the whole contact region before falling off. In addition, it is observed the position of water drop changes continually on the surface of the fiber and the contact length increases sharply and then decreases slowly at ∼78.77 s (Table S2, Supporting Information). The movement of water drop is due to less resistance on the uniform fiber surface. The increase of the contact length is ascribed to the water growing and the coalescence of tiny drops at random, and the decrease is owed to the fact that the contact angle at the TCL should keep constant.16 Figure 4 shows the water collection volume of nylon fiber and bioinspired fiber with time scale. Under the given conditions, the maximal volume by two spindle knots of bioinspired fiber exceeds 4.51 μL (Figure 4b), which is larger than that by one spindle knot (∼2.41 μL) and by a common fiber (∼1.66 μL). The evident difference of the maximal volumes implies that the size of the spindle knot has important influence on the hanging ability of bioinspired fiber. In addition, this also indicated that the efficiency of water collection on bioinspired fiber is more than that of common fiber in the first 100 s (e.g., ∼7.04 × 10−5 μL/(μm·s) for two spindle knots, ∼2.73 × 10−5 μL/(μm·s) for one spindle knot, and ∼8.19 × 10−6 μL/(μm·s) for no spindle knot), which is attributed to the

drop detaches from two spindle knots. Before the water drop detaches, it is observed that tiny water drops appear on the whole contact surface between the fiber and water drop (Figure 2a, Frame 6), which reveals the liquid film has completely broken up. The maximal volume (Vm) reaches ∼4.51 μL in ∼211.05 s, which is almost three times as large as that of common nylon fiber (see below, ∼1.66 μL in ∼204.58 s for fiber radius r = 8.8 μm) in nearly the same time. It is clear that the spindle knot could improve fog-collection efficiency. Interestingly, when the periodicity of a spindle knot becomes long enough (Figure 3; ∼89.7 μm in height, ∼187.4 μm in length, and ∼842.7 μm in periodicity) that water drops are also collected on the spindle knots of bioinspired fiber (Figure 3a, Frame 1) and grow gradually (Figure 3a, Frame 2), the water drops on different spindle knots cannot coalesce together. Every spindle knot collects water respectively, and finally, the drop detaches from the one spindle knot (Figure 3a, Frame 3− 6). It is also found that, during this process, the contact length is not constant, but one side of the contact region is always fixed on a spindle knot and the water drop could not move easily (Figure 3a, Frame 3−6). As the water drop grows, more and more water drops also appear on the top surface of the spindle knot and fiber which indicates that the liquid film breaks up gradually (Figure 3a, Frame 4−6). Finally, the maximal volume reaches ∼2.40 μL in ∼109.63 s. In order to study deeply the water-collecting behavior of bioinspired fiber, water collection behavior is also focused on the common nylon fiber (radius r = 8.8 μm). As shown in 4740

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their model, for a fiber radius r = 8.8 μm, the maximal volume is ∼0.80 μL. In our experiments, since water wet the nylon fiber partially, the maximal volume should be less than 0.80 μL. In fact, the maximal volume reaches ∼1.66 μL. That implies the model could be restricted at threshold conditions and the TCL is not simply two circles. Moreover, the volume increases with the increase of the value of sin α, but in a nonlinear relation, which is opposed to Lorenceau’s theory.26 When sin α is above 0.75, the larger the sin α, the sharper the volume increases, which indicates that the length of TCL surpasses 4πr and the length of TCL increases gradually. This is in good accord with the observations of Figure S2a. On the basis of the results above, the model of water collection of a common fiber can be improved as shown in Figure S2b. It could be described in four stages. At the initial stage (Figure S2b, Frame 1), a small, upward clam-shell conformation can be observed stably because of contact line pinning. Then, for a large enough drop (Figure S2b, Frame 2−4), with the effect of gravity, the shape of the drop, particularly the barrel conformation, becomes elongated in the downward direction. The liquid film of two sides of contact range begins to break up slowly and the length of TCL increases gradually. In a third stage (Figure S2b, Frame 5), with the increase in volume of water drop, the drop changes to downward clam-shell conformation and the liquid film continues to break up slowly. Eventually, the drop volume is too large (Figure S2b, Frame 6), the liquid film of fiber surface breaks up entirely and the length of the TCL cannot increase any more. The gravity overcomes the surface force and the drop falls off the fiber. It is clear that the length of TCL increases gradually as the water drop grows. Although it is difficult to get the accurate value of the length during the water collection process, when the water drop just detaches the fiber (the liquid film breaks up entirely), we could use L ≈ 2m (m being the contact length between fiber and water drop) to estimate the length of TCL. At this moment, sin α is very close to 1 (Table S2, Supporting Information), and we do not consider the influence of sin α. Thus the eq 1 could be written as

Figure 4. Comparison of water-collection ability with time scale. (a) Nylon fiber, the radius of fiber r = 8.8 μm. The maximal volume of a hanging drop is up to ∼1.66 μL, taking more than ∼200 s to stay on the fiber until detaching from the fiber. (b) Two spindle knots of bioinspired fiber. The maximal volume of a hanging drop is up to ∼4.52 μL, taking time of more than 210 s to stay on the fiber until detaching from it. (c) One spindle knot of bioinspired fiber. The maximal volume of a hanging drop is up to ∼2.41 μL, which takes ∼110 s to stay on the fiber until detaching from it. The bioinspired fiber displays more efficient water collection and a larger hanging ability by two spindle knots than with one spindle knot or nylon fiber.

continuous directional movement of tiny water drops on bioinspired fiber to form large water drops at spindle knots and free up space for a new cycle of collection.22,23 As for the above noted difference of water collection efficiency, this might be owed to the fact that two spindle knots have more collecting sites and larger contact length than one spindle knot to collect more water drops.22 As well-known, when the water drop hangs on thin fiber, gravity can be balanced with capillary force.24 A criterion can be derived to determine if a drop will be hung by a fiber surface by examining the interplay of gravity and surface force.25 Gravity (F) is determined from the density (ρ) and volume (V) of the liquid drop, i.e., F = ρgv, where g is the acceleration due to gravity. On the other hand, the component force of surface force in the vertical direction (f) depends on some parameters, such as the surface tension of the water (γ), its apparent contact angle with the fiber surface (θ), the off-axis angle (α; see Supporting Information Figure S1), and the length (L) of TCL, which is described as: f = γL cos θ sin α. Equating the gravity and the component force of surface force,26 i.e., F = f, the volume of the drop can be related to the off-axis angle, the apparent contact angle, and the length of TCL as follows: V=

γ cos θ L sin α ρg

Vm =

2γcosθ γcosθ L≈ m ρg ρg

(2)

We get the maximal volume (Vm) and the length (L) of TCL (L ≈ 2m) for different samples (Table S3, Supporting Information) and plotted the Vm as a function of L in Figure S3b. A linear relation is found between these two quantities, which could prove our model and the method of estimating the length of TCL is correct to some extent. As for the case of the bioinspired fiber, according to the CCD observations (Figure 2a and 3a), we also propose corresponding models of directional water collection: two spindle knots collect together and a single spindle knot collects individually, as shown in Figure 2b and 3b. The change of configurations of drop and the length of TCL on bioinspired fiber is similar to that on common fiber. It is clear that the length of TCL increases gradually during the water collection and it is very difficult to get an accurate length of TCL due to the special configuration of the spindle knot. When the volume reaches the Vm, tiny water drops appear on the whole contact surface between the fiber and water drop (this reveals that the liquid film has completely broken up) (Figure 2a, Frame 6, and Figure 3a, Frame 6), and we could use some easy methods to estimate the length of TCL. When a water drop detaches from a two spindle

(1)

Lorenceau26 has reported a method to model a large drop hanging on thin fibers and assumed that the force resulting from the horizontal fibers was equivalent to the force generated by two similar fibers connected to the drop at the same location, yet pointing radially. Since the liquid wetted the fiber, they got the volume V = 4πγr sin α/ρg and the maximal volume Vm = 4πγr/ρg (they thought L = 4πr, where r is the radius of the fiber). We measured the value of α, ra, and rb, from pictures such as those in Figure S2a (data shown in Supporting Information, Table S2). The results are displayed that the volume is a function of the sine of α (see Supporting Information Figure S3a). However, something is different: e.g., the maximal volume exceeds the theoretical value. According to 4741

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Figure 5. Relationship of the maximal volume (Vm) of hanging drop and the length (L) of TCL. (a) Water drops on two spindle knots. There is the linear relationship via fitting of data: i.e., Vm = −1.65 + 3.10L (μL) (see red line). (b) Water drops on one spindle knot. There is the linear relationship via fitting of data: i.e., Vm = 1.50 + 1.24L (μL) (see red line).

knot has the ability of limiting the contact region to be shorted, which is also helpful to increase the length of TCL. Otherwise, it seems that the water hanging ability of bioinspired fiber is chiefly related to the height and periodicity of the spindle knot.

knot surface (Figure 2), the water drop is rooted on the center of the spindle knot and the TCL is composed of two halfellipses and two lines. We use L ≈ {1/2[2πb1 + 4(a1 − b1)] + 2b1} + {1/2[2πb2 + 4(a2 − b2)] + 2b2} + 2(m − a1 − a2) = 2m + π(b1 + b2) (2a1, 2a2 and 2b1, 2b2 are the length and height of the spindle knot, as shown in Figure 2b) to estimate the length of the TCL. Equation 2 could be written as Vm =

γcosθ γcosθ L≈ [2m + π(b1 + b2)] ρg ρg

γcosθ γcosθ L≈ (2m + πb) ρg ρg

CONCLUSION

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ASSOCIATED CONTENT

In conclusion, we studied the water-collection behavior of common fiber and bioinspired fibers and proposed the models to value the ability of water collection. It is found that bioinspired fiber has more efficient water collection ability than that of nylon fiber due to a spindle knot acting as condensing sites and collecting sites of drops to thus quickly transport the collected water drops to form larger water drops at given location. In addition, we reveal two-style directional water collection on bioinspired fiber: i.e., two spindle knots collect together and single spindle knot collects individually. It seems that there are two reasons for larger hanging ability of bioinspired fiber: (1) The spindle knot could increase the length of TCL. (2) The spindle knot has the ability of rooting the contact length, which is also helpful to increase the length of TCL. It is demonstrated that the mode of two spindle knots generates the stronger larger water hanging ability and the higher collection efficiency than that of one spindle knot, which is due to the larger TCL length and more collecting sites on two spindle knots than that on one spindle knot. This study will help to design smart structured fiber materials to enhance efficiency in fog-collection. It is also of great significance to develop the application on a large scale into the fogwater collection tents and web, filtering projects for the noxious emission of aerosol and dust pollution from chemical plants.

(3)

When a water drop detaches from the one spindle knot surface, the TCL is composed of one-half-ellipse and two lines and the length of TCL can be written, L ≈ {1/2[2πb + 4(a − b)] + 2b} + 2(m − a) = 2m + πb (denoting 2a and 2b as the length and height of the spindle knot, as shown in Figure 3b). Equation 2 could be written as Vm =

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(4)

According to eqs 3 and 4, we plot the maximal volume Vm as a function of the length (L) of TCL for different samples (Table S3, Supporting Information), as shown in Figure 5. A very good linear relation is also found between these two quantities, which indicates the models and the methods of estimating the length of TCL are feasible. According to the numerical coefficient, we use eqs 3 and 4 to infer the apparent contact angles between water and bioinspired fiber in two cases, i.e., 77.40° for two spindle knots and 66.90° for one spindle knot, both of which are close to the apparent contact angles between water and fiber coated by PVDF (65.75°). The difference of the apparent contact angles might be ascribed to different configurations of water drop. According to eq 3, the increase of the periodicity and size of the spindle knot could increase the length (L) of TCL and the maximal volume (Vm) of the hanging drop. When the periodicity exceeds some values (e.g., ∼550 μm), the mode (in eq 3) changes to one spindle knot collection mode (i.e., described in eq 4) and the maximal volume of the hanging drop would decrease. Under our experimental conditions, the maximal volume of the hanging drop by two spindle knots is up to 5.16 μL, which is larger than that by one spindle knot or of a common fiber. From the observations above and our models, there may be two reasons for the larger hanging ability of bioinspired fiber: (1) The spindle knot could increase the length of TCL. (2) The spindle

* Supporting Information S

Supplementary Figures S1−S3 and Tables S1−S3. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.Z.) and [email protected] (L.J.). Notes

The authors declare no competing financial interest. 4742

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ACKNOWLEDGMENTS This work is supported by National Research Fund for Fundamental Key Project (2010CB934700), National Natural Science Foundation of China (20973018, 21004002), Fundamental Research Funds for the Central Universities (YWF-1001-C10, YWF-11-02-045, YWF-10-01-B16), Doctoral Fund of Ministry of Education of China (20101102110035), and Specialized Research Fund for the Doctoral Program of Higher Education (20111102120049, 20111102120050).

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