Fundamentals of Atomic Force Microscopy Part 2: Dynamic AFM Methods

Transcription

1 Fundamentals of tomic Force Microscopy Part 2: Dynamic FM Methods Week 2, Lecture 5 ttractive and repulsive regimes and phase contrast in amplitude modulation FM rvind Raman Mechanical Engineering Birck Nanotechnology Center 1

2 From the last lecture ω=ω 0 0 1/Q = () V (Z,) 1 E (Z,) k Q πk 1 E (Z,) + 2 Q πk tan ( φ ) = ( 2) V (Z,) 2 2 k called amplitude setpoint ratio Theory of Tapping mode FM Theory of FM-FM, and F is constan t ω changes to keep phase lag fixed at 90 V (Z,) ω=ω ' =ω 1 () k F changes to keep fixed 0 ω ω 1 ω E 0 F = k = k ( ) 2 ω Q' ω Q 0 0 πk Z changes to keep a constant frequency shift V (Z,) ω = ω' ω = ω () k o 2

3 M-FM attractive-repulsive regimes M-FM attractive-repulsive regimes Is it possible for two different Z values to lead to the same amplitude? ssume E =0, so from (1) we have 1/Q = V (Z,) k Q 2 2 The only way that two Z values, Z 1 >Z 2 lead to same amplitude is if V (Z,) = V (Z,) 1 2 since V appears squared in the denominator 3

4 M-FM attractive-repulsive regimes + CONS q V (Z,) = F q = k (Z + q) 1 dq ssume E 0 = π q= 2 Z 1 Z 2 k (nn/nm) 2 1 k (nn/nm) 2 1 d (nm) V(Z 1,)>0 d (nm) V(Z 2,)<0 It is possible to achieve the same amplitude at two different Z positions: One where V(Z 1,)>0 called attractive regime nother where V(Z 2,)<0 called repulsive regime 4

5 M-FM attractive-repulsive regimes tan 1 E (Z,) + 2 Q πk φ = V (Z,) 2 2 k ( ) E >0, but V can change sign In tapping mode (or M-FM) attractive regime refers to when V >0 so that the tip mostly encounters attractive force gradien during the oscillation cycle. For attractive regime, tan(φ)<0 therefore φ>90 degrees In tapping mode (or M-FM) repulsive regime refers to when V <0 so that the tip encounters net repulsive force gradien during the oscillation cycle. For repulsive regime, tan(φ)>0 therefore φ<90 degrees 5

6 M-FM attractive-repulsive regimes R. Garcia and. San Paulo, Phys. Rev. B, 61, R13381, San Paulo and R. Garcia, Biophysical Journal, 78, 1599, 2000 Often attractive (L) and repulsive (H) regimes have different amplitudes, but for a range of Z values the same amplitude can co-exist at different Z positions Repulsive regime imaging leads to larger forces Soft cantilevers, small amplitudes -> cantilever stays longer in the attractive regime Vice versa for stiff levers, larger amplitudes 6

7 From last class k V (Z,) = cos φ 2Q ( 3) 2 πk πk E (Z,) = sin φ Q Q ( 4) Re arranging Q sin φ= E (Z,) ( ) 2 πk 2Q cos φ= V (Z,) ( 6) 2 k 1/Q = V (Z,) 1 E (Z,) k Q πk Phase contrast 2 2 Virial and dissipation are not independent in M-FM, given an amplitude set point and the dissipation, we know exactly what the virial must be If E = 0 uniformly over the sample then sin (φ)=/, uniformly! Regardless of whether the conservative properties ( e.g. elastic modulus, van der Waals, electrostatic forces etc.) change over the sample! In reality there is always some contrast in even in the attractive regime, and phase contrast is due to a combination of contrast in conservative (virial) and dissipative interactions 7

8 sin(φ) cos(φ) Phase contrast Q E (Z,) 3 4 πk 1 2 φ φ=0 φ=π/2 φ=π φ Q sin φ= 1 + E (Z,) 2 πk 2Q cos φ= V (Z,) 2 k When entire image is taken in repulsive regime Brighter phase lag = more dissipation Brighter phase lag = less virial When entire image is taken in attractive regime Brighter phase lag = less dissipation Brighter phase lag = more virial Z adjus to attain the corresponding V 8

9 General considerations If most energy dissipation and virial is due to repulsive viscoelastic interactions then brighter phase lag = more dissipative and softer elastic modulus material If most energy dissipation (in repulsive regime) is from water capillary hysteresis brighter phase lag = more hydrophillic surface (Sahagun et al, 98(17), , Phys. Rev. Lett., 2007) When strong (dry) adhesion is present then situation is more complicated In liquids this understanding can actually change (Melcher et al, 106(33), 13655, Proc. Natl. cad. Sci, 2009) 9

10 Example 1 Reference: Magonov et al/ Surf. Sci. Lett, 375, 1997 Primary dissipation is from repulsive interactions Brighter phase lag is softer and more dissipative material What is being plotted phase lead or lag? Phase Height (left) and phase (right) images of PDES patches on a Si substrate using o= 1 00 nm. The rubbing direction during the deposition of PDES on Si was from bottom left to top right: (a) light tapping; (b) moderate tapping. In all height images the contrast covers height varia tions in the nm range. In all phase images the contrast covers phase angle variations from - 90 to 90. mplitude This is a map of phase lead! Brighter phase lead is stiffer and less dissipative material 10

11 Example 2 Reference:. Gil et al, Langmuir, 16, 5086, 2000 Primary dissipation is from capillary forces Brighter phase lag is more dissipative (more water) Brighter phase lead is less water and less dissipation These images show water adsorbed on a mica substrate. Left images correspond to topography and right images to phase lead contrast. ll of them were taken in tapping mode. The gray scale of the topographic images corresponds to about 2 nm in both images, with the brightest areas being the highest poin of the surface. The scale of the phase images is arbitrary. The scan size is 840 nm 840 nm for images a and b and 2.0 by 2. 0 microns for images c and d. Images a and b show islands of water layer of 0.7 and 1.4 nm height, with a phase contrast which is specially strong between the different water layers. In images c and d the trace of a previous scan in contact appears on the 11 surface. Due to the contact scan, the water layer has spread homogeneously over the surface.

12 ppendix When dealing with phase contrast in the attractive regime say due to capillary forces, we would like to sound a cautionary note the basic underlying assumption is that the tip oscillates harmonically at the drive frequency. Recent resul sugges that this may not always be true* in the presence of strong capillary necks * M. Kober et al, Physica Status Solidi, 2(3),