**1. Introduction**

342 Acoustic Waves – From Microdevices to Helioseismology

Raghavan, C. & Ting, E. (1991). Hyper pressure waterjet cutting of thin sheet metal.

Thomas, G. P., & Brunton, J. H. (1970). Drop impingement erosion of metals. *Proceedings of* 

Tsai, S. C., Luu, P., Tam, P., Roski, G., & Tsai, C. S. (1999). Flow visualization of Taylor-mode breakup of a viscous liquid jet. *Physics of fluids*, Vol. 11, No. 6, pp. 1331-1341 Wong, G. S., & Zhu, S. (1995). Speed of sound in seawater as a function of salinity,

Houston, Texas, August, 1991

1519, pp. 549-565

pp. 1732-1736

*Proceedings of 6th American Water Jet Conference*, pp. 493-504, ISBN 1-880342-00-6,

*the Royal Society of London. Series A, Mathematical and Physical Sciences*, Vol. 314, No.

temperature and pressure. *Journal of the Acoustical Society of America*, Vol. 97, No. 3,

Analytical mass-spectrometry (MS) is a powerful, widely-used tool for materials analysis, helping to make progress in materials and environmental sciences, chemistry, biology, astrophysics, etc (Dass 2007). Often the sample to be studied (analyte) is a solid requiring: a) volatilization/desorption of the analyte atoms/molecules and b) their consequent conversion to the charged particles (ionization) prior to mass analysis. The last two decades have seen revolutionary advances in these techniques (Dass 2007) and the use of direct laser irradiation to achieve volatilization is one of the wide-spread methods (Lubman 1990) These pulsed laser-based techniques for the desorption/emission of the atoms, molecules and ions from the surface of solids has benefitted from fundamental study of the process beginning with the invention of the lasers (Honig and Woolston 1963) . A short laser pulse hitting a solid absorbing surface delivers high energy in a small volume inducing a variety of state changes. One consequence is the evaporation/desorption of surface atoms and molecules could be used for further analysis by MS technique. However, the increasing use of MS methods in analytical chemistry of organic and biomolecules revealed that this direct desorption process had significant drawbacks for the analysis of molecular solids. Most importantly, the high energy density produced during irradiation results in not only surface heating but also in excitation of internal vibrational and electronic states of desorbed molecules leading to their partial or even complete fragmentation (Lubman 1990). This difficulty was overcome for many samples by the development of Matrix Assisted Laser Desorption and Ionization (MALDI), which by imbedding the analyte in a specialized UV absorbing molecular solid (the "matrix") allows UV lasers to both desorb and ionize large organic and biomolecules without significant fragmentation (Cole 2010). Because MALDI combines both of the needed initial processes (desorption and ionization) it very quickly following the pioneering publication (Karas, Bachmann et al. 1985) became a key analytical tool. MALDI is now one of principle research tools in proteomics (Cole 2010) and its discovery was recognized with the Nobel Prize in chemistry in 2002.

Despite the success of the MALDI technique current active areas of research include quantification and analysis in the low mass region. Application of MALDI to analyte quantification while possible requires careful attention to matrix/analyte sample

Molecular Desorption by Laser–Driven

LIAD case.

**2.1 Acoustic waves in metal foils** 

a differential equation of the forth order,

**2. Laser-driven acoustic waves in thin metal foils** 

Acoustic Waves: Analytical Applications and Physical Mechanisms 345

The interaction of pulse laser beam with metal surface is very complex phenomenon but our specific interest is in formation of the acoustic waves in irradiated material. To generate an acoustic wave a time dependent stress needs to be applied to the solid. A laser pulse is an excellent tool to generate this kind of the stress. There are two principal mechanisms of laser-induced stress formation in the solids: a) thermal stress, resulted from the non-uniform heating of the irradiated surface by the laser beam; b) mechanical stress due to mechanical impulse transferred from the leaving plasma plume formed on the surface during laser ablation. The parameters of the acoustic waves generated for these two processes are slightly different and will be discussed in details later. Here we will use acoustic wave theory but one should note that its' use is applicable only when the magnitude of the applied stress is small in comparison with the Young's modulus of the material. Large applied stresses can cause the development of the shock waves a phenomenon with different characteristics than acoustic waves (Menikoff 2007). Shock waves have been also hypothesized to be the driver of the LIAD phenomenon, and, as such cannot be entirely excluded from consideration, especially in some extreme cases. Nevertheless, during the last decade, laser-driven acoustic waves emerged in the literature as the "prime suspect" in the

The general governing equation for the generation of elastic waves in solids can be derived by combining the equation of motion and the Hooke's law. In general case it is a differential tensor equation, which interconnects the stress tensor, applied to the body, the displacement of the body's elemental volumes (strain), and their elastic properties. In order to analyze the data in detail, the appropriate stress tensor needs to be determined, and the corresponding set of partial differential equations for strain and stress must be resolved (Pollard 1977). One can simplify this analysis by taking into account specifics of the experiments. For thin foils with *h/R0*<<1 (where *R0* is the radius of the target foil, and *h* is its thickness), a round thin plate approximation can be applied to describe and analyze this problem (Smith 2000). The rise of the strain due to laser heating and the consequent development of the plasma plume can be considered as an external driving force. Generally speaking, the thin plate equation is

<sup>2</sup> 2 2 <sup>2</sup>

2 22 2 1 1 <sup>2</sup> (,) <sup>−</sup> ∂∂∂ ∂ ∂ +⋅ + ⋅ + ⋅ ⋅ − = ∂∂∂ ∂ ∂ *<sup>L</sup> v F <sup>r</sup> <sup>t</sup> r rrr t t*

θ

*vDh <sup>L</sup>* = ⋅ / ρ

where ε is the Poisson ratio, *N* is Young's modulus and

ξ

2

where *ξ=ξ(r,t)* is the surface displacement in the *z* direction (perpendicular to the sample surface), *F(r,t)* is the external driving force caused by the laser irradiation, *vL* is a parameter depending on the material density, *ρ*, thickness, *h*, and flexural rigidity, *D*. Furthermore,

vibrating thin plate is one of the most frequently analyzed mathematical problems, and its detailed analysis can be found elsewhere (McLachlan 1951; Smith 2000). In the discussion

given below, we will remain in the framework of the analysis given by (Smith 2000).

ξ

 α

, and , 3 2 *D Nh* = ⋅ ⋅− ( /12 (1 ))

α

 ξ

ε

is the oscillation decay constant. A

(1)

(2)

preparation, a detailed understanding of the crystallization process with regard to the analyte, and careful many spot analyses (to find the sample signal average which often varies by orders of magnitude as a function of laser position). (Duncan, Roder et al. 2011)

This desire to find a discriminative, sensitive and more easily quantifiable alternative to MALDI has lead us to re-examine another molecular desorption method that doesn't require the use of a matrix. The first observation of this method of molecular desorption (later called Laser Induced Acoustic Desorption, LIAD) belongs (to the best of our knowledge) to B. Lindner (Lindner and Seydel 1985). This observation has been followed by several studies including (Golovlev, Allman et al. 1997) where the abbreviation LIAD was introduced and by (Perez, Ramirez-Arizmendi et al. 2000) who applied the technique to several classes of MS problems.

LIAD has rather simple experimental layout: an analyte is deposited onto the front surface of thin metal foil (the substrate), which is irradiated from the back (i.e. the side opposite to both the analyte and the mass spectrometer) by a pulsed laser beam with power density insufficient to pierce the foil. Such irradiation results in the volatilization of the analyte. The volatilization is largely in the form of neutral molecules that can be utilized for further MS analysis using an appropriate post-ionization method. The method seems to be relatively insensitive to the sample preparation method. Commonly the sample preparation requires only evaporating a drop containing a few nano-moles of the analyte. Remarkably little desorption induced fragmentation is seen when a suitable "soft" ionization method such as VUV photoionization can be found. It is also useful to note that while the molecular signal depends on drive laser intensity the fragmentation observed varies only weakly.

The advantages of LIAD have been demonstrated by many researchers; however, the mechanism is not well understood. The first desorption mechanism was proposed (Golovlev, Allman et al. 1997). It was supposed that because the metal is opaque and completely blocks the direct interaction between the drive laser light and adsorbed, frontside molecules, the only possible way of energy transfer is the mechanical. In this model, the interaction of laser pulse with metal foil backside resulted in formation of acoustic waves that move through the foil inducing a front surface oscillation motion. The molecules that are sitting on this surface desorb due to a simple "shake-off" mechanism similar to those that we use to remove dust particles from our clothes by shaking it.

A difficulty with this model arises when considering the relatively strong surface binding energy experienced even by physisorbed molecules. In order to be efficiently desorbed from the surface, surface molecules need to achieve initial kinetic energies exceeding their surface binding energies (typically in the range of 0.05 - 0.5 eV for physically adsorbed molecules (Adamson and Gast 1997)). This corresponds to velocities of a few hundred m/s for molecules with masses of a few hundred atomic mass units. Unfortunately, acoustic vibrations have mass transfer velocities much lower than the speed of sound, and in elastic deformation mode, this velocity does not exceed a few m/s (Landau and Lifshits 1987). While laser-driven acoustic wave generation in metals is very well studied problem (Hutchins 1985), the physics of their generation in metal foils is crucial to understanding the need for development of new desorption mechanisms. In the next paragraphs we will give a brief theoretical overview and will present our experimental results on laser-driven acoustic waves in thin metal foils.

preparation, a detailed understanding of the crystallization process with regard to the analyte, and careful many spot analyses (to find the sample signal average which often varies by orders of magnitude as a function of laser position). (Duncan, Roder

This desire to find a discriminative, sensitive and more easily quantifiable alternative to MALDI has lead us to re-examine another molecular desorption method that doesn't require the use of a matrix. The first observation of this method of molecular desorption (later called Laser Induced Acoustic Desorption, LIAD) belongs (to the best of our knowledge) to B. Lindner (Lindner and Seydel 1985). This observation has been followed by several studies including (Golovlev, Allman et al. 1997) where the abbreviation LIAD was introduced and by (Perez, Ramirez-Arizmendi et al. 2000) who applied the technique to several classes of

LIAD has rather simple experimental layout: an analyte is deposited onto the front surface of thin metal foil (the substrate), which is irradiated from the back (i.e. the side opposite to both the analyte and the mass spectrometer) by a pulsed laser beam with power density insufficient to pierce the foil. Such irradiation results in the volatilization of the analyte. The volatilization is largely in the form of neutral molecules that can be utilized for further MS analysis using an appropriate post-ionization method. The method seems to be relatively insensitive to the sample preparation method. Commonly the sample preparation requires only evaporating a drop containing a few nano-moles of the analyte. Remarkably little desorption induced fragmentation is seen when a suitable "soft" ionization method such as VUV photoionization can be found. It is also useful to note that while the molecular signal depends on drive laser intensity the fragmentation observed

The advantages of LIAD have been demonstrated by many researchers; however, the mechanism is not well understood. The first desorption mechanism was proposed (Golovlev, Allman et al. 1997). It was supposed that because the metal is opaque and completely blocks the direct interaction between the drive laser light and adsorbed, frontside molecules, the only possible way of energy transfer is the mechanical. In this model, the interaction of laser pulse with metal foil backside resulted in formation of acoustic waves that move through the foil inducing a front surface oscillation motion. The molecules that are sitting on this surface desorb due to a simple "shake-off" mechanism similar to those

A difficulty with this model arises when considering the relatively strong surface binding energy experienced even by physisorbed molecules. In order to be efficiently desorbed from the surface, surface molecules need to achieve initial kinetic energies exceeding their surface binding energies (typically in the range of 0.05 - 0.5 eV for physically adsorbed molecules (Adamson and Gast 1997)). This corresponds to velocities of a few hundred m/s for molecules with masses of a few hundred atomic mass units. Unfortunately, acoustic vibrations have mass transfer velocities much lower than the speed of sound, and in elastic deformation mode, this velocity does not exceed a few m/s (Landau and Lifshits 1987). While laser-driven acoustic wave generation in metals is very well studied problem (Hutchins 1985), the physics of their generation in metal foils is crucial to understanding the need for development of new desorption mechanisms. In the next paragraphs we will give a brief theoretical overview and will present our experimental results on laser-driven acoustic

that we use to remove dust particles from our clothes by shaking it.

et al. 2011)

MS problems.

varies only weakly.

waves in thin metal foils.
