**4.1 "Shake-off "mechanism versus thermal origin of molecular desorption**

The "shake-off" mechanism of molecular desorption in LIAD for a long time was considered as the only sensible explanation of the observed phenomenon. However, as was shown above, it contradicts both with general physical considerations and with the experimentally measured parameters of acoustic vibrations of the surface as well as with the observed energy and velocity spectra of desorbed molecules.

An important consequence of the backside irradiation is the heating of the front side. Considering this effect, we should keep in mind that this heating process in LIAD is distinctly different from the case of direct front-side laser irradiation (LD). In the latter case, due to the small value of skin depth in metals, the rate of the temperature rise is extremely high. In case of backside irradiation of the foils, the front surface temperature is governed by the heat conduction through the metal foil, which makes the heating rate much slower than that for the front side irradiation geometry. For one-dimensional heat conduction problem, the specific time of the temperature rise is defined by the heat propagation time <sup>2</sup> τ α = *l* / , where *α* is the thermal diffusivity of the metal and *l* is the foil thickness. For the foil thicknesses typical for LIAD (~10 µm) and the thermal diffusivity of the most metals *α*≈0.2 – 0.7 cm2s-1, *τ* has the values in the range of a few µs. Our numerical calculations using the heat conduction equation showed that for Ta foil with the thickness of 12.5 µm and the driving laser fluence 3.5 J/cm2 (corresponding under conditions of our experiments to the peak laser intensity of about 500 MW/cm2), the front surface temperature rise is 375 K, which reaches its maximum 1.75 µs after the laser desorbing pulse ceases. If experiments

Molecular Desorption by Laser–Driven

Acoustic Waves: Analytical Applications and Physical Mechanisms 363

where E is the Young's modulus, v is the Poisson ratio, *hf* is the thickness of organic film and R is the radius of curvature of the foil surface. From the other side, the stress, resulting from

*t sf* = − ⋅Δ ⋅ − *T E*

where *α<sup>s</sup>* and *α<sup>f</sup>* are thermal expansion coefficients of the substrate and the film respectively, *ΔT* is the temperature increase. There is not much information in the literature on thermomechanical parameters for molecular crystals but based on existing data for anthracene (Bondi 1968) we can estimate the order of the generated stress values. Under the assumption that *α<sup>f</sup>* =2.8 ·10-4 K-1 , *α<sup>s</sup>* = 6.3 ·10-6 K-1, *E*= 13 GPa, *v*≈0.25, and *ΔT*=100 K, we can obtain *σt*=485 MPa. At the same time, the stress associated with acoustic vibrations is much lower: σ*m*≈1.7 kPa (taking into account that maximal value of *R* is approximately 1 m, and the film thickness never exceeded 10-7 m,). This is a negligible value, in comparison with *σt* , which means that the thermal mismatch stress is the principal reason for cracks formation. The estimate of internal energy, stored in thermally strained organic films can be done with

> 2 2 2 0

> > 2 2 2

*A*

*s f*

*E T M*

α α  π

ν

, (17)

(18)

(19)

thermal mismatch has the following value (Boley and Weiner 1960)

 ( ) /(1 ) σ αα

using of following expression (Boley and Weiner 1960)

2

2

ν ρ

*<sup>g</sup> <sup>N</sup>* ν

ν

ν

2 (1 )

by breaking intermolecular bonds and forming new desorption sites.

**4.3 Proposed mechanisms of the molecules desorption** 

The average energy per analyte molecule can easily be calculated

*a*

(1 ) () 2 2 (1 ) ⋅ + = ⋅ − ⋅Δ ⋅ ⋅ ⋅ ⋅ ⋅ − *<sup>s</sup> f f <sup>E</sup> G T <sup>r</sup> <sup>h</sup>*

αα

(1 ) ( )

− ⋅Δ ⋅ ⋅ + = ⋅ ⋅− ⋅

Here *M* is the molar mass, *ρ* is the specific gravity and *NA* is the Avogadro number. It is interesting to note that *ga* does not depend on the analyte island size but strongly depends on the thermal and mechanical parameters. Again with the use of existing data for anthracene we can estimate the value of *ga*, and for *ΔT*=100 K we will get *ga*=0.025 eV . This is not enough to break intermolecular bonds but when thermally induced stress exceeds a critical value, the film can start to fracture and the stored energy is released in a small volume in the vicinity of the stress cracks. Due to the strong spatial nonuniformity of thermo-mechanical properties of molecular crystals (Bondi 1968) the physical mechanisms involved in this process are very complicated in nature; therefore we can give only a qualitative picture of this phenomenon. Presumably, the cracks are formed along grain boundaries, defects and interfaces. The increase of the desorption laser intensity that causes a rise in *ΔT* and, in accordance with Eq. 18, an increase in energy *G*, results in the formation of additional cracks. Some part of this excess energy can be then converted into the increased free surface energy, other part – into electronic excitations, but because these processes are obviously non-adiabatic, the crack formation most likely will be accompanied

The desorption process itself appears to be the most obscure part of the LIAD phenomenon. The formation of the electronically excited states on the surface due their mechanical fracture is considered to be the main physical nature of triboemission (Nakayama, Suzuki et al. 1992), also known as "Kramer effect" (Oster, Yaskolko et al. 1999; Oster, Yaskolko et al.

start with room temperatures, the peak foil surface temperatures then can reach 668÷673 K. Because the melting point of rhodamine B is just 438 K, the thermal origin of the LIAD process can, in fact, come into the focus of our consideration. However, other experimental results obtained in this work, make this mechanism very unlikely. These results are:


Moreover, the mechanical "shake-off" mechanism is also in contradiction with the observation (4), because the amplitudes and velocities of laser generated acoustic waves should increase with the driving laser fluencies. Thus we can conclude that both mechanisms of the direct energy transfer (acoustic waves and heat conduction) cannot serve as the primary explanation of the LIAD phenomenon, and apparently more complicated processes are involved here.

### **4.2 Stress and strain of the foil surface due to the laser irradiation**

It is a well-known fact that a film deposition on a substrate surface results in many cases in the residual mechanical stress (due to the lattice parameters mismatch between the film and the substrate) and thus in some excessive potential energy stored in the film. This stress can be produced by two ways: one is the growth stress and the other is the induced (or extrinsic) stress (Freund and Suresh 2003). An external impact, such as acoustic or thermal wave generated by the laser irradiation of the substrate, should initiate the reconstruction of the film, which can result in releasing this excess energy or, possibly, generating an additional extrinsic stress. In both cases, it can cause formation of cracks in the film so that intermolecular bonds at the edges of the cracks can break. As a result of this crack formation process, excited electronic states can form at the crack edges and induce desorption of the molecules.

Despite a great variety of mechanisms of stress formation and evolution do exist, a quantitative description of this process is possible only in limited cases even for simple adsorbent-adsorbate systems. Accurate modeling of the film behavior requires precise knowledge of the thermal and mechanical properties of the film material and their interaction with substrate surface. For most organic materials, such data are unavailable, and thus only limited estimates may be done, based on the little amount of data published in the literature (Bondi 1968). Moreover, the deposited films of organic materials tend to consist of a mixture of micro-crystals with different crystallographic orientation and, therefore, there are many grain boundaries, defects, dislocations in such films that could significantly change their local mechanical properties.

A simplified numerical estimate of the stress energy, related to the thermal mismatch of the substrate foil and the analyte film on its top could be done, as follows. An equi-biaxial stress resulting from acoustic vibration of the back-irradiated metal foil may be estimated using the following expression (Boley and Weiner 1960; Freund and Suresh 2003)

$$
\sigma\_m = \frac{E \cdot h\_f}{R \cdot (1 - \nu)} \tag{16}
$$

start with room temperatures, the peak foil surface temperatures then can reach 668÷673 K. Because the melting point of rhodamine B is just 438 K, the thermal origin of the LIAD process can, in fact, come into the focus of our consideration. However, other experimental

3. slow velocities and low kinetic energies of desorbed molecules compared to those

4. the apparent independence of mean energies of the desorbed molecules in LIAD on the driving laser fluence (also observed by by Kenttamaa et al. in their recent work (Shea,

Moreover, the mechanical "shake-off" mechanism is also in contradiction with the observation (4), because the amplitudes and velocities of laser generated acoustic waves should increase with the driving laser fluencies. Thus we can conclude that both mechanisms of the direct energy transfer (acoustic waves and heat conduction) cannot serve as the primary explanation of the LIAD phenomenon, and apparently more complicated

It is a well-known fact that a film deposition on a substrate surface results in many cases in the residual mechanical stress (due to the lattice parameters mismatch between the film and the substrate) and thus in some excessive potential energy stored in the film. This stress can be produced by two ways: one is the growth stress and the other is the induced (or extrinsic) stress (Freund and Suresh 2003). An external impact, such as acoustic or thermal wave generated by the laser irradiation of the substrate, should initiate the reconstruction of the film, which can result in releasing this excess energy or, possibly, generating an additional extrinsic stress. In both cases, it can cause formation of cracks in the film so that intermolecular bonds at the edges of the cracks can break. As a result of this crack formation process, excited

Despite a great variety of mechanisms of stress formation and evolution do exist, a quantitative description of this process is possible only in limited cases even for simple adsorbent-adsorbate systems. Accurate modeling of the film behavior requires precise knowledge of the thermal and mechanical properties of the film material and their interaction with substrate surface. For most organic materials, such data are unavailable, and thus only limited estimates may be done, based on the little amount of data published in the literature (Bondi 1968). Moreover, the deposited films of organic materials tend to consist of a mixture of micro-crystals with different crystallographic orientation and, therefore, there are many grain boundaries, defects, dislocations in such films that could

A simplified numerical estimate of the stress energy, related to the thermal mismatch of the substrate foil and the analyte film on its top could be done, as follows. An equi-biaxial stress resulting from acoustic vibration of the back-irradiated metal foil may be estimated

> <sup>⋅</sup> <sup>=</sup> ⋅ − *f*

*R*

*E h*

ν

(16)

using the following expression (Boley and Weiner 1960; Freund and Suresh 2003)

*m*

σ

electronic states can form at the crack edges and induce desorption of the molecules.

significantly change their local mechanical properties.

(1 )

**4.2 Stress and strain of the foil surface due to the laser irradiation** 

results obtained in this work, make this mechanism very unlikely. These results are: 1. rather small fragmentation of molecules in LIAD, compared to that for LD; 2. distinct differences in velocity and energy distributions between LIAD and LD;

required by the thermal mechanism;

Petzold et al. 2007).

processes are involved here.

where E is the Young's modulus, v is the Poisson ratio, *hf* is the thickness of organic film and R is the radius of curvature of the foil surface. From the other side, the stress, resulting from thermal mismatch has the following value (Boley and Weiner 1960)

$$
\sigma\_t = \left(\alpha\_s - \alpha\_f\right) \cdot \Delta T \cdot \to /\left(1 - \nu\right),
\tag{17}
$$

where *α<sup>s</sup>* and *α<sup>f</sup>* are thermal expansion coefficients of the substrate and the film respectively, *ΔT* is the temperature increase. There is not much information in the literature on thermomechanical parameters for molecular crystals but based on existing data for anthracene (Bondi 1968) we can estimate the order of the generated stress values. Under the assumption that *α<sup>f</sup>* =2.8 ·10-4 K-1 , *α<sup>s</sup>* = 6.3 ·10-6 K-1, *E*= 13 GPa, *v*≈0.25, and *ΔT*=100 K, we can obtain *σt*=485 MPa. At the same time, the stress associated with acoustic vibrations is much lower: σ*m*≈1.7 kPa (taking into account that maximal value of *R* is approximately 1 m, and the film thickness never exceeded 10-7 m,). This is a negligible value, in comparison with *σt* , which means that the thermal mismatch stress is the principal reason for cracks formation. The estimate of internal energy, stored in thermally strained organic films can be done with using of following expression (Boley and Weiner 1960)

$$\mathbf{G} = \frac{E \cdot \left(1 + \nu\right)^2}{2 \cdot \left(1 - \nu^2\right)} \cdot \left(\alpha\_s - \alpha\_f\right)^2 \cdot \Delta T^2 \cdot 2 \cdot \pi \cdot r\_0 \cdot h\_f \tag{18}$$

The average energy per analyte molecule can easily be calculated

$$\mathbf{g}\_a = \frac{E \cdot (\mathbf{1} + \nu)^2}{2 \cdot (\mathbf{1} - \nu^2) \cdot \rho} \cdot \frac{(\alpha\_s - \alpha\_f)^2 \cdot \Delta T^2 \cdot M}{N\_A} \tag{19}$$

Here *M* is the molar mass, *ρ* is the specific gravity and *NA* is the Avogadro number. It is interesting to note that *ga* does not depend on the analyte island size but strongly depends on the thermal and mechanical parameters. Again with the use of existing data for anthracene we can estimate the value of *ga*, and for *ΔT*=100 K we will get *ga*=0.025 eV . This is not enough to break intermolecular bonds but when thermally induced stress exceeds a critical value, the film can start to fracture and the stored energy is released in a small volume in the vicinity of the stress cracks. Due to the strong spatial nonuniformity of thermo-mechanical properties of molecular crystals (Bondi 1968) the physical mechanisms involved in this process are very complicated in nature; therefore we can give only a qualitative picture of this phenomenon. Presumably, the cracks are formed along grain boundaries, defects and interfaces. The increase of the desorption laser intensity that causes a rise in *ΔT* and, in accordance with Eq. 18, an increase in energy *G*, results in the formation of additional cracks. Some part of this excess energy can be then converted into the increased free surface energy, other part – into electronic excitations, but because these processes are obviously non-adiabatic, the crack formation most likely will be accompanied by breaking intermolecular bonds and forming new desorption sites.

### **4.3 Proposed mechanisms of the molecules desorption**

The desorption process itself appears to be the most obscure part of the LIAD phenomenon. The formation of the electronically excited states on the surface due their mechanical fracture is considered to be the main physical nature of triboemission (Nakayama, Suzuki et al. 1992), also known as "Kramer effect" (Oster, Yaskolko et al. 1999; Oster, Yaskolko et al.

Molecular Desorption by Laser–Driven

disruption at the microscale generated by shock waves.

**6. Acknowledgment** 

cause an efficient thermal desorption of the most organic molecules.

Contract DE-AC02-06CH11357, by UChicago Argonne, LLC.

process.

Acoustic Waves: Analytical Applications and Physical Mechanisms 365

cracking due to thermal and mechanical mismatch of the analyte and substrate. Therefore, ironically, the acronym LIAD in this case does not correctly reflect the physical nature of the

From the other hand, we cannot exclude that some strong change of the experimental conditions can also change the relationship between various physically possible mechanisms of molecular desorption, similarly to the case of direct laser desorption, when the thermal mechanism dominates under wide range of conditions and makes other possible mechanisms undetectable. One can expect, for example, that strong increase of laser power density (10 GW/cm2 and above) will cause the corresponding increase of the foil temperature and formation of hot and dense plasma plume near its surface facing the laser. In some such cases and strongly depending on the foil material properties, the material motion could evolve from elastic into plastic regime of deformation. The acoustic wave relation could not then apply, and the velocity of the surface linear motion may strongly increase. "Large and heavy" objects weakly bound to the substrate surface may be then kinematically removed from it ("shaken-off"). This could indeed serve as an explanation of observations from recent experiments where the desorption of intact viruses and biological cells were reported (Peng, Yang et al. 2006). However, this regime cannot be connected with generation of the acoustic waves but most likely corresponds to a physically different mode of shock-wave generation (Menikoff 2007). One cannot exclude that under some experimental LIAD conditions only these shock-wave induced phenomena can be responsible for molecular desorption, particularly in the experiments where emission of ions was detected. In one of such pioneering experiments (Golovlev, Allman et al. 1997), where the laser generated pressure pulse was apparently much stronger than that in our work, because of confined ablation conditions (Fabbro, Fournier et al. 1990), the emission of both electrons and ions was observed. This may have been connected with significant surface

From another standpoint, the backside irradiation of very thin films (about two or three hundred nanometers), which also could be called LIAD, has demonstrated domination of the thermal mechanism in the desorption process (Ehring, Costa et al. 1996). It is clear that the thermal equilibrium between front and back sides in such thin films can establish within the time interval of tens of nanoseconds, and the absolute temperature difference between front and back sides is negligibly small. Thus, at some laser power densities, the front side temperature could reach the melting temperature of the metal that would be enough to

To conclude, the variety of desorption and emission phenomena observed on the front side of thin metal foils whose back sides are subjected to pulsed laser irradiation, combined under the general name of LIAD, could, in fact, have a number of different physical origins depending on specific experimental conditions. According to our observations conducted at moderate laser power densities (0.1 - 1 GW/cm2) and foils thicknesses of about 5 – 20 µm, that appear to be the most commonly used conditions in LIAD experiments, the predominant desorption mechanism is connected with the reorganization of the deposited analyte film and the consequent breaking of molecular bonds on the edges of these cracks.

This work is supported by the U.S. Department of Energy, BES-Materials Sciences, under

2001). The essence of this effect is the emission of charged particles and photons initiated by surface distortion (in particular by mechanical deformation, scratching, bending, etc.) and do not connected with thermal excitation. The luminescence of thin metal discs, irradiated from back side by the laser pulses (Abramova, Shcherbakov et al. 1999; Abramova, Rusakov et al. 2000) can also serve as evidence of formation of excited electronic states by the laserdriven stress in thin foils.

The mechanism of molecular desorption due to such laser-generated stress has been proposed earlier by Vertes (Vertes and Levine 1990; Vertes 1991) for MALDI, and was based on the thermal stress generation in the layer of organic film deposited on solid substrates. One should notice, however, a clear differences in the physical conditions between these sample volatilization methods. For MALDI, the absorption of the laser pulse energy occurs in an optically and thermally dense film, which experiences thermal stress due to its nonuniform and fast heating. In the case of LIAD, the laser radiation is absorbed by the back side of the metal foil substrate, opposite from where the sample was deposited. The amount of energy transmitted through the metal foil to the analyte layer on the front site should be so strongly attenuated, compared to the direct (front side) irradiation, that it cannot directly be sufficient for desorbing molecules with velocities observed in our experiments. On the other hand, a typical average thickness of the analyte film in LIAD can be estimated to be on the order of several molecular layers. Because of this, the specific density of energy stored in each analyte island due to intrinsic stress can be high, and during laser irradiation of the back side of the foil, the laser irradiation can simply trigger the release of this energy and to induce molecular desorption event.

The other experimental fact that could help in the interpretation of LIAD phenomenon is the similarity of the energy and velocity spectra of desorbed neutral molecules in case of LIAD and Electron Stimulated Desorption (ESD) (Young, Whitten et al. 1989). The primary mechanism of ESD is supposed to be the formation of the repulsive states in the surface due to electron excitation.

Thus we could hypothesize that in case of LIAD, due to complete opaqueness of metal foil for laser radiation, the only channel for energy transfer is the formation of acoustic and thermal field by laser pulse impact. As shown above, the result can be the mechanical distortion of the analyte film followed by film cracking and delamination and the consequent formation of excited and repulsive states electronic for analyte molecules.

This will increase the number of desorption sites and finally the total number of desorbed molecules as observed in the nonlinear laser intensity dependence. But because the formation of the any individual cracks is defined only by the intermolecular bonding forces in the vicinity of the crack, the translational kinetic energy of desorbed molecules should still remain independent of driving laser intensity, also matching our observations and other recent LIAD publications.
