Photoinduced and Thermal Relaxation in Surface ... - ACS Publications

Subscriber access provided by UNIV OF SOUTHERN QUEENSLAND

Article

Photoinduced and Thermal Relaxation in Surface-grafted Azobenzenebased Monolayers: A Molecular Dynamics Simulation Study. Dmitry Bedrov, Justin B. Hooper, Noel Clark, and Matthew A Glaser Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b00120 • Publication Date (Web): 30 Mar 2016 Downloaded from http://pubs.acs.org on April 2, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Photoinduced and Thermal Relaxation in Surface-grafted Azobenzene-based Monolayers: A Molecular Dynamics Simulation Study Dmitry Bedrov and Justin B. Hooper Department of Materials Science & Engineering University of Utah Matthew A. Glaser and Noel A. Clark Department of Physics University of Colorado at Boulder Abstract Extensive atomistic molecular dynamics simulations have been employed to study the structure and molecular orientational relaxation of azobenzene-based monolayers grafted to a solid substrate. Systems with surface coverage of 0.6 nm2/molecule were investigated over a wide temperature range ranging from 298K, where the mesogens show local ordering and the monolayer dynamics was found to be glassy, up to 700K where the azobenzene groups have a nearly isotropic orientational distribution, with a sub-nanosecond characteristic orientational relaxation timescale. Biased simulations that model single-molecule thermal excitation and conformational isomerization have been conducted to obtain insight into the mechanisms for photo-induced athermal fluidization and monolayer reorganization observed experimentally in this system. Our simulations clearly indicate that trans-cis conformational isomerization transitions of azobenzene units can lead to reorientation of mesogens and to the formation of a monolayer with strong macroscopic in-plane nematic order. While local heating created by excitation process can facilitate this process, thermal excitation alone is not sufficient to induce ordering in the monolayer.

Instead, the work done by a molecule undergoing cis-trans

isomerization on the cage of neighboring molecules is the key mechanism for photo fluidization and orientational ordering in dMR monolayers exposed to linearly polarized light leading to relaxation dynamics that can be described in terms of higher effective temperature. The obtained simulation results are discussed in light of recent experimental data reported for these systems.

1

ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 46

I. Introduction The effects of irradiation with light have been explored in a variety of self-assembled soft materials, including liquid crystals (LCs), block copolymers, and hydrogels. Photo-chemically induced changes in most of these systems are achieved through cis-trans isomerization of azobenzene groups,1 with the photolabile group either mixed in as a dopant or covalently bonded to the rest of the structure. A wide range of light-induced phenomena have been explored, including mechanical response (formation of optical gratings in polymers through surface relief,2 curling of thin polymer films,2,3 transport of liquids4), changes in chemical affinity (wetting properties, 5 photo-surfactants in interfacial and colloidal systems 6 ), chemical and electrical transport properties of porous materials, “catch-and-release” of chemical moieties including DNA,7 chiroptic switches with variable helical twisting power,8 and reversible sol-gel transitions in hydrogels.9,10 Linearly polarized light (LPL) has been applied to control the morphology of block co-polymers,2,6 and to cause the macroscopic reorientation of polystyrene nanocylinders2 and of smectic layers in nano-phase segregated side-chain polymer LCs.11 Liquid crystalline systems are particularly interesting because photo-induced structural changes are often sensitively coupled with the thermodynamic phase behavior. A variety of photonic effects have been observed in LCs, including optically induced changes in the helix pitch of cholesterics, 12 photochemical “color switching”, and other photorefractive effects.13,14 Azobenzenes may be integral parts of the mesogens or dopants mixed in with the LC phase.

Changing the

conformation of the chromophores from trans to cis typically lowers the orientational order parameter of the LC and may induce, for example, a nematic to isotropic phase transition, an event that has a dramatic and readily observable effect on the optical appearance of the sample.15,13 It has been demonstrated recently that in certain LC systems, exposure to light can actually increase the degree of order.16,17,18 Spin-coated polymer films doped with azo dyes19 and azo-based self-assembled monolayers (SAMs)20 have been shown to act as dynamic alignment layers for nematic LCs because they become anisotropic when exposed to LPL. These azo-based phenomena are the result of two basic effects, photo-induced shifts in the cis-trans population causing change of average molecular properties such as length, 21 and athermal photofluidization, the ability of azo isomerization to substantially reduce the viscosity of glassy hosts without noticeably heating them.20,22 Effects like the global realignment of a

2


Page 3 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

hexagonal block copolymer film2 and material transport of glassy systems

23

require

photofluidization. We reported in ref. [20] a basic new insight into photofluidization, showing that azobenzene photon absorption produces an effective high temperature attack on the orientational barriers of a molecule in a glassy host, at Teff ~ 800K, an effective temperature that melts the local barriers to produce a local glass transition. Similar conclusions has been obtained from the analysis of photoinduced IR band shifts on bulk materials containing azobenzene derivatives.24 In this circumstance the characteristic time determining the viscosity becomes the average time for a photon absorption event for each molecule, which varies inversely with intensity.

The resulting viscosity reduction is at the heart of all of the mechanical and

orientational effects described above, a key understanding that will be employed in our design of photoactive nanosegregated LCs. In this work we report the first atomistic molecular dynamics (MD) simulation study of structural correlations and dynamical and thermal relaxation in monolayers comprised of 2-(4Dimethyamino-phenylazo)-N-(3-triethoxysilane-propyl)-benzamide (dMR) molecules grafted to a solid substrate as shown in Figure 1. The photofluidization and orientational effects in the SAMs comprised of these molecules have been previously investigated by some of us experimentally.20 Using atomistic molecular dynamics (MD) simulations, in this work we extend that work to provide a complementary molecular scale understanding of the mechanisms and factors that define the peculiar behavior of these photoresponsive materials. The specific objectives of this work are: a) to understand the packing, orientational distribution and local ordering of dMR molecules in the monolayer; b) to investigate molecular relaxations as function of temperature and cis-trans isomerization rates; c) to investigate how fast the thermal energy from an excited molecule can dissipate through the monolayer and whether this thermal dissipation depends on the local ordering of neighboring molecules, and d) to demonstrate the feasibility of using MD simulations to model the photo-induced alignment in dMR monolayers observed in experiments.

3


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 46

Figure. 1. (a) Schematic illustration of a dMR molecule attached to the surface. (b) A snapshot of the side view of a dMR monolayer at the surface.

II. Simulation Details A. Force field To model this system we have chosen a fully atomistic, non-polarizable force field.

The

parameters for the non-bonded van der Waals interactions were adapted from the APPLE&P force field,25 which has been extensively validated and used for simulations of a variety of materials including organic and ionic crystals26,27,28 and polymers.29

Partial atomic charges were fit to

describe the electrostatic potential around the dMR molecule in its minimum energy geometry as obtained from ab initio calculations using the Gaussian 09 package30 at the MP2//cc-pvDz level of theory. The electrostatic potential from quantum chemistry calculations was computed on a grid around the molecule excluding the regions inside the van der Waals radius of the atoms. Subsequently the partial atomic charges in the APPLE&P force field were fitted to obtain the best representation of the ab inito values of electrostatic potential at all grid points. Bond lengths were fixed at distances corresponding to those obtained in the ab initio calculations for the minimum energy geometry.

Description of bends and dihedrals were

transferred from chemically similar groups within the APPLE&P force field. However, several dihedrals that are specific to dMR molecule and are key to its relaxation behavior (indicated in

4


Page 5 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 1a) were parameterized against available ab initio data. For example, for the central azobenzene torsion we expect the cis to trans conformational transitions in the monolayer will be similar to the one reported by Tiberio et al.31 for azobenzene in hexane, which places the cis state 20 kcal/mol higher in energy than the trans state, with a maximum height for transition barrier occurring at dihedral angle of 90 degrees and a barrier height of roughly 60 kcal/mol. Figure 2 represents our fit of this key dihedral, demonstrating good agreement with Tiberio's data. Other important dihedrals are those that represent the chemistry of attaching the azobenzene group to the tether that attaches it to the substrate surface. These dihedrals are also labeled in Figure 1a. Due to steric crowding and strong electrostatic interactions between the atoms comprising these torsions and the azobenzene unit, the rotations around these dihedrals and the deformation of other degrees of freedom (e.g., bends, out-of-plane bending) are strongly coupled. Therefore, it is hard to define a simple dihedral energy profile/path (such as shown in Figure 2 for the central azobenzene torsion) defining the transition from one local minimum conformational state to another. Therefore, for parameterization of these torsions we focused on capturing the relative energies between conformers in local minimum energy configurations obtained from ab initio calculations using the M052X//cc-pvDz level of theory. The snapshots, characteristic dihedral angle combinations for these states, their relative energies obtained from these calculations, and the prediction of both dihedral angles and energy differences from the parameterized APPLE&P force field are shown in Figure SI1-3 and Table SI-1 of Supplementary Information (SI).

Figure 2. Energy profile for the central C-N=N-C dihedral in the azobenzene unit as predicted by parameterized force field

5


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

B. System set-up and simulation methodology A monolayer system comprised of 256 molecules was prepared in the following way. Initially, a square surface with side length L=37 nm (corresponding to a surface area per molecule of 5.3 nm2/molecule) has been divided into 16x16 square lattice. Each molecule was placed and attached to the surface within one lattice cell. The location of the attachment point for each molecule within the cell (xi,yi) was randomly picked subject to no-overlap condition with the molecules from neighboring cells. All molecules were initially in trans conformation of the azobenzene unit and had a random orientation in the x-y plane. Subsequently, a simulation run over 1 ns was used to shrink the x and y dimensions (directions parallel to the surface) of the surface to 12x12 nm2 dimensions allowing the desired surface coverage of 0.6 nm2/mol which is very similar to that observed in experiments (0.55 nm2/mol). During this simulation the attachment points did not change their scaled coordinates, i.e. xi/L and yi/L ratios remained constant. This initial set up simulation was conducted at 298K and illustrated in Figure SI-4. A configuration of the prepared monolayer is shown in Figure 1b. Subsequently, a 5 ns equilibration run was conducted in the NVT ensemble for each system after its preparation. Production runs of formed dMR monolayers were conducted in the NVT ensemble at several temperatures in the 298 K-700 K range. Covalent bond lengths were constrained using the velocity-Verlet form of the SHAKE algorithm. 32 The Ewald summation method with 3D peridiocity was used for treatment of long-range electrostatic forces. To insure that electrostatic interactions from periodic images are insignificant, a significant amount of vacuum has been added in the z direction (perpendicular to the surface), with a cell dimension of 38nm in this direction. A cutoff of 10 Å was used for all van der Waals interactions and for the real space part of the electrostatic interactions in the Ewald summation. A multiple time step reversible reference system propagator algorithm33 was employed. A time step of 0.5 fs was used for bonding, bending, dihedral, and out-of-plane deformation motions, while a 1.5 fs time step was used for non-bonded interactions within a cutoff radius of 6.0 Å. Finally, the non-bonded interactions in the range between 6.0 and 10.0 Å and the reciprocal space part of electrostatic interactions were updated every 3fs. The length of production runs ranged from 10 ns (at T=700K) up to 50 ns (at T=400K). The length of the production runs was chosen to ensure complete relaxation of molecular orientations. For temperatures below 400 K, simulations were conducted for 50 ns. However, as

6


Page 6 of 46

Page 7 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

we will show below, this time scale was not sufficient to observe the complete relaxation of molecular orientations and therefore results from these systems were used only to show qualitative trends. In addition to systems with all molecules in trans (all-trans) conformation of the azobenzene units, we also have simulated systems in which 25% of dMR molecules were initially set in the cis conformation. For these simulations, we took an equilibrated configuration of the system with all-trans conformations and for 25% of randomly selected molecules applied a biasing potential to drive the azobenzene units over the large transition barrier (see Figure 2) into the cis conformation. Then, equilibration and production simulations using original dihedral potentials were conducted. Taking into account that the barrier for the cis-to-trans transition is on the order of 40 kcal/mol, there were no spontaneous reverse cis-to-trans transitions observed during simulations of these systems, even at elevated temperatures. At 700 K the 40 kcal/mol barrier corresponds to ~29 kT of energy, which is an order of magnitude higher than the energy scale of thermal fluctuations, and hence, such transitions are highly improbable on the time scales accessible to brute force simulations. Finally, as we discuss below in section III-D, the simulations with dynamic "biasing" of molecules to/from the cis conformation were conducted in order to mimic the process of photoexcitation and to investigate the influence of such stochastic transitions on the monolayer structure. III. Results and Discussion A. Monolayer structure Figures 3 (a,b) show top-view snapshots of dMR monolayers after equilibration. It is clear that at 298 K dMR molecules form locally ordered regions in which the azobenzene units are aligned. Using the azobenzene unit orientation defined by vector Re in Figure 1a) we can calculate a two dimensional nematic order parameter as SN which is the largest eigenvalue of the tensor QN=Σ (2uiui−Ι), where ui is a unit vector along Re for the i-th molecule, the sum is over all azobenzene units in the system and I is the unit matrix. As we can see from Figure 3 the formed domains are randomly oriented which, in principle, should result in SN=0. However, due to finite size of the system, the instantaneous value of SN is not zero and the resulting average (over the entire trajectory) of SN in our systems is ~0.2. While the molecules appear to be tightly packed

7


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 46

within the domains, there are a number of low-density regions at domain boundaries, indicating that the monolayer density is far from saturation. At higher temperatures, the local ordering is largely absent and molecules have very little alignment with their neighbors.

Figure 3. Snapshots (top view) of equilibrated dMR monolayers at (a) 298 K and (b) 700K.

In addition to the nematic order parameter, the molecular orientation can be characterized by the angle θ between the vector ui and the surface (see Figure 1a). The probability distributions of θ are given in Figure 4. At 298K there is a strong preference for azobenzene units to have a small tilt toward the surface with an average tilt angle of ~17 degrees. This is in good agreement with the experimentally estimated average angle of 25 degrees.20 Note that experimentally it is hard to determine whether the azobenzene units of dMR molecules are tilted towards the surface (as shown in Figure 1a) or away from the surface. Our simulations show that most molecules are tilted towards the surface (i.e. θ < 0), which is a consequence of conformational restrictions/preferences for the benzene-tether connection discussed above. As the temperature increases, the preferential orientation disappears and at 700 K an almost uniform distribution of θ over a relatively wide range (from -50 to +50 degrees) is observed, indicating that at higher temperatures tilting toward and away from the surfaces are equally probable. The structure of the monolayer can be further characterized by examination of mass density profiles of various groups or atoms in the direction (z) perpendicular to the surface. Figure 5a shows the total density profile (left axis) in the z direction for the dMR monolayer at 298 K. The sharp first peak is due to attachment groups of the tether to the surface. After this first peak

8


Page 9 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

the density profile increases and reaches its maximum of ~1700 kg/m3 at 9 Å separation from the surface and then goes to zero at about 12 Å. Therefore, the monolayer is very compact in the direction perpendicular to the surface. Figure 5a shows profiles of the relative fractions for several atom types. The fractions were defined as ni(z)/ni(total) where ni(z) is the number of atoms of type i found in the narrow slab parallel to the surface and located at position z while ni(total) is the total number of these atoms in the system. We can see that the main contributors to the density peak at 9 Å are the nitrogen atoms from the azo linkage between benzene rings and carbon atoms from those rings. A couple of additional observations can be made from the analysis of profiles shown in Figure 5a. First, the nitrogen atoms from the azo linkage are narrowly distributed within a ~2 Å wide peak. This peak is located right in the middle of the distribution of benzene carbon atoms which is consistent with the fact that azobenzene units have their long direction oriented parallel to the surface but their benzene rings are oriented perpendicular to the surface. The latter allows more efficient packing of azobenzene units in the monolayer. Second, the distribution of dimethyl nitrogen atoms is shifted closer to the surface (compared to the azolinkage nitrogens), which is consistent with the slight tilt of the azobenzene units towards the surface discussed above.

Figure 4. Probability distribution of the angle between the end-to-end vector of the azobenzene unit and the surface plane as defined in Figure 1.

The profiles analyzed in Figure 5a were obtained for the monolayer in which all dMR molecules were in the trans conformation for the dihedral around N=N bond. In Figure 5b we compare these profiles with the density profiles from simulations in which 25% of randomly selected molecules have been biased to have the cis orientation,

9


to model the molecular

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 46

configuration of the dMR molecules after photoexcitation. Figure 5b shows that in the system containing molecules in the cis conformation the maximum in the overall density has reduced from 1700 kg/m3 to 1550 kg/m3 and the distribution of N-dimethyl atoms has developed a shoulder at larger separations from the surface, consistent with the methyl group pointing out of the monolayer when molecules are in cis conformation. These density profiles indicate that while transition to cis orientation of a noticeable fraction of azobenzene units leads to minor changes in density profiles, effectively it reduces the overall density and results in redistribution of structural groups in the monolayer. Both of these effects may lead to increased amount of "free" volume in this glassy structure and, hence, may have a significant impact on the local and collective molecular relaxations in the monolayer.

Figure 5. Monolayer density profiles (left axis) and fractional density distributions of selected atoms/groups (right axis) at 298K as a function of separation from the surface: (a) for a monolayer with all azobenzene units in the trans conformation and (b) for a monolayer with 25% of the azobenzene units in the cis conformation.

10


Page 11 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

B. Dynamic Relaxation To characterize dynamical relaxations of molecules in the investigated monolayers we used the end-to-end vector autocorrelation function (ACF) for the azobenzene units. The end-toend vector (Re) was defined between the dimethyl nitrogen atom and the carbon atom on the benzene ring attached to the tether as illustrated in Figure 1a. The ACFs for this vector obtained at various temperatures are plotted in Figure 6. At room temperature there is very little relaxation of Re orientation and it is likely associated with small oscillations of molecules in the local cages formed by the neighbors. However, at high temperatures (600K and 700K) the end-to-end ACFs are clearly relaxing on sub-nanosecond timescales. These relaxations can be fitted using the Kohlrausch-Williams-Watts (KWW) function: (1) The KWW function clearly provides a good fit to the obtained ACFs as can be seen from Figure 6 (dashed lines). The KWW parameter β obtained from the fits ranges from 0.58 (lower T) to 0.67 (higher T). The deviation of this parameter from unity is often used as a measure of dynamic heterogeneity in the relaxation process. The obtained values indicate that there is a moderate amount of heterogeneity in the orientational relaxation, which, as expected, increases with decreasing temperature.

Figure 6. Autocorrelation function (ACF) of the azobenzene unit end-to-end vector (Re) obtained from dMR monolayer simulations at different temperatures (symbols). Dashed lines show the fit to the KWW equation (see text for discussion). The solid lines for T < 500 K show the ACF for a monolayer with 25% of the azobenzene molecules in the cis conformation.

11


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 46

The characteristic relaxation times (τ) for the Re vector relaxation can be obtained by integrating the fitted KWW functions from zero to infinity. Figure 7 shows the resulting τ as a function of inverse temperature. Upon decreasing the temperature from 700 K to 400 K the rotational relaxation of dMR molecules slows down by more than two orders of magnitude and shows an apparent divergence of relaxation time with decreasing temperature. The latter is consistent with the experimentally observed glassy behavior of these monolayers at room temperature.20 The characteristic relaxation times obtained at elevated temperatures can be fitted using the Vogel-Fulcher (VF) equation: (2) where parameter T0 represents the critical temperature which is usually a few degrees below the glass transition temperature Tg. The fit of the obtained characteristic times with the VF equation (also shown in Figure 7) resulted in T0= 272.32K. Extrapolation of this fit to room temperature shows that relaxation times

>1sec can be expected below 310K, which is again in good

agreement with experimentally observed behavior of these monolayers at room temperature.

Figure 7. Temperature dependence of the characteristic relaxation times obtained from integration of the end-to-end ACFs shown in Figure 6. The dashed line shows the VF fit and the extrapolation to room temperature.

12


Page 13 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

We also analyze these relaxation data from the simulations using the theoretical description that modeled the thermal and photo-induced glassy dynamics of the dMR SAMs as measured by the decay of the in-plane birefringence following writing by polarized actinic light.20 In these measurements it was found that the relaxation of the in-plane order parameter of the dMR cores, S(t), which is proportional to the birefringence Δn(t), is well described by the function S(t) η

∝ 1/[1 + t/τt] . This dynamic form, governed by the exponent η and characteristic scaling time τt, exhibits little change for t < τt, beginning to substantially decrease only for t ~ τt, and transitioning for longer times to a power law decay of exponent η. Since birefringence probes the average of the contributions of single anisotropic molecules, this relaxation can be interpreted in terms of the confinement of single molecules. The molecules experience energetic barriers to reorientation, U, formed by their neighbors, which we assume to be distributed with a probability f(U = Ut + U). The f(U) that generates S(t) above is shown in the inset of Figure 8a, consisting of a barrier gap, a range Ut of energies where there are no barriers, plus a distribution of larger energy barriers starting at Ut that decreases exponentially in probability with increasing U above Ut. The decay function that results from this barrier height distribution is shown as a log-log plot in Figure 8a, with the flat regime transitioning to the power-law regime at the “corner” t ~ τt, which, in turn, is related to Ut by τt = τr * exp[Ut/kBT], where τr is the inverse trial rate for molecular orientation fluctuations.20 This barrier distribution provides as excellent description of the photo-induced in-plane birefringence of dMR monolayers. Since both the birefringence and end-to-end autocorrelation functions (ACFs) are probes of collective dynamics as measured by the motions of single molecule dynamics, we have analyzed the relaxations in Figure 6 of the end-to-end molecular reorientation in the ACF in the unwritten state in terms of the relaxation model for induced orientational order in the written state, η

assuming that the end-to-end ACF will have the form C(t) = 1/[1 + t/τt] . This posits that the unwritten and written relaxations are controlled by the same mechanisms of local dynamics. Figure 8b shows that C(t) does provide a reasonable fit to the autocorrelation data, with the resulting Ut and Um given in Figure 8c, where we have taken τr = 1psec. The shift of the corners to higher t with decreasing temperature is simply the result of the Boltzmann factor in τt, as evidenced by the constancy of Ut vs. T in Figure 8c. The width of the exponential distribution, Um, also depends only weakly on T, becoming somewhat narrower with increasing T. Both Ut

13


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 46

and Um are characteristics of the local dynamics. In photowritten dMR monolayers, Um grows with the net fluence, F, of the actinic polarized light, increasing as ln(F) in the limit of large fluence where many photons per molecule have been absorbed.

Written dMR monolayers

exhibited Um in the range 400K < Um < 1600K, depending on F, and Ut ≈ 7800K, nearly independent of F. The smaller values of Ut and Um found in the ACF simulation data indicate that the local ordering in the unwritten globally random starting condition is somewhat weaker than that of the photoinduced starting states used in the dMR experiments. This is confirmed below where it will be shown that Ut ~ 5000K for relaxation of order in a simulation with an initially ordered state.

Figure 8. a) Schematic illustration of orientational energy barrier distribution f(U) and the corresponding orientational decay function C(t) used for the analysis of experimental data in ref.[20]. b) End-to-end vector ACF obtained from MD simulations at different temperatures and the corresponding fits using C(t) functional form. c) Temperature dependence of Ut and Um parameters obtained from the fits (see discussion in the text).

.

14


Page 15 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Taking into account that during photo excitation process azobenzene units change their conformation around the N=N bond from trans to cis orientation, it is interesting to investigate the influence of the latter on the end-to-end relaxation of dMR molecules in the monolayer. As illustrated in Figure 2, the cis conformation is more compact and therefore the azo group of molecules in this conformation will be positioned slightly above the monolayer high-density regions. Therefore, the presence of cis conformers creates extra free volume within the monolayer and hence can, in principle, facilitate molecular reorientation. To test this supposition we analyzed the Re relaxation in the system with 25% of molecules switched to the cis conformer. These relaxations (averaged for all molecules in the system) for several temperatures are also shown in Figure 6 as solid lines. Despite a noticeable fraction of dMR molecules being in cis conformations the end-to-end reorientation of azobenzene units in the monolayer shows only a small speed up. Therefore, the fact that, due to the photoexcitation process, some dMR molecules are in the more compact cis orientation does not affect the glassy nature of these monolayers at room temperature. As discussed above, even the monolayers with all dMR molecules in the trans conformation and at a grafting density of 0.6 nm2/molecule are not at their maximum packing density and, therefore, have plenty of free volume at the boundaries of locally oriented domains. Addition of extra free volume due to conformational transitions into the cis state for 25% of the molecules has a minor influence on the orientational relaxation of dMR molecules in the monolayer. This indicates that the glassy behavior of the dMR monolayers investigated here (and in experiments) is determined more by the orientational constraints/correlations of azobenzene units with their neighbors within local domains than by the overall tight packing (high density). C. Thermal Relaxation Next, we examine the thermal relaxation of dMR molecules in the monolayer. Taking into account that photoexcitation is accompanied by substantial amount of thermal energy deposition into the excited molecule, it is instructive to investigate how fast the thermal energy dissipates in the monolayer. The classical MD simulations employed in this work certainly do not allow direct modeling of the excitation process. Nevertheless, we can mimic this process to some extent using biasing potentials. The latter will be discussed in the next section, while here the thermal activation of selected molecules was modeled by instantaneous rescaling of atom velocities. Such

15


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 46

rescaling increases the instantaneous temperature of the selected molecule (Ti). As the simulation continues, the Ti of the excited molecule as well as its close neighbors are monitored as a function of time to assess how quickly thermal energy dissipates to the surroundings and how much the local surroundings are heated up. These thermal "excitation" simulations have been conducted for several molecules with different local environments as illustrated in Figure 9 (a-d). Specifically, we investigated thermal relaxation of molecules that are located in the middle of the oriented domains, such as those shown in Figure 9(a,b), as well as of those molecules located at the boundaries or low local density regions as illustrated in Figure 9(c,d).

At time zero, the

velocities of atoms in the selected molecule were rescaled such that the instantaneous temperature of the molecule was equal to 2000 K while the rest of the system remained unperturbed. Then standard MD simulations in the NVT ensemble at 298K were continued. For each selected for excitation molecule a separate simulation was conducted and therefore there were no correlations between any two excited molecules.

Figure 9. (a-d) Snapshots showing several molecules (highlighted in green) selected for thermal excitation in single-molecule thermal excitation simulations. (e) Time evolution of the instantaneous temperature of several excited molecules. .

Figure 9e shows the evolution of the excited molecule temperature as obtained from six of those independent simulations with different dMR molecules selected for thermal perturbation. The selected molecules 1-3 were in the environments similar to those shown in Figure 9(a,b) while molecules 4-6 had environments like those shown in Figure 9(c,d). Taking into account that the instantaneous temperature of a molecule can have significant fluctuations due to small number

16


Page 17 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

of degrees of freedom defining this property, the thermal relaxations of all molecules shown in Figure 9e look very similar, independent of their local environments. Most of the thermal energy is dissipated to the surroundings on a time scale of ~100 ps, after which the temperature of the excited molecule becomes comparable to the average temperature of the monolayer.

Figure 10. (a) Snapshots of the local environment of a thermally excited molecule (highlighted in green) and identification of its close neighbors. (b) Time evolution of the instantaneous temperature of the thermally excited molecule and its neighbors. .

Next, it is important to understand how the thermal energy from the excited molecule is distributed to the surroundings during the dissipation process. Is the energy transferred only to a few near neighbors that might have some favorable orientation relative to the excited molecule (e.g., a parallel alignment of the azobenzene units as illustrated in Figure 10a for neighboring molecule #1) or is it evenly dissipated to all surrounding molecules? Another important question is: how much local heating can be generated during this process? Figure 10 shows the thermal relaxation of the neighboring molecules for one such simulation. The excited molecule (highlighted in green) has five near neighbors, of which one (#1) is aligned parallel to the excited molecule, while others are oriented almost perpendicular to the azobenzene axis. Nevertheless, Figure 10b shows that the temperature evolutions for these neighboring molecules are similar as well. Similar temperature evolution and heat dissipation were observed in simulations of other five excited molecules whose relaxation was shown in Figure 9b. In all cases, the neighboring molecules heat up by ~ 100-200 degrees within the first 50 ps after excitation and then over next

17


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 46

50-100 ps cool down to the monolayer bulk temperature. This figure indicates that upon thermal excitation the local environment of the excited molecule can heat up substantially for a short (50100 ps) period of time. However, the orientational relaxations shown in Figure 6 indicate that if the monolayer region is heated up to 500 K then even over such short time period as 50-100 ps a noticeable reorientation of the azobenzene units can occur. Therefore, the evolution of the thermal energy dissipation by excited molecules observed in our simulations indicates one possible mechanism for the experimentally observed athermal photoinduced fluidization of dMR monolayers. D. Isomerization-Induced Ordering Next, we investigate the effect of photoinduced azobenzene isomerization between trans and cis conformations on monolayer ordering. As discussed in ref [20], if a dMR monolayer with initially randomized orientation of azobenzene units, i.e., no global nematic ordering, is illuminated with a linear polarized pump beam (in-plane polarization) then molecules with the azobenzene long axis oriented (mostly) parallel to the polarization direction will be susceptible to a photo-induced isomerization, i.e., trans to cis transition upon excitation. After the excited molecule has spent some time in the cis conformation, it returns to the energetically more favorable trans conformation. If the orientation of the long axis of the molecule relaxed after excitation still aligned parallel to the polarization direction, it will soon get excited again. However if upon return to the trans orientation the long axis aligns more perpendicular to the polarization direction, the probability for this molecular to get excited will decrease significantly. Therefore, eventually the system has an excess of molecules perpendicularly oriented to polarization direction. Moreover, the relaxation of the remaining excitation-susceptible molecules can be influenced by the orientational ordering of non-susceptible neighboring molecules. Therefore, eventually the excited molecules reorient such that they are aligned with molecules that are not susceptible to photoexcitation, i.e., aligned along the pump beam polarization vector, and, therefore, the whole system eventually develops photoinduced nematic ordering. To mimic this process, we designed biased simulations with the protocol illustrated in Figure 11. In these simulations, a dMR monolayer equilibrated at 298 K or 400 K was taken as the initial configuration. We chose the y-direction to be the direction aligned with the polarization vector of the pump beam and therefore all molecules whose azobenzene end-to-end vector has an

18


Page 19 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

angle between 45-135º relative to the y-direction were considered susceptible to the trans-cistrans isomerization (shown as green molecules in Figure 12a). Figure 12a shows that, initially, the system has about 50/50 split between dMR molecules susceptible and not susceptible to the isomerization, as expected. Given the very large energy barriers for the trans-cis (60 kcal/mol) and cis-trans (40 kcal/mol) transitions we do not expect to observe a statistically significant number of such events in brute force molecular simulations, even on timescales of hundreds of nanoseconds. Therefore, we have biased these izomerization transitions in the following way. During each period of time Δttr, four molecules (which is one ~1% of total number of molecules in the simulated system) were randomly selected out of the pool of isomerization-susceptible molecules. Then for 1.5 ps the azobenzene group central C-N=N-C dihedral potential was switched to a one-fold potential with a maximum energy (barrier) for the trans configuration and a minimum for the cis configuration. This process is illustrated in Figure 11 by the wide arrow 12 while the biasing dihedral potential is shown as an S-shaped dashed line. During the 1.5 ps period when the biasing potential is active, the C-N=N-C dihedral relaxes from trans to cis configuration for the selected "excited" dMR molecule (process 3 in Figure 11). Then the biasing potential is turned off and the excited molecule is allowed to relax for time Δtcis in the cis state according to its natural dihedral potential (shown as the solid line in Figure 11). Because the natural barrier for the cis-trans transition is 40kcal/mol during this Δtcis period no molecules undergo a reverse transition to the trans state. Instead, they relax their intramolecular degrees of freedom and adjust its molecular orientations with neighboring molecules. After simulating over Δtcis period, the excited molecules are subjected to another biasing potential which now forces the molecule back to trans configuration as illustrated by processes 4-6. This biasing also occurs over 1.5ps after which the molecules are returned to the original natural dihedral potential. Therefore, this combination of biased conformational transitions effectively results in randomly selecting susceptible molecules, driving them to cis orientation where they can relax their configurations for a short period of time, and then are driven back into trans configuration. Note, that in this procedure we assumed that all molecules that have their azobenzene end-to-end vector angle between 45-135º relative to the y-direction have the same probability for excitation. In practice the probability for the molecule excitation will likely have more complex dependence on the orientation of the molecule (e.g., proportional to cosine square of the angle between the end-toend vector and polarization direction) as well as local environments. Nevertheless we believe that

19


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 46

the selected in this work simple criterion for excitation qualitatively captures key cooperative processes between molecules that lead to induced ordering.

Figure 11. Schematic illustration of the biasing protocol for conformational isomerization simulations. The solid line shows the natural dihedral potential for the central C-N=N-C dihedral. The dashed lines show the one-fold biasing potentials that were applied to selected molecules for short periods of time to force them between cis and trans conformations. Numbers and arrows indicate the sequence in which the biasing and natural potentials were applied in the isomerization simulation protocol (see text for details).

.

We assume that the biasing protocol described above can mimic the process that induces reorganization and reorientation of dMR molecules in the monolayer in experiments, leading to nematic alignment of the monolayer after a sufficient number of excitation events. In these biased simulations we used two sets of Δttr:Δtcis =30:15 or 90:60 ps combinations. The selected time intervals were sufficient to allow relaxation of the intramolecular degrees of freedom of excited molecules before the isomerization of the next randomly selected molecule. Teboul et al. used a similar protocol and time scales for biased isomerization transitions in molecular simulations of related azobenzene molecules in various matrices.34,35 Because isomerization was done using biasing potentials (rather than real photon absorption) this process was not accompanied by a significant increase of the thermal energy of the excited molecule. The maximum thermal energy increase for an excited molecule in this process is the potential energy difference due to application of the biasing potential. For example, a maximum of 60 kcal/mol change in dihedral potential energy can be converted to thermal energy as the excited molecule is driven from the cis

20


Page 21 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

to the trans state (process 6 in Figure 11). If all of this potential energy went into kinetic energy of the molecule the instantaneous temperature of the molecule would increase by ~700 degrees. However, in the highly packed environments modeled here a noticeable portion of this potential energy is transformed into the steric energy needed to do work on neighboring molecules to allow conformational changes in molecular geometry. Therefore, while some local heating occurs during the biasing simulations, it is not as significant as that discussed in the previous section. Figure 12b shows the evolution of the fraction of susceptible molecules in the monolayer. Because the time intervals for the biased transitions during simulation were selected at random, the simulation time scales become irrelevant and therefore the evolution is plotted as a function of the number of excitation events. The latter can, in principle, be related to the true experimental times for a given photon flux. Starting from a uniform population of susceptible and nonsusceptible molecules, after about 5000 excitation events at 298K we see that most of the molecules have been converted into the non-susceptible state, which means they have changed their orientation to be aligned along the y-direction. This can be clearly seen on the right snapshot of Figure 12(a), which shows a well-aligned monolayer with only few molecules still oriented mostly perpendicular to the y-direction (highlighted in green). This is also evident from examination of Figure 12c, where the evolution of nematic order parameter shown as function of number of excitation events. After ~ 5000 events, SN reaches a plateau value of ~ 0.8. These observations confirm our assumption that the designed simulation protocol with occasional biasing of trans→cis→trans transitions of randomly selected molecules with appropriate orientation can lead to macroscopic alignment of the entire monolayer. We also found that during this biased simulations that the molecules returning back from cis conformer to trans are likely to have their azobenzene unit orientation to be extended out-of-plane of the monolayer. However, very quickly the conformation of the tether for these molecules would adjust accordingly and the azobenzene unit adapts orientation parallel to the surface and aligning with other dMR molecules in the monolayer.

Therefore, instantaneously we only observe 4-5 molecules (those which

recently underwent "excitation" process) that have an out-of-plane orientation. Figures 12b,c also show that our results are independent of the selected values of Δttr and Δtcis. We carried out simulations in which the time between biased transitions and the amount of time spent in the cis state by excited molecules were increased by a factor of three and four, respectively, and find that this has minimal influence on the evolution of the system (as a function

21


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 46

of number of isomerization events), indicating that in both simulations these biasing transitions represented uncorrelated single-molecule events. In addition, we also conducted biased simulations at a higher temperature, 400K. Here, we find that after initial reorientation of about half of the susceptible dMR molecules the order parameter saturates at SN ~ 0.4, and ~ 25% of the molecules are always available for excitation. As shown in Figs. 6 and 7, at 400K the intrinsic orientational relaxation times of dMR molecules are on the order of multiple nanoseconds. Therefore, this system is not glassy and hence the orientational order relaxation competes with molecules alignment due to excitation. At these conditions, i.e. above the glass transition, one can expect that the stationary extent of ordering in the monolayer will depend on the relative values of the excitation rate and the orientational relaxation time. This also means that at this temperature, the ordering predicted by our biased simulations will depend on the selected values of Δttr:Δtcis combination.

Figure 12. (a) Snapshots of the monolayer with molecules susceptible to isomerization biasing highlighted in green. The left snapshot corresponds to the initial random orientation of molecules at 298 K, and the right snapshot shows the same system after 8000 biased "excitation" events (see text for details). (b) Evolution of the fraction of dMR molecules susceptible to random isomerization. The evolution is shown for two different rates of biased excitation events (see text for details) at 298 K, and for a single rate of excitation events at 400 K. (c) Evolution of the nematic order parameter of the system as a function of the number of biased excitation events.

Finally, to ensure that the trans→cis→trans conformational transitions accompanying molecular excitation events represent the key mechanism defining dMR monolayer ordering, we have conducted another biased simulation where instead of forcing conformational transition we

22


Page 23 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

have excited susceptible molecules with about 1eV of kinetic energy. In this simulation every Δttr we randomly select four molecules that are susceptible to excitation (based on their orientation relative to y-axis) and rescaled the velocity of atoms of these molecules by factor of two. This increases the kinetic energy of each molecule by factor of four which for dMR molecules at 298 K roughly corresponds to ~ 1 eV of energy. Examination of SN evolution in this case did not show any substantial increase in monolayer ordering after more than total of 3000 excitation events, indicating that thermal excitation alone cannot lead to the experimentally observed phenomenon. E. Thermal Erasing of the Isomerization-Induced Ordered State The final question we want to address is: how does the ordered dMR monolayer relax back to the disordered state? For this purpose, we have taken the final configuration obtained from the conformationally biased simulations at 298 K described in the previous section, i.e. a configuration very similar to the one shown on the right side of Figure 12a. Here, almost all molecules are aligned in the y-direction with an initial nematic order parameter of SN(0) = 0.8. This configuration is then quickly (within 1 ps) heated up to the desired temperature (350 K, 400 K, 500 K, or 600 K) and then a normal unbiased simulation is conducted at the corresponding temperature. Figure 13 shows the time evolution of the normalized order parameter (SN(t)SN_eq)/(SN(0)-SN_eq) in these systems, where SN_eq is the average nematic order parameter at the corresponding temperature (SN_eq > 0 due to the finite size of the system). This process emulates the experimentally studied thermal erasing of the monolayer order. As expected, the nematic order parameter of the simulated system begins to decrease from its initial value until the monolayer order is erased; the higher the temperature, the faster the erasing process is. For comparison, Figure 13 also indicates the corresponding orientational relaxation times for dMR molecules (from Figure 7). The erasing process is consistent with those equilibrium orientational relaxation times. The data of Figure 13 show that the characteristic time of the relaxation decreases by a factor of 100 as the temperature is increased from 400K to 600K (τ400/τ600 ≈100). Assuming a barrier gap for reorientation of a single molecule of kTt = Ut as in Figure 8a, this implies that τ400/τ600 ≈ 100 ≈ exp[Ut/400kB] / exp[Ut/600kB] giving Tt ≈ 4.6*1200K = 5500K. This is in substantial agreement with the corresponding experimental value in the photooriented dMR

23


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 46

monolayers which was found to be Tt = 7800K,20 and somewhat lower than Tt ~ 3400K from Figure 8c for the relaxation of the initially isotropic system. From Figure 13 it is clear that on the time scale of our simulations there is no erasure of the monolayer order at 298K where the dMR monolayer dynamics is glassy, also in agreement with the observation of τ300 ≈ 1 sec in the dMR monolayers.20

Figure 13. Evolution of normalized nematic order parameter during thermal erasing of the monolayer. The initial configuration of dMR monolayer was similar to that shown on the right side of Figure 11a. Also indicated are orientational relaxation times for azobenzene units obtained from the end-to-end vector autocorrelation function in unbiased simulations, also shown in Figure 7.

IV. Concluding Remarks. Molecular simulations conducted on the dMR monolayers, with grafting density corresponding to typical values considered in experiments, demonstrated that at room temperature the dMR molecules form locally orientationally ordered domains that include several molecules. However, at the surface coverage of 0.6 nm2/molecule there is no long-range ordering and there are plenty of "vacancy" defects in the monolayer. Nevertheless, simulations indicate that orientational relaxations of dMR molecules in such monolayer are restricted and the monolayer is glassy at room temperature, which is consistent with experiments. Simulations that emulated thermal and conformational excitation that occur during photoexcitation of dMR molecules were able to provide the molecular level insight into mechanisms of monolayer photofluidization

24


Page 25 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

observed for these materials experimentally. Our simulations show, that while the thermal excitation of one dMR molecule can noticeably heat the local environment of that molecule (few closest neighbors), the heat is dissipated very quickly (on the order of 100 ps) to the monolayer and thermal excitation of an orientational subpopulation of molecules does not induce orientational order in the monolayer. By contrast, cis-trans isomerization of an orientational subpopulation does produce a global order in the film. This implies that the work done by a molecule undergoing cis-trans isomerization on the cage of neighboring molecules is the key mechanism for photofluidization and orientational ordering in dMR monolayers exposed to linearly polarized light leading to relaxation dynamics that can be described in terms of higher effective temperature. Our results can be also consider to gain broader understanding of light-induced fluidization of glassy azobenzene-containing materials. The photofluidization concept has been invoked to help explain the phenomenon of light-induced mass transport, which has been intensively studied since the 1995 discovery of surface relief grating (SRG) formation in azo-containing polymer films exposed to interference patterns of actinic light.36,37 This effect has been exploited as a route to the fabrication of a variety of lithographic structures with feature sizes as small as ~ 20 nm (“directional photofluidization lithography” 38). However, while a number of theoretical models have been put forward (for a recent review, see ref. [38]) the mechanisms for mass transport remain poorly understood. In particular, SRG formation depends strongly on the polarization of the actinic light; strong gratings are formed in the p-p geometry (in an interference pattern formed by two p-polarized waves) and in the RCP-LCP geometry (where RCP and LCP denote interfering right- and left-handed circularly polarized waves), but much weaker SRG formation is observed in the s-s geometry. In general, mass transport in thin films is highly anisotropic, with mass transport taking place primarily along the electric field direction of linearly polarized actinic light,22 an observation that is difficult to reconcile with the notion of isotropic photofluidization, and that has been modeled in terms of an “inchworm” translational motion mechanism.39 A central difficulty here lies in relating the short-time, molecular-scale isomerization dynamics to long-time, mesoscale mass transport. For example, while atomistic MD simulations of the photoisomerization of probe molecules in a glassy molecular matrix have identified isomerization-induced “cage breaking” (disruption of the cage of neighboring molecules by cis-

25


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 46

trans isomerization) as the key process responsible for enhanced molecular diffusion, 40 the implications of this observation for long-time mesoscale mass transport remain unclear. Surface-bound monolayers of photoresponsive molecules offer a much simpler physical context for exploring the phenomenon of photofluidization because translational motion is suppressed, so the system behavior is governed by orientational dynamics. Our simulations of photoresponsive monolayers show that orientation-dependent local heating (direct conversion of absorbed photon energy into thermal energy) is insufficient to produce orientationally-ordered monolayers, but athermal photofluidization originating in the photomechanical work done by an azobenzene molecule undergoing cis-trans or trans-cis isomerization on its cage of near neighbors can induced orientational order.

The latter process can be considered a type of

orientational cage breaking, analogous to the cage-breaking process observed in molecular dynamics simulations of bulk azobenzene-containing polymers.40 These conclusions are likely to have some generality; we expect that the athermal work done by a photoisomerizing molecule on its cage of near neighbors on short timescales is the dominant mechanism driving photoinduced orientational ordering, order-disorder and glass transitions, and mass transport in SRGs and other systems, while thermal photofluidization due to local heating plays a negligible role (similar conclusions have been reached in the context of SRG formation38). However, the collective behavior of photoresponsive systems is expected to depend sensitively on details of molecular organization and interactions, and atomistic simulation is likely to play an increasingly valuable role in advancing the fundamental understanding of photoresponsive systems and in guiding the design of novel photoresponsive materials.

Acknowledgement. This work was supported by the Soft Materials Research Center under NSF MRSEC Grants DMR0820579 and DMR-1420736. DB and JBH also would like to acknowledge computational resources provided by the University of Utah Center for High Performance Computing.

Supporting Information Available: The snapshots, characteristic dihedral angle combinations, their relative energies for dMR molecules obtained from ab initio calculations as well as the prediction of both dihedral angles and energy differences from the parameterized force field are provided. Also discussed and

26


Page 27 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

illustrated the procedure for system preparation. This material is available free of charge via the Internet at http://pubs.acs.org.

27


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 46

References 1 Bandara, H. M. D.; Burdette, S. C. Photoisomerization in Different Classes of Azobenzene. Chem. Soc. Rev. 2012, 41, 1809-1825. 2

Seki, T. Smart Photoresponsive Polymer Systems Organized in Two Dimensions. Bull. Chem. Soc. Jpn. 2007, 80, 2084-2109. 3

Bleger, D.; Yu, Z. L.; Hecht, S. Toward Optomechanics: Maximizing the Photodeformation of Individual Molecules. Chem. Commun. 2011, 47, 12260-12266. 4

Ichimura, K.; Oh, S. K.; Nakagawa, M. Light-driven Motion of Liquids on a Photoresponsive Surface. Science 2000, 288, 1624-1626. 5

Shin, J. Y.; Abbott, N. L. Using Light to Control Dynamic Surface Tensions of Aqueous Solutions of Water Soluble Surfactants. Langmuir 1999, 15, 4404-4410. 6

Eastoe, J.; Vesperinas, A. Self-assembly of Light-sensitive Surfactants. Soft Matter 2005, 1, 338-347.

7

Sortino, S. Nanostructured Molecular Films and Nanoparticles with Photoactivable Functionalities. Photochem. Photobiol. Sci. 2008, 7, 911-924. 8

Feringa, B. L.; van Delden, R. A.; Koumura, N.; Geertsema, E. M. Chiroptical Molecular Switches. Chem. Rev. 2000, 100, 1789-1816. 9

Lee, C. T.; Smith, K. A.; Hatton, T. A. Photoreversible Viscosity Changes and Gelation in Mixtures of Hydrophobically Modified Polyelectrolytes and Photosensitive Surfactants. Macromolecules 2004, 37, 5397-5405. 10

Tomatsu, I.; Peng, K.; Kros, A. Photoresponsive Hydrogels for Biomedical Applications. Adv. Drug Delivery Rev. 2011, 63, 1257-1266. 11

Okano, K.; Mikami, Y.; Yamashita, T. Liquid-crystalline Polymer with a Block Mesogenic Side Group: Photoinduced Manipulation of Nanophase-separated Structures. Adv. Funct. Mater. 2009, 19, 3804-3808. 12

White, T. J.; McConney, M. E.; Bunning, T. J. Dynamic Color in Stimuli-responsive Cholesteric Liquid Crystals. J. Mater. Chem. 2010, 20, 9832-9847. 13

Tsutsumi, O.; Ikeda, T. Photochemical Modulation of Alignment of Liquid Crystals and Photonic Applications. Curr. Opin. Solid State Mater. Sci. 2002, 6, 563-568. 14

Shibaev, V.; Bobrovsky, A.; Boiko, N. Photoactive Liquid Crystalline Polymer Systems with Lightcontrollable Structure and Optical Properties. Prog. Polym. Sci. 2003, 28, 729-836. 15

Ikeda, T.; Tsutsumi, O. Optical Switching and Image Storage by Means of Azobenzene Liquid-Crystal Films. Science 1995, 268, 1873-1875.

28


Page 29 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

16

Prasad, S. K.; Nair, G. G.; Hegde, G. Dynamic Self-assembly of the Liquid-crystalline Smectic A Phase. Adv. Mater. 2005, 17, 2086-2091. 17

Prasad, S. K.; Nair, G. G.; Hegde, G. Nonequilibrium Liquid Crystalline Layered Phase Stabilized by Light. J. Phys. Chem. B 2007, 111, 345-350. 18

Kosa, T.; Sukhomlinova, L.; Su, L. L.; Taheri, B.; White, T. J.; Bunning, T. J. Light-induced Liquid Crystallinity. Nature 2012, 485, 347-349. 19

Kawanishi, Y.; Tamaki, T.; Ichimura, K. Photoregulation of Liquid-crystalline Orientation by Anisotropic Photochromism of Surface Azobenzenes. in Polymers for microelectronics: Resists and dielectrics, Thompson, L. F.; Willson, C. G.; Tagawa, S., Eds. Amer Chemical Soc: Washington, 1994; Vol. 537, pp 453-465. 20

Fang, G.J.; Maclennan, J.E.; Yi, Y.; Glaser, M.A.; Farrow, M.; Korblova, E.; Walba, D.M.; Furtak, T.E.; Clark, N.A. Athermal Photofluidization of Glasses. Nat. Commun. 2013, 4, 1521. 21

Hugel, T.; Holland, N. B.; Cattani, A.; Moroder, L.; Seitz, M.; Gaub, H.E. Single-molecule Optomechanical Cycle. Science 2002, 296, 1103-1106. 22

Karageorgiev, P.; Neher, D.; Schulz, B.; Stiller, B.; Pietsch, U.; Giersig, M.; & Brehmer, L. From Anisotropic Photo-fluidity Towards Nanomanipulation in the Optical Near-field. Nat. Mater. 2005, 4, 699703. 23

Barrett, C. J.; Rochon, P. L.; Natansohn, A. L. Model of Laser-driven Mass Transport in Thin Films of Dye-functionalized Polymers. J. Chem. Phys. 1998, 109, 1505–1516.

24

Vapaavuori, J.; Laventure, A.; Geraldine-Bazuin, C.; Lebel,O.; Pellerin C. Submolecular Plasticization Induced by Photons in Azobenzene Materials. J. Am. Chem. Soc. 2015, 137, 13510−13517.

25

Borodin, O. Polarizable Force Field Development and Molecular Dynamics Simulations of Ionic Liquids. J. Phys. Chem. B 2009, 113, 11463-11478. 26

Bedrov, D.; Borodin,O.; Smith, G.D.; Sewell, T.D. A Molecular Dynamics Simulation Study of Crystalline 1,3,5-triamino-2,4,6 -trinitrobenzene (TATB) as a Function of Pressure and Temperature. J. Chem. Phys. 2009, 131, 224703. 27

Hooper, J.B.; Borodin, O. Molecular Dynamics Simulations of N,N,N,N-tetramethylammonium Dicyanamide Plastic Crystal and Liquid Using a Polarizable Force Field. Phys. Chem. Chem. Phys. 2010, 12, 4635-43. 28

Borodin, O.; Smith, G.D.; Bedrov, D.; Sewell, T.D. Polarizable and Nonpolarizable Force Fields for Akylnitrates and PETN. J. Phys. Chem. B. 2008, 112, 734-742. 29

Hooper, J.B.; Bedrov, D.; Smith, G.D.; Borodin, O.; Dattelbaum D.M.; Kober, E.M. A Molecular Dynamics Simulation Study of the Pressure-Volume-Temperature Behavior of Polymers Under High Pressure. J. Chem. Phys. 2009, 130, 144904.

29


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 46

30

Gaussian 09, Revision A.02, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. 31

Tiberio, G.; Muccioli, L.; Berardi, R.; Zannoni, C. How Does the Trans–Cis Photoisomerization of Azobenzene Take Place in Organic Solvents? ChemPhysChem. 2010, 11, 1018-1028. 32

Palmer, B. J. Direct Application of Shake to the Velocity Verlet Algorithm. J. Comput. Phys 1993, 104, 470-472. 33

Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Explicit Reversible Integrators for Extended Systems Dynamics. Mol. Phys. 1996, 87, 1117-1157. 34

Teboul, V. Stimuli Thresholds for Isomerization-Induced Molecular Motions in Azobenzene-Containing Materials. J. Phys. Chem. B 2015, 119, 3854−3859.

35

Teboul, V.; Saiddine, M.; Nunzi, J.-M. Isomerization Induced Dynamic Heterogeneity in a Glass Former below and above Tg. Phys. Rev. Lett. 2009, 103, 265701. 36

Rochon,P.; Batalla,E.; Natansohn,A.; Optically Induced Surface Gratings on Azoaromatic Polymer Films. Appl. Phys. Lett. 1995, 66, 136-138. 37

Kim, D.Y.; Tripathy, S.K.; Li, L.; Kumar, J.; Laser-Induced Holographic Surface Relief Gratings on Nonlinear Optical Polymer Films. Appl. Phys. Lett. 1995, 66, 1166-1168. 38

Lee,S.; Kang, H.S.; Park, J.-K.; Directional Photofluidization Lithography: Micro/Nanostructural Evolution by Photofluidic Motions of Azobenzene Materials. Adv. Mater. 2012, 24, 2069-2103. 39

Juan, M. L.; Plain, J.; Bachelot, R.; Royer, P.; Gray, S.K.; Wiederrecht, G.P.; Multiscale Model for Photoinduced Molecular Motion in Azo Polymers. ACS Nano 2009, 3, 1573-1579.

40

Teboul, V.; Saiddine, M.; Nunzi, J.-M.; Accary, J.-B.; An Isomerization-Induced Cage-Breaking Process in a Molecular Glass Former Below T(g). J. Chem. Phys. 2011, 134, 114517.

30


Page 31 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure Captions. Figure 1. (a) Schematic illustration of a dMR molecule attached to the surface. (b) A snapshot of the side view of a dMR monolayer at the surface. Figure 2. Energy profile for the central C-N=N-C dihedral in the azobenzene unit as predicted by parameterized force field. Figure 3. Snapshots (top view) of equilibrated dMR monolayers at (a) 298 K and (b) 700K. Figure 4. Probability distribution of the angle between the end-to-end vector of the azobenzene unit and the surface plane as defined in Figure 1. Figure 5. Monolayer density profiles (left axis) and fractional density distributions of selected atoms/groups (right axis) at 298K as a function of separation from the surface: (a) for a monolayer with all azobenzene units in the trans conformation and (b) for a monolayer with 25% of the azobenzene units in the cis conformation. Figure 6. Autocorrelation function (ACF) of the azobenzene unit end-to-end vector (Re) obtained from dMR monolayer simulations at different temperatures (symbols). Dashed lines show the fit to the KWW equation (see text for discussion). The solid lines for T < 500 K show the ACF for a monolayer with 25% of the azobenzene molecules in the cis conformation. Figure 7. Temperature dependence of the characteristic relaxation times obtained from integration of the end-to-end ACFs shown in Figure 6. The dashed line shows the VF fit and the extrapolation to room temperature. Figure 8. a) Schematic illustration of orientational energy barrier distribution f(U) and the corresponding orientational decay function C(t) used for the analysis of experimental data in ref. [20]. b) End-to-end vector ACF obtained from MD simulations at different temperatures and the corresponding fits using C(t) functional form. c) Temperature dependence of Ut and Um parameters obtained from the fits (see discussion in the text).

31


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 9. (a-d) Snapshots showing several molecules (highlighted in green) selected for thermal excitation in single-molecule thermal excitation simulations. (e) Time evolution of the instantaneous temperature of several excited molecules. Figure 10. (a) Snapshots of the local environment of a thermally excited molecule (highlighted in green) and identification of its close neighbors. (b) Time evolution of the instantaneous temperature of the thermally excited molecule and its neighbors. Figure 11. Schematic illustration of the biasing protocol for conformational isomerization simulations. The solid line shows the natural dihedral potential for the central C-N=N-C dihedral. The dashed lines show the one-fold biasing potentials that were applied to selected molecules for short periods of time to force them between cis and trans conformations. Numbers and arrows indicate the sequence in which the biasing and natural potentials were applied in the isomerization simulation protocol (see text for details). Figure 12. (a) Snapshots of the monolayer with molecules susceptible to isomerization biasing highlighted in green. The left snapshot corresponds to the initial random orientation of molecules at 298 K, and the right snapshot shows the same system after 8000 biased "excitation" events (see text for details). (b) Evolution of the fraction of dMR molecules susceptible to random isomerization. The evolution is shown for two different rates of biased excitation events (see text for details) at 298 K, and for a single rate of excitation events at 400 K. (c) Evolution of the nematic order parameter of the system as a function of the number of biased excitation events. Figure 13. Evolution of normalized nematic order parameter during thermal erasing of the monolayer. The initial configuration of dMR monolayer was similar to that shown on the right side of Figure 11a. Also indicated are orientational relaxation times for azobenzene units obtained from the end-to-end vector autocorrelation function in unbiased simulations, also shown in Figure 7.

32


Page 32 of 46

Page 33 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 1.

(a)

(b)

33


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2.

34


Page 34 of 46

Page 35 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 3.

35


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4.

36


Page 36 of 46

Page 37 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 5.

37


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6.

38


Page 38 of 46

Page 39 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 7.

39


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8.

40


Page 40 of 46

Page 41 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 9.

41


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 10.

42


Page 42 of 46

Page 43 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 11.

43


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 12.

44


Page 44 of 46

Page 45 of 46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 13.

45


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 46

Table of Content Graphic

46


Photoinduced and Thermal Relaxation in Surface ... - ACS Publications

Recommend Documents