How does the isomerization rate affect the photoisomerization-induced transport properties of a doped molecular glass-former?

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How does the isomerization rate affect the photoisomerization-induced transport properties of a doped molecular glass-former?

J.-B. Accary and V. Teboul

Citation: J. Chem. Phys. 139, 034501 (2013); doi: 10.1063/1.4813410 View online: http://dx.doi.org/10.1063/1.4813410

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How does the isomerization rate affect the photoisomerization-induced transport properties of a doped molecular glass-former?

J.-B. Accary¹and V. Teboul^1,2,a)

1Physics Department, Université d’Angers, CNRS UMR 6200, MOLTECH-Anjou, 2 Bd Lavoisier, 49045 Angers, France

2Department of Chemistry, University of California, Berkeley, California 94720, USA (Received 10 April 2013; accepted 25 June 2013; published online 17 July 2013)

We investigate the effect of the isomerization ratefon the microscopic mechanisms at the origin of the massive mass transport found in glass-formers doped with isomerizing azobenzene molecules that result in surface relief gratings formation. To this end we simulate the isomerization of dispersed probe molecules embedded into a molecular host glass-former. The host diffusion coefficient first increases linearly withfand then saturates. The saturated value of the diffusion coefficient and of the viscosity does not depend onfbut increases with temperature while the linear response for these transport coefficients depends only slightly on the temperature. We interpret this saturation as arising from the appearance of increasingly soft regions around the probes for high isomerization rates, a result in qualitative agreement with experiments. These two different physical behaviors, linear response and saturation, are reminiscent of the two different unexplained mass transport mechanisms observed for small or large light intensities (for small intensities the molecules move towards the dark regions while for large intensities they move towards the illuminated regions).© 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4813410]

I. INTRODUCTION

Two decades ago, Rochon, Batalla, and Natansohn¹and Kim, Tripathy, Li, and Kumar² found independently the appearance of surface relief gratings (SRG) by illuminating thin polymer films doped with azo-dyes that isomerize when illuminated. There is now a clear consensus that SRG formation is due to a still unexplained^3–6isomerization-induced massive mass transport mechanism.⁷ Interestingly, various important unexplained physical mechanisms ranging from the glass- transition^8–10 and the jamming-transition¹¹ to shear thinning and thickening^12,13 are in possible relation^14,15 with the SRG formation mechanism. Amazingly however, depending on the light intensity, two opposite behaviors are observed¹⁶ leading in both cases to SRG formation. For small intensities the molecules move towards the dark regions while for high intensities they move towards the illuminated regions.^3,16 This result suggests at least two different physical mechanisms.

The main consequences of a variation of the light intensity in the SRG context are a modification of the electric field of the incident light impinging on the material, and a modification of the photo-isomerization rate of the probes. In this work we will focus our attention on the isomerization rate effects.

Various mechanisms have been proposed to explain the observed massive mass transport at the origin of the SRG for- mations. The proposed mechanisms include the mean field induced by the dipolar attraction between chromophores,^17,18 the mechanical stress induced by the orientation of the chromophores,^19,20 the effect of the incident light electric field gradient,²¹ an isomerization-induced cage breaking around the chromophore,¹⁵ the pressure gradients created by

a)Electronic mail: [email protected]

the isomerizations,^22,23and the reptation of the chromophore along the polarization direction.²⁴However, following Natan- sohn and Rochon,³ we expect several physical mechanisms to appear sequentially during the SRG formation. For short time scales the chromophore’s isomerization induces molecular rearrangements around the chromophore resulting in its own motion and the motion of surrounding molecules.^15,22–25 These isomerization-induced motions include the rotation of the chromophore. Note that this short time scale increases when the temperature drops due to the viscosity increase of the material. Then due to the preferential light absorption in the chromophore’s dipole direction, the chromophores finally align in a direction perpendicular to the electric field of the incident light,^3,24 leading to the appearance of new physical mechanisms^17–21 and to an optical saturation effect.^3,24 Re- cent experiments²⁶show that the two sort of physical mechanisms (dipoles induced or isomerization induced) cohabit also for larger time scales, a result that is expected as long as the isomerizations are still present.

Molecular dynamics (MD) simulation is an invaluable tool to unravel the physics of phenomena at the microscopic level.^27–35 In this paper we use MD simulations to study the isomerization rate dependence of the host material dynamical properties. Our aim is to search for the presence of different dynamical regimes, triggered by the isomerization rate (f=1/τpifτpis the period), and that could be related with the two different experimental behaviors discussed previously.

We expect the physics to depend on the ratio of the host material relaxation time with the isomerization period.^36–39 We find that the diffusion coefficient of the host material increases first linearly with the isomerization rate and then saturates. The linear increase is expected from the linear response theory for perturbations small enough to not

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034501-2 J.-B. Accary and V. Teboul J. Chem. Phys.139, 034501 (2013)

modify significantly the host material properties. The saturation regime then appears when the host material properties are more deeply affected. We find in the saturation regime a softening of the host material around the isomerizing probe, leading to heterogeneous properties of the material. This appearance of a localized softening when the intensity increases is in qualitative agreement with recent experiments.^7,40 We interpret the saturation as originating from this localized softening. The host diffusive motions induced by the probe isomerizations have in this regime some difficulty to propagate to the rest of the material leading to the saturation of the diffusion.

In this work, we are interested only in the short times physical mechanisms that are directly induced by the isomerizations. We are aware however that a saturation appears at large time scales even for small intensities due to the alignment of the chromophores. However the saturation that we observe in our work is a different physical process that appears due to the isomerizations and that is not related to the alignment of the chromophores. Note that the effect of this alignment has already been studied extensively.^17–21,41As our simulations model realistically the shape modification of the molecule during the isomerization, we expect to find interesting new informations on the first processes that take place inside the material when the isomerization is set on. We also expect our investigations to lead to interesting new informations on the physics of the glass-transition as the perturbations are here induced at the nanoscale (the scale of the isomerizing molecule). Indeed, if a number of studies already exist about perturbations applied on glass-formers (mostly shear induced effects^42–45), nanoscale perturbations are very scarcely inves- tigated in that domain.

II. CALCULATIONS

We simulate the photoisomerization of one “dispersed- red one” (DR1) molecule (C16H18N4O3, the probe) inside a matrix of 500 methylmethacrylate (MMA) molecules (C₅H₈O₂, the host). A detailed description of the simulation procedure can be found in previous works.14,15,25,46The main differences are that: (i) The concentration of probe molecules is here much lower and the size of the box larger. (ii) To speed up the calculations, we model the host interactions here with a recent coarse-grain potential function.⁴⁷ For the probe molecule, we use however the same all-atom site-to-site interaction potential⁴⁸as previously. The interaction potentials^47,48 and the positions of grains are summarized in TablesIandII.

SRG formation has been reported in a number of materials^3,4 ranging from polymers to molecular glass-formers. This rel- atively universal behavior points to some universality in the mechanisms at the origin of SRG. Our aim here is thus not to reproduce perfectly a particular material’s property but to use MMA as a paradigm to study the universal mechanisms.

The coarse grain model is coined in that direction, using only physically relevant and universal Lennard-Jones potentials to model the molecule. The main drawback of coarse graining is the modification of the characteristic temperatures of the material.⁴⁷ We use the Gear algorithm with the quaternion method⁴⁹ to solve the equations of motions with

TABLE I. Parameters for the DR1 and coarse grain MMA potentials from Refs. 47 and 48. There are no charges in the models. We use the following relations to obtain the interactions between different atoms/grains:

σij=(σii·σjj)^0.5andij=(ii·jj)^0.5. The two molecules are modeled as rigid bodies.

DR1 Coarse grain MMA

Atom Type (kJ/mol) σ(Å) Grain (kJ/mol) σ(Å)

C (rings) 0.293 3.55 1 1.765 3.34

C (others) 0.276 3.50 2 0.129 4.54

O (−C) 0.711 3.07 3 2.293 3.46

O (−N) 0.711 3.00 4 2.858 3.34

N 0.711 3.25

H (rings) 0.125 2.42

H (others) 0.125 2.50

at =10⁻¹⁵s time step. The temperature is controlled using a Berendsen thermostat.⁵⁰ The density is set constant at 1.19 g/cm³. We thus have 7541 atoms in a 41.26 Å wide cu- bic simulation box. We model the isomerization as a uniform closing and opening of the probe molecule shape^51–54 during a characteristic timet₀=1 ps; while the period of the isomer- izationcis-transand thentrans-cisis a variable that we refer to asτp in the article. As a resultτp/2 appears as the period between two energetic impulses inside the material and may thus have a physical role. During the isomerization, the shape of the DR1 molecule is modified slightly at each time step using the quaternion method with constant quaternion variations, calculated to be in the final trans orcisconfiguration after a 1 ps isomerization. This method corresponds to opposite continuous rotations of the two parts of the molecule that are separated by the nitrogen bounding. We have used two rotations with different axis for each part of the molecule

TABLE II. Positions of the atoms and grains (in Å) inside the MMA molecule. The 15 atoms of the MMA molecule are modeled as 4 grains (i.e., center of forces) to increase the simulation efficiency. These 4 grains are located on the positions of the first 4 carbons of the list. However the positions of the masses of the 15 atoms are considered in the equations of motions.

Details on this coarse grain model may be found in Ref.47. In contrast, the DR1 molecule is modeled with a center of force on each atomic position.

Atomic positions(masses) Grains(forces)

Atom x (Å) y (Å) z (Å) Grain

C 1.21 0.78 1.51 1

C 0.0 −1.42 1.55 2

C 0.0 0.0 −0.53 3

C 0.0 −2.81 3.42 4

C 0.0 0.0 1.00

O 0.0 −1.51 2.87

O 0.0 −2.38 0.78

H 2.12 0.32 1.15

H 1.15 1.81 1.15

H 0.00 1.03 −0.89

H 0.89 −0.51 −0.89

H –0.89 −0.51 −0.89

H 0.00 −2.74 4.51

H –0.89 −3.34 3.09

H 0.89 −3.34 3.09

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in order to obtain the isomerization. The respective constant quaternion variations of the two parts of the molecule during the isomerization are chosen in order to take into account the difference of inertia moments between these parts. The most massive part is then moving slightly slower than the lighter part of the molecule. Due to the change in the conformation of the molecule, the inertia moment and center of masses of theDR1 molecule are reevaluated at each time step during the isomerization.

We use a coarse grain model to accelerate strongly the simulations and ameliorate the statistics of our results. Due in part to the coarse graining, the characteristic temperatures of the material are different from the experimental ones for our material. We estimate the melting temperatureTmof our coarse grained material around 300 K, using the appearance of a plateau in the mean square displacement as a signa- ture of the supercooled state. Note that a previous study⁵⁵ showed that the induced diffusion coefficient reaches its thermal counterpart around that temperatureTm. We evaluateTg

to be slightly above 105 K in our model. More important for our study, the out of equilibrium behavior begins in our simulations at around 120 K when the isomerization is turned off. At large distances from the chromophore the dynamics is unchanged by the isomerizations, at least on the time scale of our simulations. As a result we will focus our study on the medium behavior around the chromophore. We thus have evaluated the possible size effects^56,57 on this localized behavior using different simulation boxes from 36 to 72 Å wide with a number of host molecules ranging from 336 to 2688.

The power of the incident light inducing the isomerizations is related to the isomerization period with the simple formula

P =E_γ/τ_p, (1)

whereEγ =hC/λis the energy of the photon that induces the isomerization. For the visible wavelength ofλ=5435 Å used in Ref.16we obtain Eγ =3.66 10⁻¹⁹J. The surface within which a photon can initiate the isomerization of our chromophore with this wavelength isS≈π·λ²/4≈2.3 10⁷Å². Using these formula an incident light intensity of 845 W/cm² as in Ref.16leads toτ_p =Eγ/(I.S)≈0.2 10⁻¹² s, while a light intensity of 230 mW/cm²leads to a much larger value of τp ≈0.7 10⁻⁹ s. These values are however rough estimates and the light intensity inducing the different effects will also depend on the host material. In order to evaluate a possible aging^58–65 in our results, we have recorded for each data pre- sented here, two successive runs of 10 ns each and compared the results. We display the two different aging data with empty and full symbols in the figures. We model the isomerization to take place at periodic intervals whatever the surrounding local viscosity. This approximation has recently been validated experimentally,^66,67as the viscosity necessary to stop the isomerization of this probe molecule is extremely large. We do not use any smoothing procedure on our curves. The curves thus show the magnitude of the statistical fluctuations which are small due to the large number of configurations (>10 000) averaged.

III. RESULTS AND DISCUSSION

Following the linear response theory, the response, here the diffusion coefficientD, must be proportional to the exci- tation, thus to the number of probes isomerizations per unit time f = 1/τp. However, due to the presence of coopera- tive motions,^8,68–72 supercooled liquids are subjects to various breakdowns^73–76of the linear response theory.⁷⁷Previous works^42–45,76 on excited amorphous materials suggest to expect either a power law⁴² or a linear response^43,44,76 when the perturbation is small enough to not persistently affect the medium. In contrast for large enough perturbations we expect the host material to be deeply affected leading to a saturation of the response due to the host softening. This is what Figure 1 shows for various temperatures, namely the diffusion first increases linearly with the isomerization frequency f=1/τpand then saturates. In the figure we fit the data with a simple saturation law of the form

D_driven=D_thermal+D˜_∞(1−e^−(τ⁰^/τ^p⁾^γ). (2) In this relation Dthermalis the diffusion coefficient when the isomerization is switched off, ˜D_∞ is the saturation value of the induced part of the diffusion, and τ₀ is a time constant.

In the low frequency limit, relation (1) reduces to a power law response: ˜Dind =D˜_∞(τ₀/τp)^γ, which is linear ifγ =1.

We find that our results are well fitted with a linear response, i.e., using the parameterγ =1. The time parameterτ₀in formula(2)quantifies the limit between the linear response for τ_p > τ₀ (f<1/τ₀) and the saturation regime for larger frequencies (f>1/τ0).τ₀ thus corresponds to an optimum for the response and the SRG formation with respect to the energy transmitted by the probe to the host material. In the temperature range studied we findτ₀≈80 ps depending slightly on the temperature. The slope of the linear response ( ˜D_∞·τ₀) is the susceptibility of the material to our isomerization- induced perturbation. In the temperature range studied, this slope increases slightly with temperature, leading to an increase of the saturation diffusion coefficient with temperature.

In the small perturbation limit, the response thus decreases with the temperature. Similarly the saturation limit ˜D_∞ decreases when the temperature drops, a result due to the increase in viscosity of the host material. The induced diffusion is thus more efficient when the temperature increases.

We note that recent experiments^78–80show that the SRG formation increases when the temperature drops, and even dis- appear at high enough temperature. However these results are not at all in contradiction with our findings. Because the SRG formation is the result of a competition between the induced diffusion ˜Dindthat creates the SRG and the thermal diffusion Dthermal that destroys them. Thus the SRG evolution may be evaluated in our simulations from a comparison between ˜Dind andDthermal. As when the temperature increases, Dthermal increases much more rapidly than ˜Dind, our simulations lead to the same comportment as the discussed experimental data.^78,79

We observe two different behaviors in Figure 1 (linear response and saturation) depending on the isomerization rate. It is tempting to associate these two different behaviors with the two experimental behaviors discussed above (i.e., for

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0 50 100 150 200 250 300 350

Ddriven-Dthermal ( o A2 / ns )

1/τp (ns^-1)

T=200K

T=140K

T=100K

0.01 0.1 1 10

0.1 1 10 100 1000

Ddriven-Dthermal ( o A2 / ns )

1/τp (ns^-1) (a)

(b)

FIG. 1. (a) Diffusion coefficient of the host molecules versus the isomerization frequency f = 1/τp. The temperatures are from bottom to top:

T=100 K (black circles solid and open); T=140 K (solid and open red circles); T=200 K (open red and solid grey triangles). These temperatures are effective temperatures of the coarse grain model. The lowest temperature (T=100 K) is belowTg ≈105 K in the model while the two others are aboveTgbut belowTm≈300 K. AsDdrivenreachesDthermalaroundTm,⁵⁵ the curves must decrease at some temperature in between 200 K and 300 K.

However, the uncertainty of the difference (Ddriven−Dt hermal) increases with temperature in our simulations making 200 K the largest temperature that could be displayed here. TheDthermalvalues in this figure areD_{t hermal}^200K

=14.0 Å²/ns,D_{t hermal}^140K =2.34 Å²/ns, andD_{t hermal}^100K ≈0 Å²/ns. In order to evaluate a possible aging mechanism associated with the isomerization we show two sort of data on the figure. For each temperature the open symbols stand for direct simulations from an equilibrated configuration without isomerizations while the solid symbols stand for simulations that follow a 10 ns first run with the isomerization set on. The dashed lines are fit to the points with the following equation:Ddriven−Dt hermal=D˜_∞(1−e⁻^(τ⁰^/τ^p⁾^γ), with γ=1. (b) As (a) but in a logarithmic scale.

small intensities the host material is seen to move towards dark regions while for large intensities the opposite effect is observed). The linear response is the physical mechanism present for the small intensities for which the host material move towards dark regions. It has been suggested²⁴ that the increase in local diffusion may explain this experimental behavior. In this model the molecules move in the diffusive illuminated regions until they reach a non-diffusive dark region leading to mass transport from illuminated to dark regions. In contrast, if the saturation regime is the mechanism present for the large intensities for which the host material move towards illuminated regions, it is clear that a different explanation has

to be found in this case. In this paper we will however concen- trate our attention to more reasonable questions. We will try to find the answer to the question of the origin of the observed linear response and of the saturation regime. In the linear response regime, Figure1shows that the diffusive motions are mostly governed by the isomerization ratefand only slightly by the temperature. This result suggests that the diffusive motions are, in this regime, directly induced by the isomerizations in accordance with various mechanisms.15,17–19,21–24In contrast with the saturation regime the diffusive motions are totally governed by the temperature and do not depend any- more on the isomerization rate. This is equivalent to having a new softer material without isomerization. This result suggests that in the saturation regime the isomerization affects the medium by softening it (the diffusion increases) but do not contribute directly to the motions. The saturation tells us that the isomerization induced motions are less efficient when the isomerization rate f is large. A possible reason is that the cage does not have enough time to reconstitute itself before the next isomerization. We evaluate the time it takes for the cage to reconstitute itself in our system as between 1 and 10 ps depending on the temperature. Thus if this effect contributes for the larger frequencies displayed in Figure 1 it will not contribute for the beginning of the saturation that takes place for τ_p/2≈40 ps. Another reason that comes to mind is that the material becomes softer around the probe due to the large number of isomerizations, privileging local motions and decreasing the isomerization induced motions efficiency. In this picture the host material is more structurally heterogeneous in the saturation regime than in the linear response regime. The regions around the probe are too soft for the isomerization-induced diffusion to propagate, because the cage breaking mechanism is replaced by local diffusive rearrangements. As discussed above, the temperature dependence of the diffusion coefficient in the saturation regime supports this picture. We note that for the largest frequencies f studied the diffusion coefficient decreases slightly (see last circles on the right). As there is some shear induced by the isomerization due to the difference in the occupied volumes of thetrans andcisisomers^3,46 we interpret this decrease as shear thickening.^42–45 As a result there is also an optimum period (or frequency) in the saturation regime. Interestingly enough the three curves collapse into a master curve when ˜D is rescaled by ˜D_∞(i.e., by plotting ˜D/ ˜D_∞versusf). A rescal- ing of the isomerization ratef=1/τpusing a Deborah number De=τα/τpis amazingly not needed in this procedure and results in a separation of the collapsed curves. This result confirms that the characteristic timeτ₀or frequencyf0=1/τ0is only slowly varying (or not varying) with temperature.

Figure2shows the evolution of the inverse of theαre- laxation time 1/ταas a function off=1/τp. Theαrelaxation timeτ_αis a quantity proportional to the local viscosity of the host material. For that reason, and becauseτ_α quantifies the lifetime of transient structural fluctuations, it is of particular interest to us. The Stokes-Einstein relation states that the inverse of the viscosity (i.e., 1/τα) is proportional to the diffusion coefficient. However, glass-formers below their melting temperature exhibit a breakdown of that relation.^73,74 A direct calculation ofταis thus necessary here. We defineταas

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0.1 1 10

0.1 1 10 100 1000

1/ταdriven - 1/ταthermal ( ns-1 )

1/τp (ns^-1)

FIG. 2. Inverse of theαrelaxation time 1/ταversus the isomerization rate f=1/τpfor various temperatures. Theαrelaxation time is obtained from the relationFS(Q,τα)=e⁻¹.ταis equivalent to the local viscosity here and can be used as a measure of that viscosity. From bottom to top the temperatures are T=100 K, 140 K, and 200 K. As in Figure1(a)the open and solid symbols correspond to different aging procedures. We relatef=1/τpto the light intensityIwith the rough formula: 1/τp≈(π λ³/4hC)I.

the time t=τα for which the incoherent intermediate scattering functionFS(Q,t) reaches the valuee⁻¹. In this relation Q=1.38 Å⁻¹is the wave vector of the first peak of the structure factorS(Q) of our material, andFS(Q,t) is obtained from the following relation:⁸¹

FS(Q, t)= 1 N.Nt₀

Re

⎛

⎝

t₀

j

e^i.Q.(r^j^(t+t⁰⁾⁻^r^j^(t⁰⁾⁾

⎞

⎠. (3)

This function, normalized at t=0, describes the autocorre- lation of the density fluctuations at the wave vector Q. In Figure2we plot 1/ταversusf=1/τp. The isomerization rate fis the quantity of physical importance to us because it is proportional to the light intensity (see Eq.(1)) or equivalently to the perturbation energy per unit time. As a result we have to plot the inverse of the relaxation time 1/τα and notταin order to be able to find the linear response at small rate. 1/ταhas also the interest of being a quantity proportional to the diffusion coefficient at large temperatures (forT≈Tm). Figure2 shows the same main behavior for 1/τα as Figure 1 for the diffusion coefficient, namely a linear increase followed by a saturation and then a small decrease due to shear thickening. The shear thickening effect is however larger for 1/ταin Figure 2 than forDind in Figure 1. The slope of the curves around 1/τp 0 is also more temperature dependent in Figure2for 1/ταthan in Figure1forDind. These results suggest that the relaxation time τα (i.e., the viscosity) is governed by the host material properties more clearly than the diffusion coefficient Dind which is in turn mainly governed by the isomerizations induced motions. We note that: (i) The relative increase in the 1/τα saturation value when the temperature increases is approximately the same as the relative increase observed for the diffusion coefficient in Figure 1.

(ii) The time τ₀ that separates the linear response from the saturation is also approximately the same for 1/ταandD. As for the diffusion coefficient, this timeτ₀ increases when the temperature drops. However it increases much more slowly

0.1 1 10

0.1 1 10 100 1000

1/ταdriven - 1/ταthermal ( ns-1 )

1/τp (ns^-1)

FIG. 3. Inverse of theαrelaxation time 1/ταversus the isomerization rate f=1/τpfor various distance from the isomerizing chromophore. The temperature is T=100 K. From top to bottom the distances intervals from the chromophore are: 0<R<10 Å; 10<R<20 Å; 0<R<∞; and 20<R

<40 Å.

than the relaxation time. Figure3shows the same relaxation times τα as in Figure2 but for different distances from the chromophore. Around the chromophore (black circles) the viscosity that is related to τ_α is much smaller and the diffusion is much larger than in the rest of the medium leading to the upper curves in the figure (because we plot 1/τα). This figure illustrates the heterogeneous picture discussed above.

Around the probe, the viscosity continues to decrease following the linear response of 1/ταversus 1/τp, while at larger distances from the probe 1/ταis already in the saturation regime.

The differences between 1/τα around the probe (black circles) and at a distance from the probe (red circles) is much larger in the saturation regime than in the linear regime. This result shows that the medium is more heterogeneous in the saturation regime, with soft regions localized between 0 and 10 Å around the probe(s) (black circles) surrounded by regions that are much less affected (red circles) as they did not evolve much with the isomerization rate. This result supports the picture of soft regions around the probe at the origin of the saturation mechanism. If the evolution of the viscosity for the three lower curves (i.e., forR>10 Å from the probe) is similar, the upper curve behaves differently. We thus observe a decoupling between the evolution of the viscosity around the isomerizing probe and the viscosity at larger distances from it. As the viscosity decrease forR>10 Å is clearly also induced by the probe isomerization, this result suggests that the isomerization effect on the viscosity does not propagate well when large frequencies are involved, resulting in the saturation regime. We thus attribute the saturation as a consequence of the host softening around the probe that will favor local rearrangements instead of long range diffusive motions. The mean relaxation (blue diamonds) is an average between fast (black circles) and slow (triangles) relaxations. Shear thickening (the decrease of the curves) appears at large distances from the chromophore (triangles) and for the largest frequencies. Around the chromophore (black circles) we do not observe this effect. Figure 4(a) displays the radial distribution function (RDF) g(r) between host molecules situated at a

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

0 5 10 15 20

g(r)

r (^oA) R < 10

o

A

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0 5 10 15 20

g(r)

r (

o

A) 10

o

A < R < 20

o

A (a)

(b)

FIG. 4. (a) Radial distribution function between host molecules with the origin around the chromophore (0<R<10 Å) for various isomerization rates.

Green dotted curve:τp=5 ps; blue dashed curve:τp=100 ps; red continuous curve:τp=1000 ps. The temperature is T=100 K. (b) As (a) but at a larger distance from the chromophore (10<R<20 Å). The three curves su- perimpose showing that the host main structure is unchanged at this distance from the chromophore.

distanceR<10 Å from the chromophore and the others host molecules. We see in the figure that the very first peak of the RDF is slightly larger for the larger isomerization periods. This result shows that due to the opening of the chromophore the first shell of neighbors around the chromophore is slightly less organized when the period is small. Figure4(a) thus shows a small structural modification around the chromophore in the saturation regime but this modification disap- pears rapidly when we move away from the chromophore as seen in Figure4(b). This result suggests that the small structural modification around the probe that appears in the saturation regime is at the origin of the material softening in this region. This result confirms the picture of a soft region around the probe at the origin of the saturation regime. The incoherent intermediate scattering functionsFs(Q,t) in Figures 5(a) (around the chromophore) and 5(b) (in the whole box) dis-

0 0.2 0.4 0.6 0.8 1

0.0001 0.001 0.01 0.1 1 10

Fs(Q,t)

t (ns) R < 10 ^oA

0 0.2 0.4 0.6 0.8 1

0.0001 0.001 0.01 0.1 1 10

Fs(Q,t)

t (ns) (a)

(b)

FIG. 5. (a) Incoherent intermediate scattering functionFs(Q,t) around the chromophore (0<R<10 Å) for various isomerization ratesf=1/τp. The temperature is T=100 K. (b) Incoherent intermediate scattering function Fs(Q,t) for host molecules chosen in the whole simulation box. The different curves correspond to various isomerization ratesf=1/τp. The temperature is T=100 K.

play the typical behavior of supercooled liquids, namely a two step relaxation. The diffusion is clearly localized around the chromophore, and the relaxation timesτ_α are shorter as we approach the chromophore molecule. The different isomerization frequencies also induce relative differences that are much larger around the chromophore. As expected, the larger frequency (i.e., the smaller period:τp =5 ps) displayed leads to the larger diffusion. For this curve we observe peaks showing bursts of induced motions when the isomerizations take place.

These peaks are located at the isomerization periods and are washed out for larger periods due to the averaging procedure, and lead in Figure 5(a)to smooth oscillations in the curves for intermediate values of the period. Figure 5(b)shows the functionFs(Q,t) averaged in the whole simulation box. The relaxation is faster for the smaller periods (larger frequencies). However, the different relaxations appear very similar whether we are in the saturation regime or in the linear response regime. At large frequencies (in the saturation regime) the curves merge showing that the relaxation time evolves more slowly. This saturation is more marked for the whole simulation box (Figure 5(b)) than around the chromophore

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(Figure5(a)). We note that even in the saturation regime, the two steps relaxation is still visible.

IV. CONCLUSION

We have studied the evolution of the diffusion coefficient and of the inverse of the α relaxation time with the chromophore’s isomerization rate in a supercooled glass-former doped with isomerizing chromophores. Our aim was to search for the presence of different dynamical regimes due to the coupling between the relaxation time of the material and the isomerization period. We found two different regimes: a linear response regime for small perturbations followed by a saturation regime for large perturbations. We found that these regimes are present for the whole set of temperatures studied. These regimes are reminiscent of the two different unexplained experimental behaviors for high or low intensity levels. The linear response regime may indeed be associated with the low intensities experimental behavior, while the saturation regime is the dominant mechanism for the high intensities that lead to the second unexplained experimental behavior. We then focused our attention on the physical origin of the saturation regime. We found that this regime is charac- terized by increasingly soft regions around the chromophores surrounded by more viscous regions. The structure (radial distribution function), theαrelaxation time (i.e., the viscosity), and the diffusion coefficient evolution concurred to demon- strate this picture. We then observed that the inverse of theα relaxation time calculated at various distances from the chromophore displays a decoupling between a still linear increase of 1/ταwith the isomerization ratef=1/τparound the chromophore, and the appearance of the saturation regime at larger distances. We concluded that the saturation is a consequence of the host softening around the probe (appearing for largef) that favors local rearrangements instead of long range diffusive motions.

ACKNOWLEDGMENTS

We acknowledge support from Université d’Angers un- der an “ARIANE-Aides à la mobilité” funding grant. We are grateful to David Chandler’s group in Berkeley for interesting discussions.

1P. L. Rochon, E. Batalla, and A. L. Natansohn,Appl. Phys. Lett.66, 136 (1995).

2D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar,Appl. Phys. Lett.66, 1166 (1995).

3A. Natansohn and P. Rochon,Chem. Rev.102, 4139 (2002).

4J. A. Delaire and K. Nakatani,Chem. Rev.100, 1817 (2000).

5G. S. Kumar and D. C. Neckers,Chem. Rev.89, 1915 (1989).

6K. G. Yager and C. J. Barrett,Curr. Opin. Solid State Mater. Sci.5, 487 (2001).

7P. Karageorgiev, D. Neher, B. Schulz, B. Stiller, U. Pietsch, M. Giersig, and L. Brehmer,Nature Mater.4, 699–703 (2005).

8L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, and W. Van Saarloos,Dynamical Heterogeneities in Glasses, Colloids and Granular Media(Oxford University Press, New York, 2011).

9K. Binder and W. Kob,Glassy Materials and Disordered Solids(World Scientific, Singapore, 2011).

10P. G. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, 1996).

11T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer,Phys. Rev. Lett.

98, 058001 (2007).

12X. Cheng, J. H. McCoy, J. N. Israelachvili, and I. Cohen,Science333, 1276 (2011).

13E. Brown and H. M. Jaeger,Science333, 1230 (2011).

14V. Teboul, M. Saiddine, and J. M. Nunzi,Phys. Rev. Lett.103, 265701 (2009).

15V. Teboul, M. Saiddine, J. M. Nunzi, and J. B. Accary,J. Chem. Phys.134, 114517 (2011).

16S. Bian, J. M. Williams, D. Y. Kim, L. Li, S. Balasubramian, J. Kumar, and S. Tripathy,J. Appl. Phys.86, 4498 (1999).

17T. G. Pedersen and P. M. Johansen,Phys. Rev. Lett.79, 2470 (1997).

18T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, Phys. Rev. Lett.80, 89 (1998).

19V. Toshchevikov, M. Saphiannikova, and G. Heinrich,J. Phys. Chem. B 113, 5032 (2009).

20V. Toshchevikov, M. Saphiannikova, and G. Heinrich,J. Chem. Phys.137, 024903 (2012).

21J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy,Appl.

Phys. Lett.72, 2096 (1998).

22C. J. Barrett, P. L. Rochon, and A. L. Natansohn,J. Chem. Phys.109, 1505 (1998).

23C. J. Barrett, A. L. Natansohn, and P. L. Rochon,J. Phys. Chem.100, 8836 (1996).

24P. Lefin, C. Fiorini, and J. M. Nunzi,Pure Appl. Opt.7, 71 (1998).

25M. Saiddine, V. Teboul, and J. M. Nunzi,J. Chem. Phys.133, 044902 (2010).

26F. Fabbri, Y. Lassailly, S. Monaco, K. Lahlil, J. P. Boilot, and J. Peretti, Phys. Rev. B86, 115440 (2012).

27K. Binder, J. Horbach, W. Kob, W. Paul, and F. Varnik,J. Phys.: Condens.

Matter16, S429 (2004).

28V. Van Hoang,Physica B400, 278 (2007).

29V. Van Hoang,Philos. Mag.91, 3443 (2011).

30B. Kezic and A. Perera,J. Chem. Phys.137, 014501 (2012).

31V. Teboul,J. Phys.: Condens. Matter20, 244116 (2008).

32V. Teboul and Y. Le Duff,J. Chem. Phys.107, 10415 (1997).

33V. Teboul,Int. J. Nanotechnol.5, 851 (2008).

34S. Chaussedent, V. Teboul, and A. Monteil,Curr. Opin. Solid State Mater.

Sci.7, 111 (2003).

35D. Limmer and D. Chandler,J. Chem. Phys.135, 134503 (2011).

36C. Hanotin, S. Kiesgen de Richter, P. Marchal, L. J. Michot, and C.

Bavarian,Phys. Rev. Lett.108, 198301 (2012).

37W. Nie and Y. Lan,Phys. Rev. E86, 011110 (2012).

38M. Reiner,Phys. Today17, 62 (1964).

39J. L. Barrat,J. Phys.: Condens. Matter15, s1 (2003).

40T. Srikhirin, A. Laschitsch, D. Neher, and D. Johannsmann,Appl. Phys.

Lett.77, 963 (2000).

41J. M. Ilnytskyi, D. Neher, and M. Saphiannikova,J. Chem. Phys.135, 044901 (2011).

42R. Besseling, E. R. Weeks, A. B. Schofield, and W. C. K. Poon,Phys. Rev.

Lett.99, 028301 (2007).

43R. Yamamoto and A. Onuki,Phys. Rev. Lett.81, 4915 (1998).

44R. Yamamoto and A. Onuki,Phys. Rev. E58, 3515 (1998).

45H. Mizuno and R. Yamamoto,J. Chem. Phys.136, 084505 (2012).

46V. Teboul and J. B. Accary,J. Phys. Chem. B116, 12621 (2012).

47J. B. Accary and V. Teboul,J. Chem. Phys.136, 094502 (2012).

48W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives,J. Am. Chem. Soc.

118, 11225 (1996).

49M. P. Allen and D. J. Tildesley,Computer Simulation of Liquids(Oxford University Press, New York, 1990).

50H. J. C. Berendsen, J. P. M. Postma, W. Van Gunsteren, A. DiNola, and J.

R. Haak,J. Chem. Phys.81, 3684 (1984).

51C. M. Stuart, R. M. Frontiera, and R. A. Mathies,J. Phys. Chem. A111, 12072 (2007).

52Y. Ootani, K. Satoh, A. Nakayama, T. Noro, and T. Taketsugu,J. Chem.

Phys.131, 194306 (2009).

53T. Fujino, S. Y. Arzhantsev, and T. Tahara,J. Phys. Chem. A105, 8123 (2001).

54G. Tiberio, L. Muccioli, R. Berardi, and C. Zannoni,ChemPhysChem11, 1018 (2010).

55V. Teboul, J. B. Accary, and M. Chrysos, Phys. Rev. E 87, 032309 (2013).

56L. Berthier, G. Biroli, D. Coslovich, W. Kob, and C. Toninelli,Phys. Rev.

E86, 031502 (2012).

(9)

57V. Teboul,Eur. Phys. J. B51, 111 (2006).

58W. Kob and J. L. Barrat,Phys. Rev. Lett.78, 4581 (1997).

59G. Parisi,J. Phys. A30, L765 (1997).

60A. Montanari and F. Ricci-Tersenghi,Phys. Rev. Lett.90, 017203 (2003).

61K. Vollmayr-Lee, J. A. Roman, and J. Horbach,Phys. Rev. E81, 061203 (2010).

62G. Foffi, E. Zaccarelli, S. Buldyrev, F. Sciortino, and P. Tartaglia,J. Chem.

Phys.120, 8824 (2004).

63F. Sciortino and P. Tartaglia,J. Phys.: Condens. Matter13, 9127 (2001).

64D. El-Masri, L. Berthier, and L. Cipelletti, Phys. Rev. E 82, 031503 (2010).

65L. Cipelletti and L. Ramos,J. Phys.: Condens. Matter17, R253 (2005).

66T. A. Singleton, K. S. Ramsay, M. M. Barsan, I. S. Butler, and C. J. Barrett, J. Phys. Chem. B116, 9860 (2012).

67G. J. Fang, J. E. Maclennan, Y. Yi, M. A. Glaser, M. Farrow, E. Korblova, D. M. Walba, T. E. Furtak, and N. A. Clark,Nat. Commun.4, 1521 (2013).

68D. Chandler and J. P. Garrahan,Annu. Rev. Phys. Chem.61, 191 (2010).

69Y. S. Elmatad and A. S. Keys,Phys. Rev. E85, 061502 (2012).

70A. S. Keys, L. O. Hedges, J. P. Garrahan, S. C. Glotzer, and D. Chandler, Phys. Rev. X1, 029901 (2011).

71A. W. Bosse, J. F. Douglas, B. C. Berry, R. L. Jones, and A. Karim,Phys.

Rev. Lett.99, 216101 (2007).

72R. L. Jack, D. Kelsey, J. P. Garrahan, and D. Chandler,Phys. Rev. E78, 011506 (2008).

73A. Furukawa and H. Tanaka,Phys. Rev. E86, 030501(R) (2012).

74F. Affouard, M. Descamps, L. C. Valdes, J. Habasaki, P. Bordat, and K. L.

Ngai,J. Chem. Phys.131, 104510 (2009).

75M. Sellitto,Phys. Rev. E80, 011134 (2009).

76S. R. Williams and D. J. Evans, Phys. Rev. Lett. 96, 015701 (2006).

77D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987).

78L. Mazaheri, S. Ahmadi-Kandjani, and J. M. Nunzi,Opt. Commun.298–

299, 150 (2013).

79P. U. Veer, U. Pietsch, and M. Saphiannikova,J. Appl. Phys.106, 014909 (2009).

80P. U. Veer, U. Pietsch, P. L. Rochon, and M. Saphiannikova,Mol. Cryst.

Liq. Cryst.486, 66/[1108] (2008).

81J.-P. Hansen and I. R. McDonald,Theory of Simple Liquids(Academic Press, New York, 1996).