Determination of Local Dye Concentration in Hybrid Porous Silica Thin

Article pubs.acs.org/JPCC

Determination of Local Dye Concentration in Hybrid Porous Silica Thin Films Anna Synak,*,† Piotr Bojarski,*,† Beata Grobelna,‡ Leszek Kułak,§ and Aneta Lewkowicz† †

Institute of Experimental Physics, University of Gdansk, Wita Stwosza 57, 80-952 Gdansk, Poland Faculty of Chemistry, University of Gdansk, Sobieskiego 18/19, 80-952 Gdansk, Poland § Department of Technical Physics and Applied Mathematics, Technical University of Gdansk, 80-952 Gdansk, Narutowicza 11/12, Poland ‡

ABSTRACT: The idea of determination of local dye concentration in a nanoporous matrix is proposed based on donor− acceptor energy transfer. The method was tested for a Rhodamine 110−Rhodamine 101 system in silica and methylated silica nanolayers. Evaluation of acceptor (Rhodamine 101) local concentration was carried out by comparing the results of Monte Carlo simulation of energy transfer from donor (Rhodamine 110) to acceptor (Rhodamine 101) with the experimental data of donor fluorescence decay in which concentration was treated as a best fit parameter. The obtained values of acceptor local concentration were about 10 times higher than the mean bulk concentration. Further possible implementations of this method are discussed.

1. INTRODUCTION Hybrid strongly luminescent materials have been drawing a lot of attention recently due to their numerous applications in multidisciplinary science such as physical chemistry, nanomaterials, or nanomedicine.1−11 A common problem that can be encountered in the quantitative description of the properties of such materials is the determination of local mean concentration of the fluorophores in the porous inorganic matrix. Concentration is a decisive factor of many physical and chemical processes occurring in various matrices, optical materials, and optoelectronic devices. Typically, in a liquid solution and rigid homogeneous matrix, the spacial fluctuations of dye concentration in a given sample are insignificant, and the determination of such a bulk concentration is rather easy based on standard spectroscopic methods. However, in inhomogeneous media such as multicomponent polar-nonpolar solutions, biological membranes, cells or nanostructured materials, the dye molecules can be nonuniformly distributed as a result of specific local interactions with the surrounding molecules or skeleton of the matrix.12−18 In porous materials, molecules are often located in a small volume of a nanocage or nanochannel leaving vicinal skeleton of inorganic material free from their presence. This should lead to significant increase in a local © XXXX American Chemical Society

mean concentration of a dye. The enhanced local dye concentration can lead to amplified intermolecular phenomena such as energy transfer, charge transfer, or aggregation, which should be visible, for example, in the accelerated donor fluorescence decay or its decreased fluorescence quantum yield. Therefore, the estimation of such a local concentration is crucial to understand important photophysical processes such as, for example, energy transfer or molecular aggregation (that are strongly concentration-dependent19,20) taking place at distances smaller than or comparable to the linear dimensions of the cage. We propose a method of estimation of such a mean local concentration based on the comparison of spectroscopic experimental data obtained for two-component excitation energy donor−acceptor system with the respective results of Monte Carlo simulation.19−21 We would like to demonstrate the difference between the predictions of energy transfer models in the case of mean bulk concentration and the local one estimated from Monte Carlo. In this report we would like Received: February 21, 2013 Revised: March 28, 2013

A

dx.doi.org/10.1021/jp401839j | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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to focus on the first results of donor fluorescence decay in the presence of acceptor at its different bulk concentrations. As an experimental system we choose Rhodamine 110 (donor)− Rhodamine 101 (acceptor) incorporated into two matrices: the silica one and the methylated silica one, differing in the pore structure and properties of matrix. If the donor concentration is significantly smaller than the critical concentration for energy migration between donors, the latter process is usually of limited importance, and the energy transfer occurs directly from an excited donor to unexcited acceptors, where it is trapped or emitted in a different spectral region from that of the donor. If this condition is not fulfilled, then energy migration can take place besides the energy transfer process. Additionally, the emission spectrum of the acceptor is, in the case studied, well separated from donor absorption so that the reverse energy transfer from excited acceptors back to the donor set can be neglected.19,22 Nowadays a lot of attention is paid to such media in which fluorophores are not uniformly distributed, but are organized in a specific way. In such a case, the description of multistep energy transfer and trapping is even far more complex, and it can not be directly expressed in terms of analytical theories. However, if we have some knowledge on fluorophores distribution in a medium or local concentrations and organization of the dyes, Monte Carlo method can successfully be used to obtain information on the mechanism of energy transfer in practically any medium. On the other hand, it seems that local concentration of the dye or their organization could be determined based on the results of Monte Carlo simulation of energy transport. This is, for example, the case of gel matrices with nanopores, in which dye molecules can be incorporated up to very high local concentrations despite the low average fluorophore bulk concentration. Below, we present in more detail some procedures and examples of Monte Carlo analysis in this medium.

of sodium hydroxide (0.1 M) as a catalyst were added. The sol was applied on the glass after 30, 60, 90, and 120 min. Microscopic glasses were used as substrates. The thoroughly cleaned pieces of microscopic glass were dipped into the sols and slowly withdrawn from the liquid. The formed transparent films were dried in a dust-free environment. By using the sol− gel process, the following bulk concentrations of the acceptor R101 were obtained: 10−5, 5 × 10−5, 10−4, 6 × 10−4, 9 × 10−4, 2 × 10−3 M. Concentration of Rhodamine 110 was constant for all samples and equal to 5 × 10−5 M. Low-temperature sol−gel method is used here as straightforward technology to obtain hybrid materials, the structure of which can be controlled at the molecular level. The main advantage of materials obtained by this method is high porosity favoring the encapsulation of various compounds, the ability to control the shape and also biocompatibility. The good optical properties subject to a total transparency of gels allow to study radiative and nonradiative mechanisms of energy transfer between incorporated molecules. Previously, it was shown that spectroscopic properties of hybrid materials strongly depend on gelation time, and the optimal conditions for performing experiments for given gelation time were estimated.23 Following those results after performing separate tests, the samples prepared after 90 min gelation were selected. 2.2. Apparatus. Time-resolved emission spectra (TRES) were recorded at 293 K with the pulsed spectrofluorometer described previously in detail.25 The laser system (PL 2143A/ SS Nd:YAG laser and the PG 401/SH optical parametric generator emitting pulses of full-width at halfmaximum, fwhm ≈ 30 ps, EXSPLA, Vilnius, Lithuania), was used as an exciting light source. The 2501S Spectrograph, Bruker Optics Inc. (Billerica, MA) and C4334-01 Streak Camera, Hamamatsu (Hamamatsu, Japan), makes a heart of the detection path. All operations are fully automated and controlled by the original Hamamatsu HPDTA software, which allows for real-time data analysis. The single measurement results are obtained as a quasi three-dimensional, colorful flat image, with the wavelength in the horizontal axis, the time in the vertical axis, and the intensity expressed by a range of colors, in which blue and red represent minimum and maximum values of intensity, respectively. From such a complex image (640 × 480 pixels), one can obtain spectra corresponding to specific time interval by slicing the image along the wavelength axis at a certain time after the moment of excitation. By moving the spectrum slice along the time axis, one can observe a time evolution of the emission spectrum, the shape changes and the changes of the position of the light intensity maximum. By slicing the streak camera image at a certain time interval, and moving the slice along the wavelength axis, spectral evolution of time decays is observed. Both kinds of the image analysis are very helpful in the investigations of the dynamics of deactivation processes.23,26 2.3. Monte Carlo Simulations. In a Monte Carlo simulation,19,20,27 N donors with concentration CD and M acceptors with concentration CA, are randomly distributed in a three-dimensional cube. The absorption and emission transition moments ε⃗Aj , ε⃗Ej of molecules are therefore randomly distributed. The dynamics of the system considered is described by the following equation:

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. The thin film samples were prepared by the sol−gel method23,24 using dip-coating techniques. All reagents used in this study were of at least analytical grade. Rhodamine 110 chloride (R110) and Rhodamine 101 inner salt (R101) were spectroscopically pure (dye contents 99%), free from any foreign fluorescent admixtures, and they were purchased from Aldrich (Munich, Germany). Tetramethyl orthosilicate (TMOS) and trimethoxymethylsilane (Me-TMOS) were purchased from Aldrich; however, methanol and sodium hydroxide were purchased from POCH Company (Gliwice, Poland). Deionized water was obtained from a Hydrolab system installed in our laboratory. Silica films (SiO2) were obtained using the procedure developed by us. At first, R110 and R101 were dissolved in methanol. Next, TMOS was added, and both solutions were mixed by vigorous stirring. After a while, water and three drops of sodium hydroxide (0.1 M) as a catalyst were added. Highly transparent sols were obtained after stirring for a few minutes, which were subsequently used for film deposition. The gelation time was measured from the moment of water addition, and it was selected for the purpose of this work as 30, 60, 90, and 120 min. Methylated silica films (Me-SiO2) were synthesized in a similar manner. In this case a 1:1 mixture of TMOS and MeTMOS was dissolved in methanol. Then, methanol solution of R110 and R101 was added. After a while, water and three drops B


The Journal of Physical Chemistry C dPxixj(t ) dt

=−

1 Px x (t ) + τ0D i j N

−

∑

Article

wxDD P (t ) ixk xkxj

k = 1, k ≠ i

wxDD P (t ) − kxi xixj

k = 1, k ≠ i

N+M

∑

wxDA P (t ), kxi xixj

k=N+1

1≤i≤N

dPxixj(t ) dt

=−

1 Px x (t ) + τ0A i j N+M

+

In the donor ensemble: P1: photon emission by excited donor or nonradiative energy conversion, with the total rate 1/τ0D, P2: energy migration (energy transfer to the molecules of the same kind), with the transfer rate wDD xixj , P3: nonradiative energy transfer from the excited donor to an acceptor, with the transfer rate wDA xixj . In the acceptor ensemble: P1′ : photon emission by excited acceptor or nonradiative energy conversion, with the total rate 1/τ0A, P′2: energy migration in the acceptor ensemble with the rate wAA xixj, If the jth donor molecule is excited, the values of the following global transfer rates

N

∑

∑

(1)

N

∑ wxDAx Px x (t ) i k

k j

k=1

N+M

∑

wxAA P (t ) − ixk xkxj

k = N + 1, k ≠ i

wxAA P (t ), kxi xixj

k = N + 1, k ≠ i

N+1≤i≤N+M (2)

with initial condition c1j =

Pxixj(0) = δij

(3)

where δij is Kronecker’s delta, wxixj , X,Y ∈ {D, A} is the probability density of energy transfer from the jth molecule to the ith molecule, defined by the Förster formula XY

wxXY ixj

κij2 ⎛ R 0XY ⎞ ⎜ ⎟ = τ0D ⎜⎝ rij ⎟⎠

N

N+M

∑

c 2j =

wxDD , ixj

c 3j =

i = 1, i ≠ j

∑

wxDA , ixj

i=N+1

cj = c1j + c 2j + c3j

(6−9)

are calculated. Otherwise, when the ith acceptor is excited, the global transfer rates

6

c1′i =

(4)

1 , τ0A

N+M

wxAA , jxi

∑

c 2′i =

ci′ = c1′i + c 2′i

j = N + 1, i ≠ j

(10−12)

The kij is the real dipole orientation factor, RXY 0 is the Förster critical radii, τ0D is the donor mean decay time in the absence of acceptors, and rij is the distance between the ith and jth molecules. The effect of the finite size of generated system is reduced by introducing periodic boundary conditions (the cube is surrounded by replicas of itself) with minimum image convention (the molecule interacts with another molecule or its periodic image).The pseudorandom number generator (mixed congruent generator with the period of 232), which passed several statistical tests, was also verified by checking the simulated statistical clusters concentration against the analytically expected values and is used in Monte Carlo simulation. The “step-by-step” Monte Carlo simulation method19,28−31 consists in the employment of the random-number generator for the cyclic formulation of answers to two questions: (1) When will any of the preset luminescent processes take place in the simulated system? (2) What kind of process is it? To determine which molecule is originally excited, the photoselection method is used. Initially excited molecules are selected according to a probability distribution cos2νj, where νj is the angle of the jth absorption transition moment with the zaxis. It means that the most likely molecules to be excited are those whose transition dipole moments are parallel to the passage direction of the electric vector of the excitation light (z axis). To do that, a random number rj is generated from the interval [0, 1] and, if the following relationship is fulfilled: cos2 ϑj ≥ rj

1 , τ0D

are obtained. The time at which any of the investigated processes occur is calculated by inverting the distribution function of the probability, pj (t, Pk)dt, that if at time t the jth molecule is excited, then process Pk appears in the time interval (t,t + dt): 3

pj (t ) =

∑ pj (t , Pk) = cj exp(−cjt ) k=1

(13)

i.e., using random number r1j from the interval [0,1] after inversion of distribution function:

∫0

tj

pj (t ) dt = r1j ,

t j = −(1/cj) ln(1 − r1j)

(14,15)

the time moment, tj, is calculated. The same procedure can be applied to the excited acceptors. In the next step, it is determined what kind of process takes place at time tj. By generating the next random number, r2j, such a value of index k for which the following inequality is satisfied can be found: k−1

k

∑ cij < r2jcj ≤ ∑ cij , i=1

k = 1, 2, 3 (16)

i=1

If k = 1, then the activated molecule is quenched by a photon emission or nonradiative energy conversion, and it means that this pass of simulation is finished. If k = 2 or k = 3, the energy migration or transfer process takes place, and it is necessary to determine which molecule will be now activated. For this reason the third random number, r3j is generated, and the value of index n is found, which fulfills one of the inequalities:

(5)

then the jth molecule is activated. Molecules that do not meet this relationship are excluded from the set of initially excited molecules. In the Monte Carlo simulation, the excitation energy deactivation of the jth molecule can occur through one of the following processes:

n−1

∑ i=1

C

n

wxDD ixj

< r3jc 2j ≤

∑ wxDDx , i j

i=1

for k = 2, n ≤ N (17)



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or n−1

∑

n

wxDA < r3jc3j ≤ ixj

i=N+1

wxDA , ixj

∑

for k = 3, n > N

i=N+1

(18)

where n is the number of next activated molecule. If a given donor becomes excited (k = 2) (the particular excited donor molecule is known), all transfer rates can be calculated, and again the time moment and the kind of process that takes place is determined. If the acceptor becomes excited (k = 3) through the excitation energy transfer from a donor, then it is determined which process P′1 (photon emission) or P′2 (energy migration in the acceptor ensemble) takes place. Using the next random number r4j, such a value of index k′ can be found, which fulfills the following inequality: k ′− 1

k′

∑ cli′ < r4jci′ ≤ ∑ cli′ , l=1

k′ = 1, 2

Figure 1. Absorption and fluorescence spectra for Rhodamine 110 and Rhodamine 101.

(19)

l=1

If k′ = 1, then the photon emission by acceptor or nonradiative energy conversion takes place, and this pass of simulation is finished. If k′ = 2, then the process of energy migration in the acceptor ensemble takes place, and it is necessary to determine which next acceptor will be excited. Generating the next random number r5j, such a value of index m can be found, which fulfills the following inequality: m−1

∑

Based on the measured absorption and fluorescence spectra, the values of critical parameters describing energy transfer in both types of matrices were determined. The values of critical distances were determined from the following formula:32 R 0XY

m

wxAA lxi

< r5jc 2′i ≤

l=N +1

∑

wxAA , lxi

(20)

Now, m is the number of the next excited acceptor for which we can calculate all transfer rates and determine the kind of a process and time moment at which the particular process occurs. This procedure can be continued until the consecutive excited acceptor will emit the photon finishing current step of simulation. The donor decay curve is obtained in a way similar to the real experiment, i.e., the time scale (e.g., [0, 3 τ0D]) is divided into appropriate number of intervals (e.g., 4096), and if photon emission at the time tj is “observed”, then the number of photons is increased in the respective “channel”. Finally, the normalized decay curve (histogram) is obtained using a simple formula: k

ΦD(Δtk) = 1 −

j=1

Iν(D, A) =

∫0

∞

fD (ν)εA (ν)

dν ν4

(24)

In eq 24, v is the wavenumber, εA(v) is the molar decimal extinction coefficient of the acceptor, and f D(v) is the normalized fluorescence spectral distribution (∫ f D(v) dv = 1). The obtained values (for low donor and acceptor concentration C = 0.00005 M) occurred identical in both matrices, and they amount to RDD = 46 Å, RDA 0 0 = 56 Å. The corresponding critical concentrations were determined from the formula32 3 1 C0XY = 4π N ′(R 0)3 (25)

k max

∑ nj /∑ nj ,

(23)

where η0D is the absolute donor fluorescence quantum yield in the absence of acceptor, n is the mean refractive index of the medium, N′ denotes the number of fluorophores in one millimole, ⟨κ2⟩ is the orientation factor averaged over all molecular configurations (averaged orientation factor), and Iν(D,A) is the overlap integral:

m>N

l=N +1

⎛ 9κ 2 ln 10η ⎞1/6 0D = ⎜⎜ Iν(D, A)⎟⎟ 5 4 ⎝ 128π n N ′ ⎠

Δtk = (k /k max )t

j=1

(21,22)

These critical concentrations amount to CDD = 4.1 · 10−3 M 0 −3 DA and C0 = 3.10 M, respectively. The donor fluorescence lifetimes determined from TRES measurements are τ0D = 2.7 ns in the SiO2 matrix and τ0D =3.1 ns in the Me-SiO2 matrix. Figure 2 presents the original TRES image in RGB colors taken directly from the apparatus for donor−acceptor system R110−R101 in (a) silica matrix and (b) methylated silica matrix after excitation at 470 nm. In these images, vertical direction corresponds to time, horizontal direction is wavelength, and colors reflect emission intensity. The red color corresponds to the highest intensity, whereas the blue color corresponds to the lowest fluorescence intensity. Black color means no fluorescence signal. Measurements were made in a 10 ns time

where nk denotes the number of photons in the kth channel, and kmax is the total number of all channels.

3. RESULTS AND DISCUSSION Figure 1 shows strong overlap between the fluorescence spectrum of R110 (donor) and absorption spectrum of R101 (acceptor) as well as similar spectral overlaps for donor emission and absorption and for acceptor emission and absorption. However, there is practically no overlap between the acceptor fluorescence and donor absorption. This means that in the system studied, both energy transfer from donor to acceptor and energy migration in donor and acceptor sets can take place. However, the reverse energy transfer from acceptors to donors can not take place in the system studied.22 D



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Figure 2. Time-resolved emission spectra of donor−acceptor system R110−R101 in (a) silica matrix and (b) methylated silica matrix. Figures show original TRES images. Upper left panel: TRES image of the fluorescence spectrum of the donor in the absence of acceptor; upper right panel: TRES image of the fluorescence spectrum of the donor−acceptor system for the same concentration of both species; lower left and right panels: TRES images of the fluorescence spectrum of the donor−acceptor system for increasing acceptor concentration.

window for the SiO2 matrix and 20 ns time window for the MeSiO2 matrix. The upper left panel presents TRES results for the donor in the absence of acceptors and the other three for the donor−acceptor system (R110−R101), in which bulk acceptor concentration changed from 0.00005 to 0.002 M. Despite practically exclusive excitation of the donor in a donor− acceptor system, the acceptor fluorescence band is visible, and it becomes stronger with the increase in acceptor concentration as a result of effective energy transfer from the donors. For example, from Figure 2a (for CD = 0.00005 M and CA = 0.0001 M) it can be seen that energy transfer is more than 50% effective at bulk acceptor concentration CA = 0.0001 M, which is more than 1 order of magnitude lower than the critical −3 concentration for energy transfer CDA 0 = 3 × 10 M for which it is expected that the efficiency of energy transfer would gain 50%. This surprising result can be only explained by the strong

enhancement of local acceptor concentration in the porous matrix. Comparison with Figure 2b suggests that energy transfer is even much more effective in the case of the Me-SiO2 matrix. Having in mind the same values of critical parameters for both matrices and the same bulk concentrations of donors and acceptors in both matrices, this latter effect should be attributed to the higher local concentration of acceptors in Me-SiO2 matrix resulting from different structure of both matrices. The blending of inorganic precursor (TMOS) with MeTMOS can lead to materials with properties different from those prepared for single component ones. Nonreactive organic groups (CH3) may be used for the design and control of porosity and flexibility.33 In the case of methyl group, the change of porosity is a result of reduction in the degree of cross-linking of the matrix. Additionally, the introduction of a E



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Figure 3. Time evolution fluorescence spectra of a donor−acceptor system in (a) silica matrix and (b) methylated silica matrix. The specified time moments 1.5 ns, 2 ns, and 2.5 ns denote the time after the excitation for which each spectrum was extracted from the TRES image.

Table 1. The Acceptor to Donor Fluorescence Peak Intensity Ratio for Silica Matrix and Methylated Silica Matrixa time moment after excitation

SiO2 matrix

Me-SiO2 matrix

1.5 ns 2 ns 2.5 ns

0.60 0.62 0.56

0.48 1.03 1.84

Table 2. Comparison of the Experimental Bulk Concentration of Acceptor (R101) with Concentration Obtained in Monte Carlo Simulations for Silica Matrix and Methylated Silica Matrixa experimental concentration of acceptor [M] SiO2 ; Me-SiO2 0.00005 0.0001 0.0006

a

The peak intensity ratio was determined with an accuracy of about 0.02.

local concentration of acceptor obtained from Monte Carlo simulations [M] SiO2 Matrix 0.00036 0.00096 0.00550

Me-SiO2 Matrix 0.0012 0.0020 0.0057

a The bulk donor concentration was CD = 0.00005 M. Fitted local concentrations were determined with an accuracy of at least 1% for each concentration.

methyl group causes an increase in the hydrophobicity of the obtained material, which, in turn, causes a reduction of rinsing out the dye, and thus an increase in the local concentration of the dye in the pores of the material. Slicing the three-dimensional images shown in Figure 2 horizontally yields fluorescence spectrum at a given time moment after the excitation for the donor−acceptor system, where CD = 0.00005 M and CA = 0.0001M. Such time-resolved spectra are presented in Figure 3a,b.

Figure 3a,b presents an example of comparison between time-resolved fluorescence spectra for the donor−acceptor system studied in SiO2 (Figure 3a) and the Me-SiO2 matrix (Figure 3b) for bulk concentrations CD = 0.00005 M and CA = 0.0001 M. From the comparison between the corresponding

Figure 4. Monte Carlo simulation results and experimental decays of fluorescence of the donor−acceptor system R110−R101 in (a) silica matrix and (b) methylated silica matrix. Symbols correspond to experimental data for the bulk donor concentration CD = 0.00005 M and the following acceptor concentrations: red dots (CA = 0.00005 M), pink triangles (CA = 0.0001 M), and blue squares (CA = 0.0006 M) for both type of matrices. Dashed lines in the same colors correspond to the results of Monte Carlo simulations for the same bulk donor and acceptor concentrations as above. Solid lines correspond to the results of best-fit Monte Carlo simulations for respective experimental data sets for fitted donor concentration CD = 0.0005 M and the following acceptor concentrations: red line: CA = 0.00036 M, pink line CA = 0.00096 M, blue line CA = 0.0055 M in silica matrix. In the methylated silica matrix, the best fit between Monte Carlo simulations and experimental data has been obtained for the following acceptor concentrations: red line CA = 0.0012 M, pink line CA = 0.002 M, blue line CA = 0.0057 M. F


The Journal of Physical Chemistry C donor−acceptor spectra in both matrices, it can be concluded that the acceptor-to-donor peak intensity ratio is different at the same time moment after excitation. This ratio is higher for MeSiO2 than for SiO2 matrix (Table 1). This, of course, confirms the fact that in the Me-SiO2 matrix the energy transfer occurs faster and is more efficient. Figure 4a,b presents the donor fluorescence intensity decays for the R110−R101 system in SiO2 and Me-SiO2 matrices, respectively. Symbols correspond to experimental data for the bulk donor concentration CD = 0.00005 M and the following acceptor concentrations: red dots (CA = 0.00005 M), pink triangles (CA = 0.0001 M), and blue squares (CA = 0.006 M). Solid lines correspond to the results of best-fit Monte Carlo simulations for respective experimental data sets for fitted donor and acceptor concentrations and the dashed lines were obtained based on calculations for the bulk concentrations of donor and acceptor. The disagreement between the latter theoretical curves and experimental data for the values of bulk concentrations is dramatically high evidencing the effect of strong enhancement of local dye concentration in porous matrices. Very good agreement between experimental data and Monte Carlo was, however, found for the fitted values of local dye concentrations shown in Table 2. Table 2 presents the comparison of the experimental concentrations of donors and acceptors with the local concentrations obtained from the Monte Carlo simulations for both matrices. For both types of matrices, the local concentration of acceptors is about 1 order of magnitude higher than the respective bulk concentration. It can also be seen from the table that the local concentrations of the acceptors in the Me-SiO2 matrix are about 2, 3 times higher than those in SiO2 matrix, which results probably from the lower product of pores density and pore size. The procedure presented here enabled proper description of the donor fluorescence decay in the presence of acceptors at any acceptor concentration, and, most importantly, it enabled the estimation of local dye concentration in both types of matrices.

ACKNOWLEDGMENTS

■

REFERENCES

This research has been supported by Grant NCN 2011/03/B/ ST5/03094 (P. Bojarski, B. Grobelna) and University of Gdansk 538-5200-0980-12 (A. Synak) and International Ph.D. Project “Physics of Future Quantum-Based Information Technologies” (MPD/2009-3/4) financed by the Foundation for Polish Science (A. Lewkowicz).

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4. CONCLUSIONS AND FINAL REMARKS A quite straightforward method of determination of local dye concentration in nanoporous matrix was presented by exploiting the properties of donor−acceptor energy transfer in two types of matrices differing in their porous structure (silica and methylated silica nanolayers). Estimation of donor and acceptor (Rhodamine 101) local concentrations by best fit with the results of Monte Carlo simulations revealed about 10 times enhancement of local dye concentration due to dye encapsulation in the pores of the matrices. Next, we will present more detailed results of Monte Carlo simulation allowing one to determine local concentrations of partly organized molecular assemblies in porous strongly luminescent materials in the presence or absence of surface plasmons. We hope this will be an important step in understanding the lasing properties of such luminescent porous materials.

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*E-mail: fi[email protected]; phone: +48 (0)58 5232221; fax: +48 (0)58 3413175 (P.B.). E-mail: [email protected]; phone: +48 (0)58 5232280 (A.S.). Notes

The authors declare no competing financial interest. G



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Determination of Local Dye Concentration in Hybrid Porous Silica Thin

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