# Photons Probe Entropic Potential Variation during Molecular Confinement in Nanocavities

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−3}and to monitor dipole and entropic fields on biosurfaces.

## 1. Introduction

^{−3}range, has the potency to monitor electric dipole and entropic competition in small volumes. Likewise, decrypting the adsorption and diffusive behavior of various molecular analytes on porous materials [45,46,47] either from trapping within tiny cavities, or via shape, surface or volume deformation, might well boost novel potential applications in molecular sensing [37,38,48], gas separation [29,30,49], storage and applications with particular emphasis on nanomedicine [50], bioengineering [51,52], and drug delivery systems [53].

## 2. Materials and Methods

#### 2.1. Materials

^{−1}.

#### 2.2. 157 nm Laser

^{2}. The ambient pressure in the chamber was kept at 10

^{5}Pa. The chamber was purged with flowing nitrogen for 10 min prior to each irradiating step to minimize the presence of oxygen traces. Samples were irradiated at different laser fluence.

#### 2.3. AFM Imaging

#### 2.4. Fractal Analysis

_{f}) is a measure of these properties. The fractal dimension, that describes quantitatively the porosity of a surface, was derived from the AFM images by four different algorithms, and the algorithm provided by the AFM “lake pattern” software (diSPMLab Vr.5.01, Veeco, Santa Barbara, CA, USA).

#### 2.4.1. Cube Counting

_{f}.

#### 2.4.2. Triangulation

_{f}− 2.

#### 2.4.3. Variance Method

_{f}is evaluated from the slope β of a least-square regression line fit to the data points in the log–log plot of variance as D

_{f}= 3 − β/2.

#### 2.4.4. Power Spectrum

_{f}is evaluated from the slope β of a least-square regression line fit to the data points in the log–log plot of power spectrum as D

_{f}= 7/2 + β/2.

_{f}has been calculated for the four different methods using “Gwyddion, SPM data visualization and analysis tool” [59]. Note that the results of the four algorithms differ slightly. This is the result of a systematic error in different fractal analytical approaches.

#### 2.5. Nanoindentation

#### 2.6. Water Contact Angle

#### 2.7. WLRS

_{2}layer thickness of 2–3 nm.

## 3. Results

#### 3.1. Surface Morphological Characteristics of 157 nm Photon Processed PHEMA Polymeric Matrixes

^{−1}). VUV radiation penetrates PHEMA (85%) within an absorption depth less than 1 μm from the surface [36], allowing thus to tailor the surface physicochemical properties and the different functionalities at the micro/nanoscale level, without affecting its bulk properties in a variety of applications. The photon modification of PHEMA hydrogel surfaces, chemistry and topography, including an effective adhering ability of different biocells to attach to the modified areas were previously investigated. Only the outer exposed surface layers of the hydrogel were affected by exposure to 157 nm laser photons, because of water photolysis, including a direct surface water depletion that turns the surface to a hydrophobic one [52].

#### 3.2. Surface Analysis

_{a}(area roughness or roughness average) is the arithmetic mean of the height deviation from the image’s mean value, ${R}_{a}=\frac{1}{n}{\sum}_{i=1}^{n}\left|{Z}_{i}-\overline{Z}\right|$. Third the area RMS (R

_{rms}) is the value defined as the square root of the mean value of the squares of the distance of the points from the image mean value: ${R}_{rms}=\sqrt{\frac{1}{N}}{\sum}_{i=1}^{N}{\left(Z-{Z}_{i}\right)}^{2}$ and finally, the maximum range R

_{max}is defined as the maximum value of the z-heights. In all examined cases of z-height, Figure 2a, area roughness, Figure 2b, area RMS, Figure 2c and maximum range, Figure 2d, the photon exposed samples were presented with notably increased surface parameter values compared to the non-irradiated samples. The surface parameters values were first rising up to ~100 laser pulses and then were slightly dropped. Because the surface parameters are area size dependent functionals (e.g., the R

_{rms}roughness is not an invariant quantity and varies with the size of an image), they are used for a first qualitative evaluation of surface modification upon 157 nm laser irradiation [61].

#### 3.3. Fractal Characteristics of 157 nm Photon Processed PHEMA Polymeric Matrixes

_{i}values above a threshold height Z are known as “islands”, while those with Z

_{i}values below the threshold described as “lakes”. At this point is important to note that some AFM software developers denote the “islands” as “lakes”. In this work, the areas with the Z

_{i}values higher than the average Z values are named “islands”. A typical “island-lake structure” of nonirradiated/irradiated 1 μm × 1 μm areas with 200 laser pulses is shown in Figure 3.

_{i}values were set up at 3.80 and 0.82 nm for the irradiated and non-irradiated layers, respectively, showing diverging surface topologies after 157 nm laser irradiation, making possible quantification of surface porosity and allowing an estimation of surface modification [17,52,53,61]. Two parameters are used to describe the porosity of a surface. One parameter is the “periphery to the area ratio” (PAR) for a set of “islands” or “lakes”, defined as the ratio of the logarithms of the perimeter Π to the area A, where $\Pi =\alpha \left(1+{D}_{f}\right){A}^{\left(1-{D}_{f}\right)/2}$, and the other is the fractal dimension D

_{f}, associated with both the surface roughness and the topological entropy [18]. To evaluate correctly the porosity of the photon processed PHEMA matrixes, the fractal dimensionality is calculated by applying four different methodologies the partitioning, the cube counting, the triangulation and the power spectrum algorithms [53]. The results are compared with the surface dimensionality extracted directly from the AFM “lake” pattern software, Figure 4.

^{3}nm

^{2}versus the number of laser pulses, Figure 5a is calculated. The number of all the area ‘‘islands’’ remains almost constant between 50–150 laser pulses and then it rises again up to 200 laser pulses, remaining constant afterwards. For a certain number of laser pulses, the generation of small area size “islands” prevails over larger area “islands”, while the concentration of small size “islands” is falling down at higher photon fluence.

^{2}. Therefore, the number of “lakes” and the fractal dimensionality indicates a size-dependent behaviour of porosity, confirming a porous character for larger size areas, and smaller “lake” sizes up to 100 nm, as expected. Finally, it is worth to notice that the trend of porosity for a given fractal area size falls with the number of laser pulses, Figure 5c, and thus it has the same trend as the relative surface strain (vide infra), showing that entropic potential diversity during sorption has its origin in water confinement within different size nanocavities.

#### 3.4. Nanoindentation

#### 3.5. Water Contact Angle

#### 3.6. WLRS

^{−14}m

^{3}, defined by the cross-sectional size of the white light beam 2.5 × 10

^{−4}m and the thickness of the polymeric layer 310–380 nm. The relative surface strain measured with WLRS at 0% and 80% RH of water analytes is 0.0009 and 0.0004, respectively.

## 4. Discussion

_{ι}Ν

_{i}) is the chemical energy during sorption, δ(ΤS) is the entropic energy, and the term $\delta \left(\Psi \left(n\right)\right)=\delta \left[\gamma \left(n\right)+{\rm E}{\left(n\right)}_{s}\iint {n}_{k}d{A}_{k}\right]$ is the algebraic sum of the surface energy δ(γ(n)) and the elastic energy strain E

_{s}(n) of the nanocavities per unit area, following irradiation with n laser pulses. The last term is zero under isothermal and isobaric adsorption conditions, $\delta \left(\Psi \left(n\right)\right)=0$ [65].

_{a}= 4 × 10

^{12}within the volume V = 7.4 × 10

^{−14}m

^{3}in the layer (bounded by the cross section of the WLRS beam of ~1.96 × 10

^{−7}m

^{2}, and the thickness of the layer of ~345 nm), for a 50% relative humidity, is comparable with the number of photodissociated moieties ~4 × 10

^{13}, within the same volume space. Therefore, the relative contribution of the chemical work during sorption in Equation (1) is negligible and hence $\delta \left({\mu}_{i}{N}_{i}\right)\approx 0$. Equally, as each one 157 nm laser photon releases one molecule from the polymeric chain via photodissociation, at the same time one electric dipole-binding site in the remaining molecular polymeric chain is created.

_{a}analyte molecules within a volume defined by the white beam, the number of trapping configurations $\left\{{N}_{b}\left(n\right)+{N}_{c}\left(n\right),{N}_{a}\right\}$ is equal to the number of permutations between the adsorbed analytes and the sum of nanocavities and the dipole adhesive binding sites [17]

_{c}(n). Therefore, x(n) and the Young modulus E(n) carry the same functional dependence with the number of 157 nm laser pulses, in agreement with previous results for PDMS polymers [17]. By using a linear functional for both x(n) and E(n), the best fit of Equation (6) to the experimental data of Figure 10 is for $\beta \left(n\right)=0.2$ and $0\le \lambda l<0.1,$ indicating a small contribution in the surface strain from electric dipole interactions.

## 5. Conclusions

^{−3}energy density range for bioapplications.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**AFM surface imaging of PHEMA layers. The scan area is 2 × 2 μm

^{2}and the 157 nm laser fluence 250 Jm

^{−2}per pulse: (

**a**) Non-irradiated PHEMA layer; (

**b**) Irradiation with 20 laser pulses (lp), 5 kJm

^{−2}; (

**c**) 70 lp, 17.5 kJm

^{−2}; (

**d**) 200 lp, 50 kJm

^{−2}. The structure of the surface is constantly modified under laser irradiation up to 200 lp.

**Figure 2.**Surface parameters of irradiated PHEMA layers for 2 μm × 2 μm scan areas: (

**a**) mean Z-height; (

**b**) area roughness (R

_{a}); (

**c**) area RMS; (

**d**) maximum range. The surface parameters keep getting larger up to ~100 lp, followed by values reduction up to 200 lp. Then, they remain constant for photon fluence higher than 50 kJm

^{−2}.

**Figure 3.**AFM image of ‘‘lake’’ (grey) and ‘‘island’’ (orange) for a fractal area of 2 × 10

^{3}nm

^{2}: (

**a**) irradiated with 200 laser pulses; (

**b**) non-irradiated.

**Figure 4.**Surface fractal dimension using four different fractal analytical methodologies and fractal shapes (rectangular-partitioning, sphere-cube counting, triangle-triangulation, star-power spectrum) calculated at a different number of laser pulses. The results are compared with those extracted directly by applying the “AFM lake pattern” software provided by the manufacturer. The lines are a guide for the eye.

**Figure 5.**Fractal parameters at different laser fluence: (

**a**) number of ‘‘islands’’ for different fractal size vs. number of laser pulses n; (

**b**) fractal dimensionality vs. number of laser pulses for different fractal size. The concentration of small size nanocavities increases at higher laser fluence; (

**c**) fractal dimension vs. fractal size at different number of laser pulses (lp).

**Figure 6.**Fractal parameters vs. AFM scanning area of the layer for “lakes”: (

**a**) a number of “lakes” vs. fractal area size; (

**b**) fractal dimension vs. different fractal area size for two AFM scan areas 1 μm × 1 μm and 2 μm × 2 μm for 200 laser pulses. While the fractal parameters diverging with the scanning area, as expected, the trend of the variation of fractal parameters for different scanning areas remain the same.

**Figure 7.**Typical force–distance (F–D) curves of PHEMA thin layer surfaces (312–387 nm) irradiated with a different number of laser pulses (250 J m

^{−2}per laser pulse): (

**a**) F–D curves of non-irradiated layer; (

**b**) F–D curves with 20 laser pulses; (

**c**) F–D curves with 100 laser pulses; (

**d**) F–D curves with 200 laser pulses.

**Figure 8.**Young’s modulus and adhesion force of PHEMA irradiated layers showing enhanced carbonization at higher laser fluence: (

**a**) Young’s modulus; (

**b**) adhesion force of PHEMA thin film surface irradiated with a different number of laser pulses (250 J m

^{−2}per laser pulse).

**Figure 9.**Water contact angle vs. the number of laser pulses showing an increment of surface hydrophobicity at higher laser fluence: (

**a**) water contact angle vs. the number of laser pulses; (

**b**) time gradient of water contact angle at different time intervals. An identical slope points to a uniform surface response at different fluence, indicating that chemical changes are saturated after a few laser pulses due to the low penetrating depth of the laser radiation at 157 nm.

**Figure 10.**The relative strain of ~345 nm PHEMA thin layers at different irradiating conditions and relative humidity (RH) measured with White Light Reflectance Spectroscopy (WLRS). The black lines at 80% RH are fittings for λl values of 0, 0.2, 2 and 20, respectively, suggesting a small contribution (λl = 0, 0.2) from electric dipole attachment of water molecules to binding polar sites in the PHEMA matrix.

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**MDPI and ACS Style**

Gavriil, V.; Chatzichristidi, M.; Kollia, Z.; Cefalas, A.-C.; Spyropoulos-Antonakakis, N.; Semashko, V.V.; Sarantopoulou, E.
Photons Probe Entropic Potential Variation during Molecular Confinement in Nanocavities. *Entropy* **2018**, *20*, 545.
https://doi.org/10.3390/e20080545

**AMA Style**

Gavriil V, Chatzichristidi M, Kollia Z, Cefalas A-C, Spyropoulos-Antonakakis N, Semashko VV, Sarantopoulou E.
Photons Probe Entropic Potential Variation during Molecular Confinement in Nanocavities. *Entropy*. 2018; 20(8):545.
https://doi.org/10.3390/e20080545

**Chicago/Turabian Style**

Gavriil, Vassilios, Margarita Chatzichristidi, Zoe Kollia, Alkiviadis-Constantinos Cefalas, Nikolaos Spyropoulos-Antonakakis, Vadim V. Semashko, and Evangelia Sarantopoulou.
2018. "Photons Probe Entropic Potential Variation during Molecular Confinement in Nanocavities" *Entropy* 20, no. 8: 545.
https://doi.org/10.3390/e20080545