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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Prediction of Oleo-Affinity on Solid Surfaces via Three-Dimensional Solubility Parameters Using Interfacial Free Energy as Interaction Threshold Masakazu Murase, and Riichiro Ohta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00154 • Publication Date (Web): 01 May 2019 Downloaded from http://pubs.acs.org on May 1, 2019

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The Journal of Physical Chemistry

Prediction of Oleo-affinity on Solid Surfaces via Three-dimensional Solubility Parameters Using Interfacial Free Energy as Interaction Threshold Masakazu Murase*, Riichiro Ohta* Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan, *E-mail address: [email protected], [email protected]

ABSTRACT

Various adhesive and wetting phenomena in nature and practical applications originate from the interaction between the surfaces of materials and other substances. In this study, we developed a method for calculating the Hansen solubility parameters (HSP) of the surface of solid materials to elucidate the surface interaction by quantitatively and visually representing adsorptivity with a three-dimensional vector. The HSP was derived from the interfacial free energy, which can easily be calculated from the contact angles of three organic solvents on the solid materials. The HSP for a glassy carbon (GC) surface calculated using our method was correlated with the adsorptivity on the GC surface of several organic molecules. The adsorptivity was evaluated using electrochemical impedance spectroscopy and molecular mechanics simulations, the latter

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of which also revealed that the HSP calculated for the Pt surface was highly correlated with its interactivity. Moreover, the HSP of the polytetrafluoroethylene (PTFE) surface obtained herein appropriately reflects the molecular structure of PTFE. The results underpin that our method enables the elucidation of various surface phenomena involving non-covalent interaction and allows the affinity between solid surfaces and tens of thousands of substances recorded in the HSP database to be predicted.

INTRODUCTION Interaction between the surfaces of materials and other substances is the origin of various interesting natural phenomena, such as the adhesion of geckos to a wall, arising from the combination of affinitive interaction and morphological effects,1 and the superhydrophobicity and self-cleaning effect of a lotus leaf, arising from the repulsive interactions between its surface and water and contaminants from surrounding environments.2 Moreover, adsorption and desorption are in equilibrium and depend on the strength of the interactions on the microscopic scale, such as that of solid materials with volatile substances in air3 as well as in controlled environments,3–5 and cell surface receptors interacting with acceptors in biological systems.6 Therefore, fundamental insights and understanding of adsorption phenomena are basic issues of surface science in chemistry,7,8 biology,9 and various other academic areas, and are of high importance in the field of manufacturing, including coating, antifouling, demolding, and sensing of chemical agents. Additionally, the ability to predict the adsorptivity on the surface of materials can facilitate and accelerate materials design for the above industrial applications.


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Adsorptivity on the surface of materials has been intensively studied by employing quantitative calculations using Monte Carlo simulations,10,11 molecular dynamics (MD) simulations,12,13 etc. These calculated results have been found to be correlated with the experimental results for the adsorptivity of specific materials, and have made correlation-based prediction of adsorptivity possible. However, these methods generally provide the adsorptivity for an adsorbate via an individual calculation process, in which the adsorbate is intentionally selected according to the range of knowledge and interest of researchers. Thus, adsorbates not considered by the researchers could unintentionally be omitted from the selection using these methods, which would be an obstacle for the thorough prediction of the adsorptivity of material surfaces. In this study, we propose a method for characterizing and predicting the adsorptivity on the surfaces of solid materials with a wide variety of adsorbates, including those that are unintentional, more simultaneously compared to conventional methods. The method expands the concept of Hansen solubility parameters (HSP) to the surfaces of solid materials, and represents the surface adsorptivity quantitatively with a three-dimensional (3D) vector. The HSP express the inherent solubility of substances by 3D vectors composed of the dispersion ( (

), and hydrogen bonding (

), polarization

) solubility parameters.14,15 The HSP of various common

chemical substances were clarified by Hansen and other HSP developers, and have been reported.16 Using the substances on the list as probe solvents, the software can predict the unknown HSP of a substance of interest using the Hansen sphere method. This method entails drawing a sphere that includes good solvents and excludes poor solvents with the so-called interaction radius (R) in 3D vector space, in which the center of the sphere is defined as its



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HSP.17 The above calculation can be conducted using a commercial software (HSPiP 4th Edition 4.1.07). Application of the above-mentioned analysis using HSP has conventionally been limited to dissoluble chemical substances17 and fine particles composed of polymers17, carbon-based nanomaterials18–20, and metallic oxides18, which are dispersible in organic or aqueous solvents. Attempts by Hansen et al. to expand the HSP to solid surfaces involved observing whether the probe solvents spontaneously spread on solid surfaces to identify solvents with HSP similar to those of the solid surfaces.21 However, they noted that the above-described method needed improvement by presenting a contradictory example in which hexane, which cannot dissolve epoxy polymers, spontaneously spreads on these polymers because of its low surface tension.21 We employed the interfacial free energy (

), which represents the stability of the interfacial

states between two materials in contact, as the degree of similarity of HSP between the surface of the solid material and substances with known HSP (hereinafter referred to as the "reference substance"). Here, the magnitude of

was used as the parameter to draw an interaction sphere,

the center of which was defined as the HSP of the surface of the solid material. Note that this interaction sphere differs from the conventional Hansen sphere, which was drawn by using the solubility as its parameters.17 In this study,

was calculated from the surface free energy of

the solid materials of interest ( ) and that of the reference substances ( experimental section, where

) as described in the

was calculated from the contact angles of the probe liquids on the

surface of the solid material using the extended Fowkes theory.22 Then, similar to the classification using a threshold for good/poor solubility in the conventional Hansen sphere method, we sorted the reference substances by setting a threshold (

) for

, where reference


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substances with those with

>

≤

have higher affinity for the surface of a solid material compared to

. After classification, we draw the interaction sphere by including the HSP

of the reference substances with

≤

and excluding the HSP of those with

>

in 3D

vector space. To verify our method, we investigated whether the HSP calculated using this method could be appropriately correlated with the surface adsorptivity of glassy carbon (GC) and platinum (Pt), which are often used as an electrode for electrochemical studies. In addition, we confirmed whether the HSP calculated for the polytetrafluoroethylene (PTFE) surface appropriately reflects the molecular structure of this polymer, as further verification. EXPERIMENTAL SECTION Materials. Glassy carbon (GC; GC-20SS; Tokai Fine Carbon Ltd.), polytetrafluoroethylene (PTFE; Flon Industry Co., Ltd.), and platinum (Pt; The Nilaco Corporation) were polished to a mirror finish using alumina paste (particle diameter: 0.05 μm). Probe liquids (diiodomethane (DIM), ethylene glycol (EG), and 1-bromonaphthalene (BN); Wako Pure Chemical Industries Ltd.) were used as purchased. Benzyl alcohol (BZA), acetone (ACT), dimethyl sulfoxide (DMSO), and 1-butanol (1BA) were used as purchased from Wako Pure Chemical Industries Ltd., as adsorbates on the GC surface. Tetrahydrofuran (THF) and acetonitrile (ACN) were used as purchased from Dojindo Laboratories Co., Ltd., as adsorbates. Method for measuring contact angles. The static contact angles (

) of the probe liquids (DIM,

EG, and BN) on the GC, Pt, and PTFE surfaces were measured by an optical contact-anglemeasuring device (DM-501; Kyowa Interface Science Co., Ltd.) at room temperature after removing contamination from the surface by rinsing sequentially with ethanol, acetone, and hexane.

was obtained from the photographic images captured at 1.0 s after contacting a



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droplet of each probe liquid (0.5 μL) on the surface. The mean values of

at five different

points for each probe liquid were used for the following calculation, and are shown in Table S1. Method for calculating interfacial free energy.

was calculated by the following

procedures: i)

values of the three probe liquids, DIM, EG, and BN, were measured on the

The

surfaces of the solid materials. The surface free energy of the solid materials ( ), composed of dispersion (

ii)


polarization (

),

) terms, was calculated using the following

equation proposed by Kitazaki and Hata:22 cos where

2

2

1

is the surface free energy of the probe liquid, is the hydrogen bonding term, and

polarization term, ,

2

, and

in Table S2. The

(1)

is the dispersion term, is the sum of

,

is the , and

. The

values of the probe liquids were obtained from the literature,22 and are shown ,

, and

equation derived by substituting

values were obtained by solving the three-way simultaneous ,

,

, and

, and the measured

value of the three

probe liquids into equation 1. iii)

was calculated as22 2

2

2

(2)


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where

is the sum of

,

, and

and is the sum of the dispersion ( Reported values of

,

, and

,

is the surface free energy of the reference substance

), polarization (


) terms.

for the reference substances,22,23 were used for the

calculation and are shown in Table S3. Setting the value of threshold to interfacial free energy. Integral values were used for the threshold (

). Setting

substances with

>

to an excessively large value causes a shortage of reference and leads to a decrease in accuracy of determination of the boundary

of the interaction sphere. In addition, a higher value of

distorts the shape of the interaction

sphere, resulting in a reduction in the accuracy of calculating HSP. As a notable case, the interaction region of materials comprising multiple molecular structures with different properties, such as amphiphilic surfactants, copolymers, and a mixture of substances, is difficult to draw as a single sphere in three-dimensional (3D) vector space, because the HSP of such materials are composed of multiple HSP according to their individual structures. For cases in which materials have two structures with different properties, Hansen et al. proposed the use of the double sphere method.24 However, such influence of the surfaces of the solid materials used herein, i.e., GC, Pt, and PTFE, on the shape of the sphere should be small, because these materials have uniform chemical structures. In addition, we adopted the smallest

using which the sphere can be

drawn encompassing the HSP plots of at least two reference substances with

≤

, which

are the smallest number of plots necessary to draw the sphere, to further minimize the above influence.



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Method for calculating the distance between the HSP of organic compounds and the surfaces of GC and Pt. The distance (

) between the HSP of the surface of solid materials and

organic molecules (OMs) was calculated as15

4

where

(3)

,

, and

method, and

,

are the HSP on the surfaces of GC and Pt, and were calculated using our , and

are the reported HSP of the OMs shown in Tables S4 and S5.16

Method for calculating and results of the rate of charge transfer resistance by electrochemical impedance spectroscopy. The rate of charge transfer resistance (

) was

calculated as25

⁄

and

where

100

(4)

are the charge transfer resistance of the electric double layer before and

after adsorption of the OM, respectively.

and

were obtained by fitting the measured

Nyquist plots to the equivalent circuit representing the electric double layer on the GC surface as shown in Figure 1.

CPE

Rsol

RCT


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Figure 1. Equivalent circuit of the electric double layer on the GC surface in an aqueous electrolyte.

is the solution resistance, while

and the constant phase element (CPE) are

the charge transfer resistance and capacitance of the electric double layer, respectively. The CPE is composed of the CPE constant (T) and the CPE index (p). The impedance of CPE ( obtained as

1/ j

) is

, where j is an imaginary unit and ω is the angular frequency.

The Nyquist plots were obtained using a potentiostat (ModuLab XM ECS; Solartron analytical Ltd.) in the frequency range from 10 kHz to 0.1 Hz with ten frequencies per decade. The AC amplitude was set at ±5 mV from the open circuit potential. The measurement system is shown in Figure 2; details of the measuring conditions are described in the caption of Figure 2.

Potentiostat

Cell Pt 0.1M KCl aq Ag/AgCl

GC

φ12.0 mm

Figure 2. System for measuring impedance on the GC surface. An aqueous solution of 0.1 M KCl (20 mL) was used as the electrolyte. Ag/AgCl and Pt were used as the reference and counter electrodes, respectively. The electrode area in contact with the electrolyte was 1.13 cm2 (φ12.0 mm).



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The Nyquist plots of the GC surface before and after the addition of the OM (1.0 mM) to the electrolyte are shown in Figure S1. The calculated values of

and

are shown in Table

S6. All chi-squared values between the Nyquist plots and fitting results were lower than 0.001, indicating that all the calculated values shown in Table S6 are of high reliability.

Method for calculating

using molecular mechanics simulations. The lattice structures of

graphite and Pt were obtained from the structure database of the Materials Studio version 8.0 software package (Accelrys Software Inc.). The graphite surfaces, prepared by cleaving the repeat unit of the lattice along the (001), (100), and (110) planes, were used as representative models of the GC whose surface consists of randomly oriented crystal planes of graphite.26 The dimensions of the models were set at 2.46 nm × 2.46 nm × 1.70 nm for the (001) surface, 2.71 nm × 2.72 nm × 1.70 nm for the (100) surface, and 2.56 nm × 2.72 nm × 1.72 nm for the (110) surface. Dangling bonds on the (100) and (110) surfaces were terminated by hydrogen atoms. The Pt surface was prepared by cleaving the repeat unit of the lattice along (100) plane, and the dimensions of the unit cell were set at 2.77 nm × 2.77 nm × 1.57 nm. The thickness of a vacuum slab was set at 3.00 nm.

The following calculations were performed using the Forcite module in Materials Studio. Condensed-phase optimized molecular potentials for atomistic simulation studies II (COMPASSII) was adopted as the force field.27,28 The OMs were placed on the graphite and Pt surfaces (Figures S2 and S3, respectively). The examined OMs were BZA, THF, 1BA, DMSO, ACT, and ACN for the graphite surfaces, and BN, toluene (TOL), methyl ethyl ketone (MEK), γbutyrolactone (GBL), DMSO, and ACN for the Pt surface. Then, the atom positions were optimized using molecular mechanics simulations, while retaining the cell sizes and shapes. The


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total energy is calculated as the sum of the energies of bonding and non-bonding interactions. The non-bonding interaction is composed of electrostatic and van der Waals terms. Ewald summation method with an accuracy of 0.00001 kcal mol−1 and a buffer width of 0.5 Å was used for the electrostatic terms. An atom based summation method and a cubic spline truncation method, with a cutoff distance of 18.5 Å, a spline width of 1 Å, and a buffer width of 0.5 Å, adopting a long range correction, were used for the van der Waals terms. The convergence criteria of the optimization were set to 0.00002 kcal mol−1 for the total energy and 0.001 kcal mol−1 Å−1 for the forces on the nuclei.

The interaction energy (

) between the surface and the OM was calculated according to the

following equation:

(5)

where and

is the total energy of the surface of the solid materials adsorbed with the OM, and are those of the surface of the solid material and the OM, respectively. The

calculation results are listed in Tables S7 and S8.

RESULTS AND DISCUSSION

We calculated the HSP for the GC surface as follows. The surface free energy of GC was calculated as

= 49.1 mJ·m−2, the components of which were

mJ·m−2, and

= 3.1 mJ·m−2, from

Then, the values of calculated from

= 42.6 mJ·m−2,

= 3.4

(Table S1) measured using the extended Fowkes theory.

between the GC surface and various reference substances were

and the pre-known γR (Table S3). Figure 3 shows the interaction sphere of the



GC surface drawn in 3D vector space by setting to setting the value of

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at 2 mJ·m−2 for

(details of our approach

are provided in the experimental section). The center of the interaction

sphere, which is the HSP of the GC surface based on our definition, is located at MPa1/2,

= 8.3 MPa1/2, and

= 11.4 MPa1/2.

Figure 3. Interaction sphere of the GC surface when

was set to 2 mJ·m−2. The center of the

sphere (green plot), i.e., the HSP of the GC surface, is located at MPa1/2, and ≤

= 17.3

= 17.3 MPa1/2,

= 8.3

= 11.4 MPa1/2. The blue plots indicate the HSP of reference substances with

. The red plots indicate the HSP of reference substances with

>

. The radius of the


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interaction sphere (R) is 3.6 MPa1/2, and Fit,15 which denotes the goodness of fit between the interaction sphere and the classification of the HSP of the reference substances by

, is 0.971.

We investigated whether the HSP of the GC surface calculated by using our method can be correlated with the increased

measured using electrochemical impedance spectroscopy

of the HSP between an OM and the GC surface in 3D vector space should

(EIS). The

represent the degree of affinity of the OM for the GC surface,16 whereas the charge transfer resistance has been used to evaluate the adsorptivity of OMs on electrode surfaces.25,29 Figure 4 shows the correlation plot of

vs.

between the GC surface and various OMs: BZA, THF,

BA, DMSO, ACT, and ACN. As seen in Figure 4, with the coefficient of determination ( indicating that

and

tends to increase with decreasing

,

) of the regression equation being approximately 0.81,

are strongly correlated. However, the correlation between

and

is not perfect, as indicated by the deviation of ACT and DMSO from the regression line. We presumed that the correlation can be improved by increasing the number of reference substances to enhance the accuracy of the interaction sphere in 3D vector space. 0.5 50

0

R² = 0.8082

-0.5

0.4 40

-1

BZA 0.3 30

∆RCT (%)

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


-1.5 0

0.5

1

1.5

0.2 20 DMSO

THF 0.1 10

ACN

1BA ACT

00

0 0

3.0 3

6.0 6

9.0 9

Ra (MPa1/2)

12.0 12

15.0 15



Figure 4. Correlation plots of α is the slope of log

vs.

, and β is log

−1.39 and 0.24, respectively).

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. The dashed curve is given as -the intercept in log

αlog

10

, where

β (α and β are

is calculated to be 0.81. The HSP of the OMs are provided in

Table S4. Moreover,

was correlated with the

between the OMs and the crystal planes of graphite,

(001), (100), and (110), as shown in Figure 5. These crystal planes were employed as models of the GC surface on which the graphite-like layers are orientated randomly. The

values of the

regression equations were approximately 0.83, 0.74, and 0.74 for the (001), (100), and (110) planes, respectively. The strong correlation of

with

on all the crystal planes indicates that

the strength of the interaction between the GC surface and OMs should be the origin of well as the adsorptivity evaluated above from

, as

.


20

b

1.5

BZA

R² = 0.8305

0 0

10

0.5

1

1.5

logRa

THF 1BA ACT

5

DMSO

ACN

1.5

15

1 0.5

R² = 0.7441

0

10

0

BZA

0.5

1

logRa

1.5

THF

5

1BA ACT

0

DMSO

ACN

0 0

5

10 Ra (MPa1/2)

20

0

15

5

10

15

Ra (MPa1/2)

1.5

log|−Eint|

c

20

1 0.5

−EInt (kcal mol−1)

15

log|−Eint|


a


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


log|−Eint|

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15

R² = 0.7388

0

BZA

10

1 0.5

0

0.5

1

logRa

1.5

THF

5

1BA ACT

DMSO

ACN

0 0

5

10

15

Ra (MPa1/2)

Figure 5. Correlation plots of and the OMs vs. log

between the model graphite surface with each crystal plane 10

. The dashed curve is given as

, and β is the log |

−0.61, β = 1.49, and

|-intercept in log|

|

αlog

, where α is the slope of β. (a) On the (001) plane, α =

= 0.8305. (b) On the (100) plane, α = −0.42, β = 1.27, and

(c) On the (110) plane, α = −0.54, β = 1.33, and We also revealed a strong correlation of

with

= 0.7441.

= 0.7388. for Pt surface by showing that the large

(~0.90) was obtained in the regression equation by the above calculation as shown in Figure 6. The HSP and interaction sphere of the Pt surface are shown in Figure S4. The model structure for the

calculation, experimental data, and calculation results for the Pt surface are shown in

Figure S3, and Tables S1–S3, S5, and S8.



100 log|−Eint|

3

80 −EInt (kcal mol−1)

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Page 16 of 25

BN

60

2 1

R² = 0.9045

0 0

0.5

1

1.5

2

logRa

40

TOL MEK

20

GBL

DMSO

ACN

0 0

5

10 Ra (MPa1/2)

15

Figure 6. Correlation plots of

20

between the model Pt surface with (100) plane and the OMs 10

. The dashed curve is given as

vs. log |

|-intercept in log|

|

αlog

, where α is the slope of log

β. α = −0.86, β = 2.44, and

, and β is the

= 0.9045.

Our method was also proven to provide appropriate HSP for the PTFE surface. The surface free energy of PTFE was calculated as 22.3 mJ·m−2,

= 0 mJ·m−2, and

= 0 mJ·m−2, from

extended Fowkes theory. Then, the substances was calculated from

= 22.3 mJ·m−2, of which the components were (Table S1) measured using the

value between the PTFE surface and various reference

and pre-known

, as provided in Table S3. Figure 7 shows

the interaction sphere of the PTFE surface drawn in 3D vector space by setting for

=

= 1 mJ·m−2

. Here, the region where the interaction sphere entered into the negative polar and

hydrogen domains is an artifact, caused by using a sphere as the interaction region for convenience; the HSP values should be physically located in the positive domains as reported.30 The center of the interaction sphere, the HSP of the PTFE surface, is located at = 0 MPa1/2, and

= 0 MPa1/2. Hansen et al. reported the HSP of PTFE to be

= 16.2 MPa1/2, = 16.2 MPa1/2,


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= 1.8 MPa1/2, and

= 3.4 MPa1/2, calculated based on the breakthrough time against some

solvents.31,32 Thus, our method and that of Hansen provided the same varied according to the method. PTFE should exhibit very low

value, whereas and

and

values because it

has neither polar nor hydrogen-bonding functional groups, similar to other perfluorocarbon molecules like perfluorobutane, perfluoropentane, and perfluorohexane as shown in Figure 8. PTFE has higher

compared with these molecules, which have low molecular weights, because

denotes the HSP component originated from the dispersion force, which generally increases with increasing molecular surface area.

Figure 7. Interaction sphere of the PTFE surface when

was set to 1 mJ·m−2. The center of

the sphere (green plot), i.e., the HSP of the PTFE surface, is located at

= 16.2 MPa1/2,

=0



MPa1/2, and ≤

Page 18 of 25

= 0 MPa1/2. The blue plots indicate the HSP of the reference substances with

. The red plots indicate the HSP of the reference substances with

>

. The radius of

the interaction sphere (R) is 3.7 MPa1/2, and Fit is 1.000.

Figure 8. HSP of the perfluorocarbon molecules in 3D vector space; green plot: HSP of the PTFE surface, calculated using our method, light blue plot: HSP of PTFE reported by Hansen et al.,31 and blue plot: HSP of small-molecular weight perfluorocarbon molecules, as per the commercial HSP calculation software (HSPiP 4th edition). CONCLUSIONS Herein we have proposed a method to calculate the HSP for the surface of solid materials, using the interfacial free energy as a threshold parameter. The validity of this method was demonstrated for GC and Pt surfaces by correlating their HSP with the adsorptivity and surface interactivity of various substances, and on the PTFE surface by showing that the calculated HSP reflect its molecular structure. Further application of our method, such as its extension to composite surfaces and to interaction analysis with mixed substances, could be anticipated by combining it with a method to calculate the HSP of mixed substances by determining the internal division between them33 and the double sphere method,24 both of which have been proposed for


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use with the conventional Hansen method. Although it is difficult to apply HSP to covalent bonding and ionic interactions, it would be possible to explain or predict versatile adsorption phenomena not involving these interactions on the surfaces of solid materials, such as those in this study, based on the distance between the HSP of various adsorbates in the database15 and the HSP of surfaces of solid materials calculated by our method. ASSOCIATED CONTENT Supporting Information. The following files are available free of charge. Nyquist plots of the GC surface measured using EIS, model structures of the graphite and Pt surfaces for molecular mechanics simulations, interaction sphere and HSP of the Pt surface, contact angle data on the GC and Pt surfaces, surface free energy data, HSP data of OMs, EIS parameters calculated from Nyquist plots, energy values obtained using molecular mechanics simulations (PDF) AUTHOR INFORMATION Corresponding Author Masakazu Murase; E-mail address: [email protected] Riichiro Ohta; E-mail address: [email protected] Funding Sources No funding Notes The authors declare no competing financial interests.



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ACKNOWLEDGMENT The authors thank Dr. T. Kinjo, Dr. S. Shirai, Dr. S. Dong and Dr. T. Iseki for the insightful discussions.

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(29) Oliveira-Brett, A. M.; Silva, L. A.; Brett, C. M. A. Adsorption of Guanine, Guanosine, and Adenine at Electrodes Studied by Differential Pulse Voltammetry and Electrochemical Impedance. Langmuir 2002, 18, 2326–2330. (30) Howell, J.; Roesing, M.; Boucher, D. A Functional Approach to Solubility Parameter Computations. J. Phys. Chem. B 2017, 121, 4191–4201. (31) Hansen, C. M. Appendix A: Table A.2. Hansen Solubility Parameters A User’s Handbook, 2nd ed.; CRC Press: Boca Raton, 2007; pp 485–505. (32) Hansen, C. M. Chapter 13: Applications – Barrier Polymers. Hansen Solubility Parameters A User’s Handbook, 2nd ed.; CRC Press: Boca Raton, 2007; pp 243–258. (33) Abbott, S.; Hansen, C. M.; Yamamoto, H. Chapter 1: The Minimum Possible Theory (simple introduction). Hansen solubility parameters in practice - complete with eBook, software and data., 5th ed. [Online]; 2015; pp 10–14. http://www.hansen-solubility.com.


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TOC Graphic δP θC

γI < γTh < γI

Solid material

Surface n

Low affinity

δH

High affinity

δD


Prediction of Oleo-Affinity on Solid Surfaces via ... - ACS Publications

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