Solvent Effects on Molecular Adsorption on Ag Surfaces: PVP Oligomers

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Solvent Effects on Molecular Adsorption on Ag Surfaces: PVP Oligomers Tonnam Balankura, Xin Qi, and Kristen A. Fichthorn J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03156 • Publication Date (Web): 02 Jun 2018 Downloaded from http://pubs.acs.org on June 2, 2018

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Solvent Eects on Molecular Adsorption on Ag surfaces: PVP Oligomers Tonnam Balankura,

†Department

†

†

Xin Qi,

∗,†,‡

and Kristen Fichthorn

of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States

‡Department

of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States

E-mail: [email protected]

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Abstract The solution-phase adsorption of solutes on solid surfaces is important in a number of applications that are currently being researched. However, most theoretical approaches to describing this phenomenon fall short of accurately describing the solution environment. Herein, we use classical molecular dynamics (MD) simulations based on an accurate many-body force eld to quantify vacuum and solution-phase (ethylene glycol) adsorption free energies of polyvinylpyrrolidone (PVP) oligomers on Ag surfaces  a system studied experimentally for solution-phase nanocrystal growth. We nd a favorable free-energy change when PVP adsorbs to Ag surfaces in the presence of solvent. However, the binding free energy for a PVP molecule in solution is signicantly smaller than that for a PVP molecule in vacuum. In vacuum, the adsorbates lose considerable entropy upon adsorption to a solid surface due to a loss in their congurational degrees of freedom. In solution, adsorption entropies are a result of a solvent-solute exchange process, in which the entropy loss of PVP solute is counterbalanced by the gain in entropy of the displaced solvent, so that the solution-phase system exhibits zero or slightly positive changes in entropy upon PVP adsorption. Solvent layering near solid surfaces can create free-energy minima near the surface, as well as free-energy barriers to adsorption. Our study underscores the importance of using explicit solvent, as well as extensive congurational sampling to quantify the thermodynamics of solution-phase adsorption. Such insight will be important in eorts to understand technologically relevant phenomena, such as crystal growth in solution, (electro)catalysis, and molecular sensing.

Introduction Solution-phase adsorption on metal surfaces is ubiquitous in many cutting-edge materials applications. For example, nanocrystals grown in solution are often stabilized by adsorbed molecules that can play a role in directing their shape.

13

Nanoparticles that respond to light

can function as biosensors, in which the adsorption of solution-phase analytes modulates

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their response to light, enabling the detection of target analytes.

4

Solution-phase adsorption

is important in electrocatalysis for applications in batteries and fuel cells, catalysis.

510

as well as in

11,12

Quantum mechanics is often required for an accurate description of chemical bonding at surfaces and plane-wave density functional theory (DFT) is particularly eective for studying surfaces. Solvent can be included explicitly in DFT calculations or by using implicit solvation models, which treat the solvent as a continuum. Explicit solvent has been included in static DFT calculations by surrounding the relevant adsorbate with solvent molecules and then optimizing the structure at zero temperature.

10,1214

However, such calculations do not pro-

vide statistical averaging of the liquid environment, which is needed to properly account for equilibrium properties of the physical system. Moreover, these calculations do not account for the exchange between the adsorbate and adsorbed solvent that occurs in solution-phase adsorption.

15

The implementation of implicit solvent

16,17

generally involves modifying the

local potential of the Kohn-Sham Hamiltonian and also modifying the expressions for the potential energy and forces to include electrostatic, cavitation, and dispersion interactions between the solute and the solvent. The electrostatic potential of a solute system surrounded by a dielectric medium is obtained by solving the linearized Poisson-Boltzmann equation, which is done in each electronic step in the self-consistent loop.

Implicit-solvent calcula-

tions are less expensive than those with explicit solvent and DFT calculations with implicit solvation models have been used to study adsorption on solid surfaces. calculations neglect solvent structuring and other local eects.

8,18,19

However, such

Gauthier et al.

discussed

that results with implicit solvent can dier greatly from those in which solvent is included explicitly.

10

Classical molecular dynamics (MD) simulations can handle signicantly larger system sizes and longer times than DFT. Finite-temperature, liquid-phase simulations with explicit solvent are feasible with MD and it is possible to achieve the sampling required for accurate ensemble averages. The accuracy of classical MD simulations hinges on the accuracy of the

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underlying force eld and it is possible to devise force elds that reproduce salient aspects of DFT calculations. It is of interest to use such force elds to extend the scope of DFT calculations and gain insight into phenomena not easily accessible with DFT, as we do in the research discussed below. In this paper, we use classical MD simulations to study the eect of ethylene glycol (EG) solvent on the adsorption of polyvinylpyrrolidone (PVP) oligomers on Ag surfaces. interface occurs in the solution-phase synthesis of Ag nanocrystals,

2024

This

where the shape

selectivity to {100}-faceted Ag nanocrystals has been attributed to the selective adsorption of PVP on Ag(100). Our MD simulations are based on an all-atom Metal-Organic ManyBody (MOMB) force eld, which reproduces many aspects of DFT calculations for this system,

25

including the binding preference of PVP for Ag(100) over Ag(111).

26,27

We use

umbrella sampling and thermodynamic integration to quantify adsorption free energies of PVP oligomers in explicit EG solvent. We observe stark contrasts between solution-phase and vacuum adsorption free energies and entropies. Our study underscores the importance of including solvent explicitly and performing sucient statistical sampling to quantify solutionphase adsorption on solid surfaces.

Methods Adsorption free energy of a single PVP oligomer In our studies of the adsorption of single PVP molecules to Ag surfaces, all simulation systems contain a Ag slab and an adsorbing molecule of interest. We employed super cells containing a Ag(100) slab with (13 (19

×

× 13) unit cells, or (53.6198 × 53.6198) Å2 , and a Ag(111) slab with

2 22) unit cells, or (55.41412 x 55.56741) Å , in which both slabs consist of 12 atomic

layers. The adsorbing molecules studied here are EG, 2-pyrrolidone (2P), as well as PVP3 and PVP5, as shown in Figure 1. The simulation systems are either solvated with 1,400 EG molecules or in vacuum.

The temperature and pressure are set to 413 K and 1 bar.

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We

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chose this temperature and pressure because they are representative of synthesis conditions in experiments.

23,28

Figure 1: Adsorbing molecules studied: (a) ethylene glycol (EG), (b) 2-pyrrolidone (2P), (c) polyvinylpyrrolidone trimer (PVP3), and (d) polyvinylpyrrolidone pentamer (PVP5). The O atoms are red, N atoms are blue, C atoms are cyan, and H atoms are white.

To model the interactions in our system, we use the MOMB force eld that was developed for the Ag-EG-PVP system by tting to dispersion-corrected DFT calculations.

25,29

In this

force eld, Ag-Ag interactions are described with the embedded atom method (EAM)

30

and organic-organic (EG and PVP) interactions are described with the CHARMM force eld.

31,32

potential

R0

The Ag-organic interactions are described using two pairwise potentials: the Morse

33

and Grimme's potential for van der Waals (vdW) interactions

values derived by Ruiz et al. for Ag that account for screening eects.

34

35

 with

C6

and

These pairwise

interactions are augmented by a many-body EAM embedding energy with a one-way electron density contribution from the oxygens in PVP and EG to Ag. All MD simulations are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code,

36

compiled with our MOMB pair style for calculating

the vdW interactions between the metal and organic species.

25

Additional simulation de-

tails are given in the Supporting Information. A typical conguration of the system after equilibration is shown in Figure 2, produced using the Visual Molecular Dynamics (VMD) software.

37

The thermodynamic properties of interest are the binding free energy and its decomposi-

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Figure 2: Schematic of a simulation cell with an adsorbed PVP3 on Ag(100) in EG solvent. The O atoms are red, N is blue, C and H atoms are cyan, and Ag atoms are silver.

EG

molecules are pink and given a smaller size, for clarity.

tion into the potential-energy and the entropy change due to binding. These thermodynamic properties are calculated for each adsorbing molecule on Ag(100) and Ag(111) in both solvated and vacuum environments. We provide an overview of these calculations below. To determine the binding free energies, we calculate the potential of mean force (PMF) using umbrella sampling

38

and umbrella integration.

the collective variables module in LAMMPS.

40

39

Umbrella sampling is performed using

Additional details of the binding free energy

calculation are described in the Supporting Information. Binding potential energies are obtained by taking the dierence of the average potential energy between adsorbed and solution-phase molecules. For the vacuum systems, the binding potential energies

∆Uvac

are calculated using

∆Uvac = hUbound,vac i − (hUAg i + hUfree,vac i) ,

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(1)

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where

Ubound,vac

surface,

UAg

is the potential energy of the vacuum system with the molecule on the Ag

is the potential energy of an isolated Ag slab,

a free molecule in vacuum, and

h. . .i

Ufree,vac

is the potential energy of

denotes an ensemble average. Specic sampling times

for each system can be found in the Supporting Information. The binding potential energies of the solvated systems

∆Usol

are calculated from the

dierence between the average potential energy of the bound and free molecule, as described by

∆Usol = hUbound,sol i − hUfree,sol i , where

Ubound,sol

(2)

is the potential energy of the solvated system with the molecule bound to

the Ag surface and

Ufree,sol

is the potential energy of the solvated system with a free molecule

in solution. To sample the potential energies, we use MD simulations of the solvated slab system where the molecule is free to diuse in the solvent phase, adsorb onto the surface, and desorb from the surface.

Since the molecule may be in dierent states in the MD

trajectories, we distinguished sampled potential energies of bound and free molecules from a range of center-of-mass distances dened by the PMF. The bound region is dened as the range of center-of-mass distances within 2 kcal/mol of the PMF minimum. The PMF is approximately zero in the range of center-of-mass distances dening the free region. Figure 3 shows an example of how the bound and free regions are dened. The other PMF proles that are not shown here can be found in the Supporting Information. From the computed free-energy change energy change due to entropy

T ∆S

∆A

and potential energy change

∆U ,

the free

is calculated via the denition of the Helmholtz free

energy

T ∆S = ∆U − ∆A .

(3)

This method of entropy calculation has been shown to be more ecient than competing methods.

41

To study the exchange between solvent and adsorbed solute when adsorption occurs, we

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PVP5 Ag(100) Bound

Free

15 10 PMF (kcal/mol)

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5 0 −5 −10 5

10

15 z (Å)

20

25

Figure 3: PMF prole for PVP5 on Ag(100) is solvent. The bound and free regions in Eq. 2 are delineated.

quantify the number of EG (solvent) molecules displaced per solvent binding. We obtain this quantity from MD trajectories, in which one side of the Ag slab contains both the adsorbate and EG solvent molecules and the other side contains only EG solvent.

We obtained the

average of the number of EG molecules adsorbed on each surface over the span of an MD trajectory, and then took the dierence between those two averages to obtain the number of EG molecules displaced per adsorbate binding.

The average number of EG molecules

adsorbed on each surface is obtained from the EG density proles along the

z

direction

orthogonal to the Ag surface. An example prole with adsorbed EG peaks dened for PVP5 on Ag(100) is shown in Figure 4.

Additional details of how the number of EG molecules

displaced is calculated are given in the Supporting Information.

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PVP5 Ag(100)

1.75 1.50 1.25 ρEG (g/cm 3)

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1.00 0.75 0.50 0.25

PVP+EG

EG only

0.00 0

1

2

3

4 z (nm)

5

6

7

8

Figure 4: Density prole for Ag solvent molecules around an Ag(100) slab with a single PVP5 molecule adsorbed on one side and solvent only on the other side. The peaks associated with the adsorbed EG layer are delineated.

Figure 5: The interfacial free-energy change per unit surface area

∆A/As

when a layer of

solution-phase PVP adsorbs onto a solid surface can be expressed in terms of the dierence between the interfacial free energies of the Ag-EG-PVP system

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γsl,PVP and the Ag-EG system

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Adsorption of a PVP Layer As illustrated on the left side of Figure 5, the binding free energy per unit surface area of an adsorbed PVP layer is the free-energy dierence between a system with an adsorbed PVP layer and a system with all the PVP in solution. This transition can also be cast in terms of interfacial free energies, as suggested in ref. 42 and shown on the right side of Fig. 5. Here, we calculate the free-energy change per segment, which is given by

∆Aseg =

where

γsl,PVP

As (γsl,PVP − γsl ) nNseg

,

(4)

is the liquid-solid interfacial free energy in the PVP-Ag-EG system,

liquid-solid interfacial free energy in the EG-Ag system, number of PVP chains in a simulation box and

Nseg

As

is the surface area,

γsl

is the

n

is the

is the degree of polymerization of PVP.

We calculated the relevant interfacial free energies using a multi-scheme method that we recently developed based on thermodynamic integration (TI).

43,44

The multi-scheme TI

method is a six-step method that brings a solid-liquid interfacial system into individual bulk liquid and solid phases. Actually, we calculated the relevant interfacial free energies in Eq. 4 at the temperature and pressure of this study (413 K and 1 bar) in our previous work, in which we obtained

γsl,PVP

43,44

for a full PVP monolayer and at a reduced coverage on Ag(100)

and Ag(111). A detailed description of the multi-scheme TI method, simulation details, and values of

γsl,PVP

and

γsl

can be found in refs. 43 and 44.

Results and Discussion The binding free energies of various single molecules on Ag(100) and Ag(111) surfaces in the vacuum and solvated environment are shown in Figure 6. Here, we see that the binding free energies of the PVP molecules increase with molecular size.

This reects that the

strongest contribution to the PVP binding potential energy (and free energy) comes from

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Binding free energies

0

Binding free energy (kcal/mol)

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−10

−20

−30

−40

Ag(100) Ag(111) EG

2P

PVP3 Vac m

PVP5

2P

PVP3 PVP5 Solvent

Figure 6: Binding free energies of single molecules (EG, 2P, PVP3, and PVP5) in vacuum and EG solvent.

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van der Waals (vdW) interactions.

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Since the vdW interaction is essentially a pairwise

interaction, its magnitude grows as molecular size increases and leads to an increase in the binding potential energy and, hence, the binding free energy with PVP chain length. Figure 6 also indicates that binding free energies are signicantly larger in vacuum than in solution for all adsorbates. A similar scenario was observed for the adsorption of bis(terpyridine) on graphite,

45

as well as for the binding of peptide segments on metal surfaces.

46,47

We will

return to discuss the origins of this trend below. The success of PVP in promoting the formation of {100}-faceted nanostructures, such as cubes and wires, has been attributed to its energetic preference for binding to Ag(100) surfaces.

3,23,4850

DFT calculations for 2P on Ag(100) and Ag(111) indicate that this small

molecule does bind more strongly to Ag(100)

26,27,51

 at least in the zero-temperature, vac-

uum environment of DFT. As we see in Figure 6, our calculations indicate that this trend continues at nite temperatures, for larger PVP analog molecules, and in solution, as the PVP-molecule binding free energies are always larger on Ag(100) than on Ag(111).

We

nd that the binding preference for the {100} surface increases with increasing chain length and that {100} binding is preferred to a greater degree in the solution environment than in vacuum. The binding free energy per segment is shown in Table 1 for both single molecules (obtained as the binding free energy divided by the number of segments) and for PVP20 in adsorbed layers (obtained using Eq. 4). For single-molecule binding, we see that as the chain length increases, the binding free energy per segment tends to decrease.

This is because

there is mismatch between the pyrrolidone segments and the Ag surfaces, which grows as the chain length increases and leads to sub-optimal congurations of the PVP chains. We see a break in the segment binding energy trend with increasing chain length in going from single PVP5 to PVP20 in an adsorbed layer, which may be attributed to a combination of chain exibility and complex PVP-PVP interactions in the layer. Since the Kuhn length of PVP in EG is approximately ve monomers long, PVP oligomers with less than ve repeat

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Table 1:

Binding free energies per segment of single molecules in vacuum, as

well as single molecules and molecules in a layer in EG solvent.

Binding free energy per segment (kcal/mol)

Ag(100)

Ag(111)

2P

−10.6 ± 0.2

−9.2 ± 0.3

PVP3

−8.4 ± 0.1

−7.8 ± 0.1

PVP5

−8.8 ± 0.1

−7.2 ± 0.1

2P

−3.3 ± 0.3

−2.5 ± 0.3

PVP3

−2.8 ± 0.1

−1.4 ± 0.1

PVP5

−2.2 ± 0.1

−1.0 ± 0.1

Adsorbed Layer  Reduced coverage

PVP20

−2.5 ± 0.3

−1.8 ± 0.3

Adsorbed Layer  Full coverage

PVP20

−1.8 ± 0.1

−1.5 ± 0.2

Single Molecules  Vacuum

Single Molecules  Solvent

units are sti and rod-like and they orient themselves parallel to the surface to minimize the potential energy.

52

For a layer comprised of PVP20, which is approximately four Kuhn-

segments long, various structures are expected, including trains of segments parallel to the surface, as well as segment loops and tails, which extend into solution. Interactions between Ag and segments in loops and tails are weakened or zero, and the average potential energy per segment is consequently decreased. We also see that dierences in the segment binding free energies between the two facets are smaller for PVP20 in a layer than for single PVP molecules  especially at full monolayer coverage. This may arise from PVP-PVP interactions, which increasingly compete with PVP-Ag interactions in determining the binding free energy as the coverage increases. We can gain more insight into the adsorption of PVP molecules by examining their PMF proles.

Figure 7 shows the PMF proles for 2P adsorption on Ag(100) in solvent and

vacuum.

Here, we see that the PMF for 2P in solvent has an oscillatory structure, with

two distinct minima and maxima, while that in vacuum exhibits only one deep minimum.

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2P on Ag(100)

0 −2

4

3

−4 2

−6 −8

ρEG (g/cm 3)

PMF in solvent PMF in vacuum

2

PMF (kcal/mol)

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

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1

−10

ρEG

2

4

6

8

10 z (Å)

12

14

0

16

Figure 7: Comparison of PMF prole for 2P adsorption in solvent and vacuum on Ag(100) (blue, left axis), overlay with the EG solvent density prole (red, right axis).

By comparing the PMF prole of 2P in solvent (blue, solid line in Fig. 7) with the solvent density prole (red, dotted line in Fig. 7), we see that the oscillatory PMF prole for 2P in solution results from layering of EG solvent. The peaks of the solvent density prole coincide with the troughs in the PMF of 2P solvent, which indicates that 2P is stabilized within the solvent layers, due to its interactions with neighboring EG molecules in the corresponding solvent layer. Thus, solvent layering can create additional free-energy minima and introduce free-energy barriers for adsorption. Interestingly, Figure 3 shows that the PMF for PVP5 adsorption in solvent has just a single minimum, contrasting with the PMF of 2P in solvent. The PMF proles of PVP3, which are shown in the Supporting Information, are similar to those of PVP5. This observation indicates that, for the peaks and troughs to be present, the size of the adsorbing molecule must be similar to the solvent molecule, because 2P is similar in size with EG, while PVP3 and PVP5 are not. We observed a similar (though weaker) oscillatory PMF prole and a

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free-energy barrier to adsorption for an Ag atom approaching Ag(111) and Ag(100) in EG solvent,

53

which reinforces the size argument. Though individual segments of PVP in larger

molecules may experience the solvent layering eect, this eect is not strong enough to be expressed in the PMF, for which the reaction coordinate is the molecule's center of mass.

Binding potential energies 0 Binding potential energy (kcal/mol)

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−10 −20 −30 −40 −50

Ag(100) Ag(111) EG

2P PVP3 Vac m

PVP5

2P

PVP3 PVP5 Solvent

Figure 8: Binding potential energies of adsorbing molecules in vacuum and EG solvent.

The binding potential energies are shown in Figure 8, where we see that these exhibit the same trends as the free energies in Fig. 6: The binding potential energies are signicantly weaker in solvent than in vacuum. We found that the lowering of the PVP binding potential energy in solvent is primarily due to favorable PVP-solvent and Ag-solvent interactions, which lower the potential energy more when the molecule is in the solution phase than when it is bound to the surface  this is documented in the Supporting Information. Moreover, the magnitudes of the binding potential energies are larger than those of the binding free energies in vacuum, but these magnitudes are comparable in solvent. This comparison foreshadows discussions of the entropy, which follow below. The entropic contributions to binding are shown in Figure 9. Here, we see that in vacuum,

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FreeΔenergyΔchangeΔdueΔ oΔen ropyΔ(T Δ S) 2

Ag(100) Ag(111)

0 T Δ SΔ(kcal/mol)

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

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−2 −4 −6 −8 −10 EG 2P PVP3 PVP5 ΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔVacuumΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔ

2P PVP3 PVP5 ΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔSolven ΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔ

Figure 9: Free-energy change due to entropy (T ∆S ) of adsorbing molecules in vacuum and EG solvent.

the free-energy changes due to entropy are all negative because the adsorbing molecule loses congurational and rotational entropy when it is bound to the surface. The entropic loss increases with molecular size in vacuum, similar to what has been observed in accelerated MD simulations of a linear alkane series adsorbed on Au(111) graphite

55

54

and the basal plane of

at low coverage. Similar trends in vacuum have been observed experimentally for

a linear alkane series on graphite.

56

Campbell and Sellers have also discussed entropy losses

that occur in experimental vacuum studies for various adsorbed molecules.

57

Interestingly,

the entropy changes are zero, or slightly positive for these molecules in solvent  a drastic dierence from the vacuum environment. Also, the entropy changes are independent (within error) of molecular size.

Although we still anticipate that solution-phase PVP molecules

will lose congurational and rotational entropy upon adsorption, this loss is oset by the entropy gain for solvent molecules that are displaced when PVP oligomers adsorb. To have a virtually constant entropy loss that is independent of molecular size, the number of solvent

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molecules liberated upon adsorption should increase with molecular size.

Number of EG molecules displaced 5 Number of EG displaced

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Ag(100) Ag(111)

4 3 2 1 0

2P

PVP3

PVP5

Figure 10: Number of EG molecules displaced when one adsorbate binds to Ag(100) and Ag(111) surfaces.

The average number of EG molecules displaced per adsorbate binding is shown in Figure 10. Here, we see that an increasing number of EG molecules is liberated as the PVP chain length increases. Thus, though larger PVP molecules lose more entropy upon adsorption due to a loss of their congurational degrees of freedom, they also displace more solvent molecules, leading to a compensating gain in entropy. These results explain why the entropy changes in solution are small and virtually independent of molecular size. Thus, our results demonstrate that the liberation of adsorbed solvent molecules when a molecule binds to a solid surface can contribute just as much (or more) to the entropy change of the system than the congurational entropy loss of the molecules due to adsorption.

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Conclusion In summary, we quantied the adsorption free energies of individual PVP oligomers on Ag surfaces in the absence and presence of EG solvent by using umbrella sampling to calculate the PMF along a reaction coordinate normal to the surface. We calculated the adsorption free energies of PVP layers from the dierence in liquid-solid interfacial free energies between EG solution and Ag surfaces with and without adsorbed PVP. We nd that the solution-phase adsorption of solutes on solid surfaces is an exchange process, in which solvent contributes signicantly to the overall free-energy change. In the EG-PVP-Ag system studied here, there is a favorable free-energy change when PVP adsorbs to Ag surfaces in the presence of EG solvent. However, the binding free energy for a PVP molecule in solution is not as large as that for a PVP molecule in vacuum. This is due to favorable PVP-solvent and Ag-solvent interactions, which lower the potential energy more when PVP is in solution than when it is adsorbed on the surface. We note that the scenario here, in which solvent lowers the binding energy from that in vacuum, has been observed in previous MD studies. possible scenario, as Zhang et al.

18

4547

However, this may not be the only

found in implicit-solvent DFT calculations that several

dierent solvents can strengthen the adsorption on CO on Cu2 O(111).

In any event, our

study shows that the inclusion of explicit solvent can signicantly change binding energies found in vacuum studies and this has important ramications for predicting temperature ranges over which solutes will bind to solid surfaces. In vacuum, the adsorbates lose considerable entropy upon adsorption to a solid surface due to a loss in their congurational degrees of freedom and this has been noted in other theoretical

54,55

and experimental studies.

56,57

In solution, adsorption entropies are a result

of a solvent-solute exchange process, in which the entropy loss of PVP solute is mitigated by the gain in entropy of the displaced solvent. In the EG-PVP-Ag system studied here, the entropy loss of the PVP solute is signicantly oset by the entropy gain of the EG solvent that is liberated on adsorption, so that the system exhibits virtually no entropy change, or

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The Journal of Physical Chemistry

even a gain in entropy upon PVP adsorption. Overall, for the systems studied here, the adsorption free energy is dominated by the potential energy.

Tang et al.

58

have discussed that the solution-phase binding of small

peptides to Au surfaces can be entropically driven. It is dicult to imagine how a relatively large molecule can, by itself, gain entropy when it transitions from being free in the solution phase to being bound to a solid surface.

However, here we show that entropy can favor

solution-phase adsorption if we consider the entropy gain of the liberated solvent molecules in addition to the entropy loss of the adsorbing solute. This raises the possibility that entropy could play a signicant role in solution-phase adsorption, perhaps to the point of dominating the free energy. Another conclusion of this study is that solvent layering near solid surfaces can create free-energy minima in the solution near the surface, where molecules can accumulate, as well as free-energy barriers to adsorption. This phenomenon seems to be especially pronounced for small solutes, that have a size comparable to the solvent molecules. We could not predict the eects of solvent layering near the surface using implicit-solvent models, which ignore solvent structuring. Thus, we elucidate important eects that can occur in solution-phase adsorption. Our study underscores the importance of including solvent explicitly, as well as performing extensive congurational sampling to quantify the thermodynamics of solution-phase adsorption. Such insight will be important in eorts to understand technologically relevant phenomena, such as crystal growth in solution, (electro)catalysis, and molecular sensing.

Acknowledgement This work is funded by the Department of Energy, Oce of Basic Energy Sciences, Materials Science Division, Grant DEFG02-07ER46414.

TB acknowledges training provided

by the Computational Materials Education and Training (CoMET) NSF Research Trainee-

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ship (grant number DGE-1449785). This work used the Extreme Science and Engineering Discovery Environment (XSEDE) supported by NSF/OCI-1053575.

Supporting Information Available The Supporting Information is available free of charge.

•

PMF proles, simulation and calculation details, sampling times, and potential energies of PVP oligomers in vacuum and in solvent (PDF)

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