Accelerated Aging of PS Blocks in PS-b-PMMA Diblock Copolymer

Feb 14, 2019 - This letter presents an accelerated physical aging of polystyrene (PS) blocks in polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA...
2 downloads 0 Views 4MB Size
Download PDF
Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

pubs.acs.org/JPCB

Accelerated Aging of PS Blocks in PS‑b‑PMMA Diblock Copolymer under Hard Confinement Mingchao Ma† and Yunlong Guo*,†,‡ †

University of Michigan, Shanghai Jiao Tong University Joint Institute, Shanghai 200240, China School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

‡

Downloaded via EAST CAROLINA UNIV on March 13, 2019 at 19:28:29 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: This letter presents an accelerated physical aging of polystyrene (PS) blocks in polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymers under hard confinement. The three-dimensional hard nanoconfinement was provided by the PMMA component owing to its high elasticity and was formed via self-assembled microphase separation. Aging was observed by measuring enthalpy recovery of the PS blocks in the copolymers for which the degree of polymerization (N) of PS blocks is fixed, whereas the N of PMMA blocks varies. Our results demonstrate that the aging speed of the PS blocks can increase by a factor of three to that of the neat PS as the N of PMMA blocks increases. Therefore, the hard confinement accelerates physical aging of the PS blocks, i.e., the relatively soft component in the copolymer.

■

INTRODUCTION Physical aging of polymer glasses is responsible for the gradual change of many physical properties with time and temperature, including volume,1−3 enthalpy,4−6 gas permeability,7−9 and elastic modulus.10−12 The aging speed, usually defined by the derivative with respect to time for a specific property, is notably influenced by the molecular weight of a polymer13−15 and the confinement effect through reduced characteristic size of the polymeric material and increased contribution from the interfaces between the polymer and other materials.16−24 For instance, Wang and Gillham found that aging rate of epoxy resin reached a minimum in the intermediate region, with increasing molecular weight.13 The change of aging rate in their study was attributed to the different chemical structures that change from monomer to sol−gel and to highly crosslinked polymer with increasing molecular weight. Boucher and Cangialosi et al. reported that the aging rate of polystyrene (PS) or poly(methyl methacrylate) (PMMA) under hard confinement induced by silicon or gold fillers in polymer nanocomposites exceeded the aging rate of the neat PS or PMMA.20−23 Here, we create a three-dimensional (3D) confinement and control its intensity on the PS blocks in polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymers by self-assembled microphase separation and altering the mole ratio between the PS and PMMA components. The aging of PS blocks under three confinement geometries was investigated via calorimetry. Microdomains, typically tens of nanometers, in diblock copolymers have various morphologies formed from microphase separation, including spheres, cylinders, gyroids, and lamellae. In all of these geometries, the domains of one polymer component are confined by the other. As such, © XXXX American Chemical Society

diblock copolymer can serve as an ideal model material to investigate aging response of polymer under 3D confinement, especially when considering the effects of domain size, geometry, and confinement intensity, as all of these can be controlled by changing the molecular weight and the mole ratio of the components.

■

EXPERIMENTS We use three PS-b-PMMA diblock copolymer materials to study the aging of the PS blocks under different nanoconfinements. The nanoconfinement is represented by the size and shape of the PS domain and the interface between the PS and PMMA domains. We keep the molecular weight of the PS blocks constant in all samples but vary the molecular weight of the PMMA blocks. Since the two components confine each other, and the elasticity of PMMA is clearly higher than that of PS,25−28 the PMMA domain provides hard confinement to the PS domains, compared to neat PS. These three PS-b-PMMA block copolymers have the same number-average molecular weights of the PS blocks (Mn,PS block) of 45 000 g/mol, whereas the number-average molecular weights of the PMMA blocks (Mn,PMMA block) are 10 500 g/mol (this sample is denoted by 45k−10.5k in the rest of this letter, similarly for other samples), 44 000 g/mol (45k−44k), and 192 000 g/mol (45k− 192k). Hence, in these samples, the mole fractions of the PMMA component are approximately 20, 50, and 80%. For direct comparison, a homo-PS with similar molecular weight Received: December 31, 2018 Revised: January 26, 2019 Published: February 14, 2019 A

DOI: 10.1021/acs.jpcb.8b12565 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 1. Heat capacity of PS-b-PMMA diblock copolymers and the corresponding homo-PS when Ta = Tg,PS − 20 °C or Tg,PS block − 20 °C. (a) 45k−10.5k, PDI = 1.06; (b) 45k−44k, PDI = 1.12; (c) 45k−192k, PDI = 1.10; and (d) homo-PS, PDI = 1.13.

Figure 2. Relaxed enthalpy of homo-PS or PS blocks in PS-b-PMMA diblock copolymers. The solid lines are linear fit of the data and β is the slope of the linear fit that represents the aging rate. The error bar represents the standard deviation of three duplicates. (a) Ta = Tg,PS − 30 °C or Tg,PS block − 30 °C, (b) Ta = Tg,PS − 25 °C or Tg,PS block − 25 °C, and (c) Ta = Tg,PS − 20 °C or Tg,PS block − 20 °C.

the aging temperature is much lower than (at least 44 °C) the Tg,PMMA block. Thus, we consider that the aging response captured in these heat capacity curves is contributed by the PS blocks. The details of this assumption and the heat capacity of neat PMMA are given in the Supporting Information. When the mole fraction of PMMA blocks increases, the heat capacity overshoot decreases at the same aging time (Ta). The aging tests of enthalpy recovery were conducted at four different Tas for all the samples, the results under other experimental conditions can be found in the Supporting Information. The enthalpy recovery of the materials after aging on various Tas were obtained by integrating the heat capacity data over

(Mn,PS = 46 000 g/mol) is also utilized in aging measurements. The physical aging of PS blocks and homo-PS was characterized by a differential scanning calorimeter. The aging response was demonstrated via the heat capacity curves and enthalpy recovery. The details of the materials and the experimental methods are given in the Supporting Information.

■

RESULTS Figure 1 illustrates a group of representative heat capacity curves when aging temperature (Ta) is Tg,PS block − 20 °C or Tg,PS − 20 °C. No notable aging response of the PMMA component can be detected in our experiment time scale, since B

DOI: 10.1021/acs.jpcb.8b12565 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

fraction of PMMA in the diblock copolymers, if we treat the case of homo-PS as zero percentage of PMMA component. That is, the PMMA microdomains dramatically accelerate the physical aging of the PS domains through hard confinement induced by the large elasticity of PMMA and the self-assembly of the copolymers.29 The intensity of hard confinement increases with higher mole ratios between PMMA/PS in the copolymers. The accelerated aging at enhanced confinement intensity suggests that the neighboring polymer blocks could strongly affect the dynamics of its partner in the copolymer. When Ta increases toward Tg, the values of β go up and reach maximum and subsequently drop down, the trend is in agreement with the finding of PS aging rate by Greiner and coworkers.30 As set forth, the PS blocks age under nanoconfinement after microphase separation. The microphase geometry in the three copolymer materials can be described by a thermodynamic theory using parameters such as the degree of polymerization (N), Flory−Huggins interaction parameter (χ), and mole ratio of the copolymer. The PS−PMMA interaction χPS−PMMA can be determined by an empirical equation

temperature. For homo-PS, the enthalpy (ΔHa) can be determined directly by the following equation ΔHa =

∫T

T2

(c p,aged(T ) − c p,unaged(T ))dT

(1)

1

where cp,aged and cp,unaged are the heat capacity of the aged and the unaged homo-PS, respectively. T1 and T2 are reference temperatures far below and far above Tg, where the heat capacity values of the unaged and the aged samples are equal. To determine the aging rates of the PS blocks, a calculation method needs to be established to identify the enthalpy relaxed from the PS blocks during aging. By this method, ΔHa,PS block was attained via eq 2. Details on the computation process are available in our recent work.29 ΔHa,PS block =

∫T

T2

(cp,copolymer,aged(T )

1

− c p,copolymer,unaged(T )) ×

Mcopolymer MPS block

dT (2)

χPS − PMMA = A + B /T

where cp,copolymer,aged and cp,copolymer,unaged are the heat capacity of aged and unaged copolymer samples, respectively. Mcopolymer and MPS block are the mean molecular weights of the entire copolymer chain and the PS block, respectively. The relaxed enthalpy results of homo-PS and PS blocks in PS-b-PMMA copolymers with different PMMA mole fractions are shown in Figure 2. Initially, when the materials age for a short period, the values of ΔHa are very small and the discrepancy of ΔHa at the shortest aging time in this study does not exhibit a clear trend over all of these samples. When aging time increases, the value of ΔHa for the sample of 45k− 192k (green in Figure 2) becomes the largest one, followed by the data of 45k−44k as the second (blue in Figure 2) at all Tas ranging from 30 to 20 °C below the glass transition temperatures. For the sample 45k−10.5k, the value of ΔHa is slightly larger than that of the homo-PS when Ta is 25 °C below the Tg. On other Tas in this work, the ΔHa of the sample 45k−10.5k is very similar with the results of the corresponding homo-PS. The aging rate (β) is quantified by the slope of a linear fit of the data. In general, the aging rate of the PS block increases with larger PMMA mole fraction. The aging rate also changes with aging temperature, as shown in Figure 3. The largest aging rate is captured at Tg,PS block − 20 °C or Ta = Tg,PS − 20 °C for all samples. Moreover, all the samples display a positive correlation between aging speed of PS blocks and the mole

(3)

where T is the phase separation temperature with degree of Kelvin (453.15 K in our study) and A and B are constants with values of 0.0294 and 3.2 k, respectively, for PS-b-PMMA diblock copolymers.31 The constants A and B are obtained from the results of Wang and co-workers.31 By the phase diagram of diblock copolymers, the microphase morphologies of the 45k−10.5k, 45k−44k, and 45k−192k samples are PMMA spheres in PS matrix, alternate lamellae of both PS and PMMA, and PS cylinders in PMMA matrix, respectively, as depicted in Figure 4. Representative deformation images of the copolymer samples by an atomic force microscope (AFM) match the results of theoretical analysis fairly well. The bright domains in these images are the PS blocks, as the PMMA blocks have higher elasticity and show smaller deformation.25−28 This speculation is in line with the mole ratios between PS and PMMA components in these samples. To eliminate the influence of surface roughness of the films and get real deformation, the applied force in AFM measurements is adjusted to ensure the average deformation is larger than 2 nm. From the AFM images, the characteristic sizes of the PS microdomain, including the average distance between spheres for 45k−10.5k, the lamellae thickness for 45k−44k, and the cylinder diameter for 45k−192k, are listed in Table 1. From the image analysis results shown in Table 1, all the microdomain sizes are same before and after aging. The results provide evidence confirming that the same confinement environment holds for PS blocks during aging process on our experimental time scale.

■

DISCUSSION Although the characteristic size of PS microdomains varies within 20−40 nm among these geometries, the confinement intensity provided by the relatively hard component, i.e., the PMMA domains, is notably different. For instance, in the 45k− 10.5k sample, the PMMA domains as spheres distributed in the matrix of PS provide weak confinement to the PS domains; most PS chains interact as in bulk so that the aging results represent similar response of the homo-PS. For the 45k−44k, the lamellae structure can provide moderate confinement for all microdomains of the PS, hence its aging behavior obviously

Figure 3. Aging rate of PS-b-PMMA diblock copolymer and the corresponding homo-PS. C

DOI: 10.1021/acs.jpcb.8b12565 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 4. AFM deformation images of PS-b-PMMA diblock copolymer samples. The bright domains are PS blocks and the dark domains are PMMA blocks. (a, c, e) Unaged and (b, d, f) Ta = 38 400 s when Ta = Tg,PS block − 15 °C. The image size is (a, b) 0.5 × 0.5 μm2 for 45k−10.5k, (c, d) 1 × 1 μm2 for 45k−44k, and (e, f) 1 × 1 μm2 for 45k−192k. The side color scale ranges from 1 to 4 nm or less for all samples.

polymer interface may not play key roles in the immense difference in enthalpy relaxation; on the other hand, the accelerated aging found in this work should be principally attributed to the influence of PMMA/PS mole ratios, which set varying intensity of the hard confinement. Particularly, the homo-PS, which can be considered as the case of zero PMMA/ PS mole ratio, sets the lower bound of the β, whereas a diblock copolymer with a sufficiently high PMMA/PS mole ratio should provide a system in which the β approaches its upper bound.

Table 1. Characteristic Size of PS Domain Geometries in the Three Copolymer Samplesa samples

aging time

45k−10.5k

unaged 38 400 s unaged 38 400 s unaged 38 400 s

45k−44k 45k−192k

characteristic size (nm) 25.9 25.9 38.1 37.8 37.2 37.3

± ± ± ± ± ±

1.8 3.1 4.0 1.8 2.8 2.4

■

a

Standard deviations are determined from six different areas.

CONCLUSIONS By utilizing PS-b-PMMA diblock copolymer as a model material, we show accelerated aging in the PS blocks that are under hard confinement provided by their copolymer counterpart, i.e., the PMMA blocks, after microphase separation. The aging rate of PS blocks increases with enhanced intensity of the hard confinement. Mole ratio of the soft and hard components in the diblock copolymer plays an important role in changing the physical aging behavior when the size effect and interfacial effect are subtle under certain circumstances.

deviates from the bulk. For 45k−192k, the PMMA microdomains enclose PS cylinders and provide a strong hard confinement via high PMMA/PS mole ratio. Therefore, the magnitude and speed of enthalpy relaxation of PS domains are both largely increased during aging. Our aging results of PS blocks under hard confinement are qualitatively consistent with the studies in the literature.19−24 However, there are some findings in literature that have opposite conclusion, that is, the hard confinement decreases the aging rate.32−34 For example, Frieberg and co-workers find that the aging rate of thin films next to a hard wall is reduced compared to the bulk.32 In fact, the study of the hard confinement effect on aging rate is very attractive and still ongoing due to lack of consistent results. The opposite trend may come from the different definition of aging rate.35 Definitely future work needs to be conducted to determine if there is an undetected underlying physics for the accelerated and/or depressed aging under hard confinement. Another remarkable point of this work is that the domain size within a narrow range of 20−40 nm and the polymer−

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b12565. Materials and the experimental methods, the assumption of aging response contribution, and the heat capacity results (PDF) D

DOI: 10.1021/acs.jpcb.8b12565 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

■

(15) Nicholson, L. M.; Whitley, K. S.; Gates, T. S. The Combined Influence of MolecularWeight and Temperature on the Physical Aging and Creep Compliance of a Glassy Thermoplastic Polyimide. Mech. Time-Depend. Mater. 2001, 5, 199−227. (16) Kushner, D. I.; Hickner, M. A. Substrate-Dependent Physical Aging of Confined Nafion Thin Films. ACS Macro Lett. 2018, 7, 223− 227. (17) Rauscher, P. M.; Pye, J. E.; Baglay, R. R.; Roth, C. B. Effect of Adjacent Rubbery Layers on the Physical Aging of Glassy Polymers. Macromolecules 2013, 46, 9806−9817. (18) Pye, J. E.; Roth, C. B. Physical Aging of Polymer Films Quenched and Measured Free-Standing via Ellipsometry: Controlling Stress Imparted by Thermal Expansion Mismatch between Film and Support. Macromolecules 2013, 46, 9455−9463. (19) Guo, Y.; Zhang, C.; Lai, C.; Priestley, R. D.; D’Acunzi, M.; Fytas, G. Structural Relaxation of Polymer Nanospheres under Soft and Hard Confinement: Isobaric versus Isochoric Conditions. ACS Nano 2011, 5, 5365−5373. (20) Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J. Enthalpy Recovery of PMMA/Silica Nanocomposites. Macromolecules 2010, 43, 7594−7603. (21) Boucher, V. M.; Cangialosi, D.; Alegría, A.; Colmenero, J.; Pastoriza-Santos, I.; Liz-Marzan, L. M. Physical Aging of Polystyrene/ Gold Nanocomposites and Its Relation to the Calorimetric Tg Depression. Soft Matter 2011, 7, 3607−3620. (22) Cangialosi, D.; Boucher, V. M.; Alegría, A.; Colmenero, J. Free Volume Holes Diffusion to Describe Physical Aging in Poly(mehtyl methacrylate)/Silica Nanocomposites. J. Chem. Phys. 2011, 135, No. 014901. (23) Cangialosi, D.; Boucher, V. M.; Alegría, A.; Colmenero, J. Enhanced Physical Aging of Polymer Nanocomposites: The Key Role of The Area to Volume Ratio. Polymer 2012, 53, 1362−1372. (24) Ramakrishnan, V.; Harsiny, S.; Goossens, J. G. P.; Hoeks, T. L.; Peters, G. W. M. Physical Aging in Polycarbonate Nanocomposites Containing Grafted Nanosilica Particles: A Comparison between Enthalpy and Yield Stress Evolution. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 2069−2081. (25) Dong, R.; Yu, L. E. Investigation of Surface Changes of Nanoparticles Using TM-AFM Phase Imaging. Environ. Sci. Technol. 2003, 37, 2813−2819. (26) Jiang, L.; Wu, J.; Nedolisa, C.; Saiani, A.; Assender, H. E. Phase Separation and Crystallization in High Hard Block Content Polyurethane Thin Films. Macromolecules 2015, 48, 5358−5366. (27) Evangelopoulos, A. E. A. S.; Glynos, E.; Madani-Grasset, F.; Koutsos, V. Elastic Modulus of a Polymer Nanodroplet: Theory and Experiment. Langmuir 2012, 28, 4754−4767. (28) Scott, W. W.; Bhushan, B. Use of Phase Imaging in Atomic Force Microscopy for Measurement of Viscoelastic Contrast in Polymer Nanocomposites and Molecularly Thick lubricant Films. Ultramicroscopy 2003, 97, 151−169. (29) Ma, M.; Huang, Y.; Guo, Y. Enthalpy Relaxation and Morphology Evolution in Polystyrene-b-poly(methyl methacrylate) Diblock Copolymer. Macromolecules 2018, 51, 7368−7376. (30) Greiner, R.; Schwarzl, F. R. Thermal Contraction and Volume Relaxation of Amorphous Polymers. Rheol. Acta 1984, 23, 378−395. (31) Wang, J.-Y.; Chen, W.; Russell, T. P. Ion-ComplexationInduced Changes in the Interaction Parameter and the Chain Conformation of PS-b-PMMA Copolymers. Macromolecules 2008, 41, 4904−4907. (32) Frieberg, B. R.; Glynos, E.; Stathouraki, M.; Sakellariou, G.; Green, P. F. Glassy Dynamics of Polymers with Star-Shaped Topologies: Roles of Molecular Functionality, Arm Length, and Film Thickness. Macromolecules 2017, 50, 3719−3725. (33) Priestley, R. D.; Rittigstein, P.; Broadbelt, L. J.; Fukao, K.; Torkelson, J. M. Evidence for the molecular-scale origin of the suppression of physical ageing in confined polymer: fluorescence and dielectric spectroscopy studies of polymer−silica nanocomposites. J. Phys.: Condens. Matter 2007, 19, No. 205120.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yunlong Guo: 0000-0002-4490-2140 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge the National Science Foundation of China for financial support through the General Program 2157408. Y.G. is very grateful to the National Youth 1000 Talent Program of China, the Shanghai 1000 Talent Plan, and the support by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China. The authors also acknowledge the start-up fund of Y.G. from both University of Michigan−Shanghai Jiao Tong University Joint Institute, and School of Materials Science and Engineering at SJTU.

■

REFERENCES

(1) Frieberg, B.; Glynos, E.; Sakellariou, G.; Green, P. F. Physical Aging of Star-Shaped Macromolecules. ACS Macro Lett. 2012, 1, 636−640. (2) Simon, S. L.; Plazek, D. J.; Sobieski, J. W.; Mcgregor, E. T. Physical Aging of a Polyetherimide: Volume Recovery and Its Comparison to Creep and Enthalpy Meas. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 929−936. (3) Huang, Y.; Wang, X.; Paul, D. R. Physical Aging of Thin Glassy Polymer Films: Free Volume Interpretation. J. Membr. Sci. 2006, 277, 219−229. (4) Cowie, J. M. G.; Harris, S.; McEwen, I. J. Physical Aging in Poly(vinyl acetate). 2. Relative Rates of Volume and Enthalpy Relaxation. Macromolecules 1998, 31, 2611−2615. (5) Odegard, G. M.; Bandyopadhyay, A. Physical Aging of Epoxy Polymers and Their Composites. J. Polym. Sci., Part B: Polym. Phys. 2011, 49, 1695−1716. (6) Cowie, J. M. G.; Ferguson, R. Physical Aging Studies in Poly(viny1 methyl ether). 1. Enthalpy Relaxation as a Function of Aging Temperature. Macromolecules 1989, 22, 2307−2312. (7) Low, Z.-X.; Budd, P. M.; McKeown, N. B.; Patterson, D. A. Gas Permeation Properties, Physical Aging, and Its Mitigation in High Free Volume Glassy Polymers. Chem. Rev. 2018, 118, 5871−5911. (8) Swaidan, R.; Ghanem, B.; Litwiller, E.; Pinnau, I. Physical Aging, Plasticization and Their Effects on Gas Permeation in “Rigid” Polymers of Intrinsic Microporosity. Macromolecules 2015, 48, 6553− 6561. (9) Ma, X.; Pinnau, I. Effect of Film Thickness and Physical Aging on “Intrisic” Gas Permeation Properties of Microporous Ethanoanthracene-Based Polyimides. Macromolecules 2018, 51, 1069−1076. (10) Hutchinson, J. M. Physical Aging of Polymers. Prog. Polym. Sci. 1995, 20, 703−760. (11) Roe, R.-J.; Millman, G. M. Physical Aging in Polystyrene: Comparison of the Changes in Creep Behavior with the Enthalpy Relaxation. Polym. Eng. Sci. 1983, 23, 318−322. (12) Soloukhin, V. A.; Brokken-Zijp, J. M.; Asselen, O. L. J. v.; With, Gd. Physical Aging of Polycarbonate: Elastic Modulus, Hardness, Creep, Endothermic Peak, Molecular Weight Distribution, and Infrared Data. Macromolecules 2003, 36, 7585−7597. (13) Wang, X.; Gillham, J. K. Physical Aging in the Glassy State of a Thermosetting System vs. Extent of Cure. J. Appl. Polym. Sci. 1993, 47, 447−460. (14) Marshall, A. S.; Petrie, S. E. B. Rate-determining factors for enthalpy relaxation of glassy polymers. Molecular weight. J. Appl. Phys. 1975, 46, 4223−4230. E

DOI: 10.1021/acs.jpcb.8b12565 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B (34) Pye, J. E.; Rohald, K. A.; Baker, E. A.; Roth, C. B. Physical Aging in Ultrathin Polystyrene Films: Evidence of a Gradient in Dynamics at the Free Surface and Its Connection to the Glass Transition Temperature Reductions. Macromolecules 2010, 43, 8296− 8303. (35) Cangialosi, D.; Boucher, V. M.; Alegría, A.; Colmenero, J. Physical aging in polymers and polymer nanocomposites: recent results and open questions. Soft Matter 2013, 9, 8619−8630.

F

DOI: 10.1021/acs.jpcb.8b12565 J. Phys. Chem. B XXXX, XXX, XXX−XXX