Hydrogen Bonding Slows Down Surface Diffusion of Molecular

Subscriber access provided by UNIV OF CALIFORNIA SAN DIEGO LIBRARIES

Article

Hydrogen Bonding Slows Down Surface Diffusion of Molecular Glasses Yinshan Chen, Wei Zhang, and Lian Yu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05658 • Publication Date (Web): 12 Jul 2016 Downloaded from http://pubs.acs.org on July 16, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31

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

The Journal of Physical Chemistry

Hydrogen Bonding Slows Down Surface Diffusion of Molecular Glasses Yinshan Chen,† Wei Zhang† and Lian Yu†,‡* †School

of Pharmacy and ‡Department of Chemistry, University of Wisconsin – Madison, Madison, Wisconsin 53705

ABSTRACT Surface grating decay has been measured for three organic glasses with extensive hydrogen bonding: sorbitol, maltitol, and maltose. For 1000 nm wavelength gratings, the decay occurs by viscous flow in the entire range of temperature studied, covering the viscosity range 105 – 1011 Pa s, whereas under the same condition, the decay mechanism transitions from viscous flow to surface diffusion for organic glasses that contain similarly sized molecules but have no or limited hydrogen bonding. These results indicate that extensive hydrogen bonding slows down surface diffusion in organic glasses. This effect arises because molecules can optimize hydrogen bonding even near the surface so that the loss of nearest neighbors does not translate to a proportional decrease of the kinetic barrier for diffusion, as in the case of van der Waals systems. This explanation is consistent with a strong correlation between liquid fragility and the surface enhancement of diffusion, both reporting a liquid’s resistance of dynamic excitation. Slow surface diffusion is expected to hinder any processes that rely on surface transport; for example, surface crystal growth and formation of stable glasses by vapor deposition.

1 ACS Paragon Plus Environment


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

Page 2 of 31

INTRODUCTION Surface mobility is important in many areas of science and technology, including catalysis, sintering, crystal growth, and fabrication by vapor deposition. A fundamental measure of surface mobility is the lateral surface diffusion coefficient Ds. While Ds has been reported extensively for crystalline metals and semiconductors,1,2 only recently have there been studies on amorphous solids. These studies include experimental measurements on amorphous silicon,3,4 molecular glasses,5,6,7,8 and metallic glasses,9 as well as simulation studies of various glass-forming liquids.10,11,12,13 These studies show that surface diffusion can be much faster than bulk diffusion, by as much as 8 orders of magnitude at the laboratory glass transition temperature Tg. The results are particularly relevant for understanding surface crystal growth on amorphous solids3,14,15 and formation of stable glasses by vapor deposition.16,17 An intriguing question in this area concerns the material dependence of surface mobility. Simulations have shown that at the same bulk diffusivity, surface diffusion is much slower in silica (SiO2)11 than in a binary Lennard-Jones liquid12,13 or the metallic liquid ZrNi.10 Experimentally, the method of surface grating decay can observe lateral surface diffusion in molecular5,6,7,8 and metallic9 glasses, but under similar conditions, cannot detect the process in silicate glasses.18 Given that silica and silicates contain highly directional network bonds (Si-O) that are absent in the other systems, these results suggest a possible effect of network bonding on surface diffusion. The available data on molecular glasses5,6,7,19 also argue for a role for network bonds in surface diffusion, here the network bonds being hydrogen bonds. Consider the molecules in the first two rows of Scheme 1: oterphenyl (OTP), tris-naphthyl benzene (TNB), nifedipine (NIF), and indomethacin (IMC). These molecules have similar sizes (TNB is the largest) and different abilities to form hydrogen bonds: OTP and TNB form no hydrogen bonds, while NIF and IMC do; between the latter two, IMC forms stronger hydrogen bonds because of its carboxylic acid group. These glass-formers have roughly the same bulk diffusion coefficient Dv at Tg (~ 10-20 m2/s),

20,21,22,23

but their surface diffusion coefficients Ds differ by almost 3 orders of

magnitude, decreasing in the same order hydrogen bonding increases.5,6,7,19 2 ACS Paragon Plus Environment

Page 3 of 31

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


To understand the effect of hydrogen bonds (network

No hydrogen bonding

bonds in general) on surface diffusion, we have studied

OTP

TNB

three extensively hydrogen-bonded glasses - sorbitol, maltitol, and maltose (Scheme 1, bottom row), using the Limited hydrogen bonding

method of surface grating decay. These molecules have

IMC

NIF

similar sizes as those previously studied that form no or limited hydrogen bonds,5,6,7,19 allowing a critical test of the effect of hydrogen bonding on surface diffusion. In

Extensive hydrogen bonding

this context, it is worth noting that there is some indication in the literature that polyalcohols have low surface mobility. Vapor deposition can prepare low-

sorbitol

maltose maltitol

energy glasses of OTP, TNB, IMC, and NIF,16,17,24 relying Scheme 1. Molecular glass-formers whose surface on an efficient equilibration of newly deposited molecules in the mobile surface layer, but is unable to do so for polyalcohols under similar conditions.25,26 It is also

diffusion has been studied. OTP: o-terphenyl. TNB: tris-naphthyl benzene. NIF: nifedipine. IMC: indomethacin. Top row: aromatic hydrocarbons forming no hydrogen bonds. Middle row: aromatic hydrocarbons with limited hydrogen bonding. Bottom row: polyalcohols with extensive hydrogen bonding (this work).

noteworthy that polyalcohols and carbohydrates constitute an important class of molecular glasses with applications in bio-preservation, food, and pharmaceutical formulations, making it technologically relevant to understand their physical stability. We find that the polyalcohol glasses studied have much slower surface diffusion than the glasses of comparable molecular sizes but with no or limited hydrogen bonds. The surface-grating decay of polyalcohol glasses occurs by viscous flow in the entire range of temperature studied, whereas under the same conditions, the other systems show a transition from viscous flow to surface diffusion as the mechanism of surface evolution. This means that surface diffusion in the polyalcohol glasses is too slow to be responsible for the smoothing of surface gratings. We find that surface diffusion in the polyalcohol glasses is at least 4 orders of magnitude slower than that in OTP glasses. This difference is attributed to the 3 ACS Paragon Plus Environment


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

Page 4 of 31

ability of molecules to preserve hydrogen bonds even in the surface environment so that the loss of nearest neighbors does not translate to a proportional decrease of the kinetic barrier for diffusion. This explanation is consistent with a strong correlation between liquid fragility and the surface enhancement of diffusion, both reporting a liquid’s resistance of dynamic excitation.

MATERIALS AND METHODS Sorbitol (≥ 99.5%), maltitol (≥ 98%) and maltose (≥ 99%) were purchased from Sigma and used as received. Table 1 summarizes some of their physical properties. The as-purchased crystalline monohydrate of maltose contained 5 wt % water. To remove this water, the material was first dissolved in water to make a 50 wt % solution, and the solution was dried in vacuum at 381 K. The dried material was ground in a mortar and dried in vacuum at 381 K for another 24 hours to yield a solid containing less than 0.5 wt % water according to Karl-Fischer titration. We prepared sinusoidal surface gratings on glasses by embossing with master gratings. Master gratings were purchased from Rainbow Symphony (1000 and 2000 nm) or prepared by replication from glass gratings through a Norland UV-curing optical adhesive (3300 and 8200 nm). The masters were generally coated with gold to prevent transfer of contaminants, although uncoated masters did not yield different results. To print a surface grating, the master was placed on a supercooled liquid (313 K for sorbitol, 363 K for maltitol, and 388 K for maltose), and the assembly was cooled in the chamber of a Linkam THMS 600E stage under N2 purge. The hot stage along with the sample was placed in a N2 purged glove bag, where the master was detached below Tg, yielding a glass film with a corrugated surface. The thickness of the glass film was 50-100 µm, much larger than the wavelength of surface gratings. The decay of surface gratings was monitored in flowing N2 by following the intensity of the first-order diffraction of a helium-neon laser (632.8 nm). The diffraction intensity was detected with a photodiode (Si Transimpedence Amplified Photodectecor from Thorlabs) interfaced with a National Instruments NI-DAQ data acquisition card. 4 ACS Paragon Plus Environment

Page 5 of 31

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


Differential Scanning Calorimetry (DSC) was performed with a TA Instruments Q2000 unit. The glass transition temperature Tg was measured during heating at 10 K/min after the sample was cooled at 10 K/min to 40 K below Tg. The onset temperatures are reported (Table 1). To measure the velocity of crystal growth in amorphous maltitol, a liquid film was prepared by melting the crystalline material between two silicate coverslips and crystallization was initiated by crystal seeds in contact with the edge of the film. The film was 50−100 μm thick. The sample was stored at a desired temperature in an oven and periodically removed to measure the progress of crystal growth with a light microscope (Olympus BX3-URA). To study surface crystal growth, the top coverslip of a sandwiched sample was removed to expose a free surface and crystal seeds were added to initiate crystallization. The sample was stored in a desiccator at a chosen temperature and measured periodically. Photomicrographs were analyzed using the ImageJ software to calculate the linear velocity of crystal growth.



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

Page 6 of 31

Table 1. Properties of the molecular glass-formers considered in this study. M, g/mol

Tg, K

ρ, g/cm3

Ω, nm3

ν, nm-2

Hydrogen bonds

No hydrogen bonding o-terphenyl (OTP) -trisnaphthyl benzene (TNB) PS1110 PS1700

230.3

246

1.12

0.34

2.0

-

456.6

347

1.15

0.66

1.3

-

1110 (Mw) 991 (Mn) 1700 (Mw) 1603 (Mn)

307

1.03

1.6

0.73

-

319

1.03

2.6

0.52

-

Limited hydrogen bonding Nifedipine (NIF)

346.3

315

1.34

0.43

1.8

Indomethacin (IMC)



315

1.34

0.44

1.7

Donor: -NHAcceptors: -NH-, -NO2, -O(CO)- (2) Donor: COOH Acceptors: COOH, N(CO)-, -O-

Extensive hydrogen bonding Sorbitol

182.2

269

1.47

0.21

2.9

Maltitol

344.3

317

1.51

0.38

1.9

Maltose

342.3

371

1.51

0.38

1.9

Donors: OH (6) Acceptors: OH (6) Donors: OH (9) Acceptors: OH (9), -O- (2) Donors: OH (8) Acceptors: OH (8), -O- (3)

Notes: (1) Tg is the onset temperature of glass transition measured by DSC during heating at 10 K/min. (2) The densities ρ are from Ref. 27 (sorbitol and maltitol), Ref. 28 (IMC), Ref.29 (OTP), Ref. 30 (TNB), and Ref.31 (PS). The values at Tg are given. Maltose is assumed to have the same density as maltitol. NIF is assumed to have the same density as IMC. (3) The molecular volume Ω is calculated from ρ and M using Ω = M/ρ/NA, where NA is Avogadro’s number. (4) The areal density of molecules on the surface ν is calculated from Ω using ν = Ω-2/3.


Page 7 of 31

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


RESULTS AND DISCUSSION Slow Surface Diffusion of Polyalcohol Glasses. Figure 1 shows the typical kinetics of surface grating decay for the three polyalcohols studied. I/I0 is the normalized first-order diffraction intensity. The decay is exponential, I/I0 = exp(-KIt), within experimental error. The grating-amplitude decay constant K is given by KI/2 because of the relation I ∝ h2. Figure 2a shows the grating decay constant K vs temperature for 1000 nm wavelength gratings. For each system, the measured K covers 5 to 6 decades. Each curve in Figure 2a that runs through data points is the expected decay rate for the viscous-flow mechanism: K = Fq = (γ/2η)∙(2π/λ), where γ is surface tension, η is viscosity, and λ is grating wavelength.32 For this calculation, γ is taken to be 0.063 N/m (the surface tension for glycerol),33,34 the viscosities of sorbitol and maltitol are from Ref. 27, and the viscosity of maltose was estimated by shifting the maltitol data in temperature by their Tg difference. Figure 2a shows that with a vertical shift C on the log scale (0.6 for sorbitol, -0.5 for malitol, and -1 for maltose), the expected decay rate Fq well matches the

Figure 1. Typical decay kinetics for the surface gratings of sorbitol, maltitol, and maltose. I/I0 is normalized diffraction intensity. The curves are exponential or stretched-exponential fits.

observed decay constant K. This agreement indicates viscous flow is the mechanism for the decay of surface gratings in the entire temperature range studied. There is no indication for any transition to another decay mechanism. (The need for a small shift C is likely the result of combined experimental errors in η, K, and γ. There is no systematic material dependence of C.)



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

Page 8 of 31

To verify the mechanism of grating decay, we measured the wavelength dependence of K for the three polyalcohols (Figure 2b). Decay by viscous flow requires K ∝ λ-1. As Figure 2b shows,

this

relation

is

indeed

observed,

confirming the mechanism of surface evolution to be viscous flow. The surface-evolution kinetics of polyalcohols just described is in contrast with that of previously studied organic glasses that have no or limited hydrogen bonding. As Figure 3 shows, the latter systems7,8 all exhibit a change of the surface-evolution

mechanism

with

falling

temperature, evident from the kink in each decay Figure 2. (a) Decay constant K vs T at  = 1000 nm for K vs. T curve. As in the case of the polyalcohols, the Fq curves are overlain with the observed K

polyalcohols. The curves are the calculated Fq term after a vertical shift on the log scale by 0.6 for sorbitol, -0.5 for maltitol, and -1 for maltose. (b) K vs  for each system. The slope is approximately -1, indicating that viscous flow is the mechanism of surface grating decay.

values to indicate the decay rate due to viscous flow. (The calculation of the Fq curve has been described for OTP,7 TNB,19 and PS.8 For IMC, we use the viscosity from Ref. 35 and γ= 0.05 N/m. We assume the IMC result holds for NIF, on the ground that two systems have the same Tg and nearly identical structural relaxation times.6) Note that at high temperatures, the observed decay rates closely track the Fq curves, indicating viscous flow is the decay mechanism, but at low temperatures, the observed decay is much faster than the Fq curve, indicating a new decay mechanism. Previous work has shown that the new mechanism of decay is surface diffusion because K scales as λ-4, as expected for this mechanism.32


Page 9 of 31

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


The comparison of Figures 2 and 3 suggests that hydrogen bonding has a significant effect on surface diffusion. Relative to molecules in Figure 3, the polyalcohols have more extensive hydrogen bonds. The fact that viscous flow controls their surface evolution in the entire temperature range studied (Figure 2) indicates that surface diffusion is slower in these systems than in molecular glasses that have no or fewer hydrogen bonds. To further explore the point, we compare in Figure 4 the

reported

diffusion

coefficients

for

molecular

glasses5,6,7,8,19,20,21,22,23, and the results from this study. Figure 4 displays both bulk and surface diffusion coefficients (Dv and Ds) against Tg-scaled temperature. In this format, the Dv values approximately collapse to a Figure 3. Decay constant K vs T at  = 1000 nm for master curve, whereas the Ds values show a larger system-to-system variation. As noted previously, the system dependence of Ds is consistent with the notion that

(a) aromatic hydrocarbons that form no hydrogen bonds (OTP, TNB, PS1.1k and PS1.7k) and (b) two aromatic hydrocarbons that form limited hydrogen bonds (IMC and NIF). The curves are calculated Fq term. A vertical shift C on the logarithmic scale was applied to some curves: C = -0.6 for TNB, 0.45 for PS1.1k, -1 for IMC (no shift for the other curves).

at the same bulk diffusivity, surface diffusion slows down with increasing molecular size and hydrogen bonding. To see the size effect, follow the series of aromatic hydrocarbons of increasing size (OTP, TNB, PS1110, and PS1700) and note that Ds decreases in the same order. To see the hydrogen-bonding effect, compare OTP, TNB, NIF, and IMC and note that these molecules have similar sizes (Table 1), but increasing strengths of hydrogen bonding. For these molecules, Ds decreases in the same order hydrogen bonding increases.



The molecular dependence of Ds just noted is fully consistent with the present results on polyalcohols. Since viscous flow accounts for the grating decay at all temperatures studied, only an upper bound can be estimated for the Ds of the polyalcohols, on the ground that surface diffusion never overtakes viscous flow as the mechanism for surface evolution. The grating decay constant due to surface diffusion is Bq4, where B = DsγΩ2ν/(kT), where Ω is the molecular volume and ν is the areal Figure 4. Bulk and surface diffusion coefficients (Dv and density of molecules on the surface.32 Setting Bq4 < Fq (decay rate for viscous flow), we can estimate

Ds) plotted against Tg/T. The Dv value nearly forms a master curve, while Ds values have stronger molecular dependence. A Ds upper bound from this work is shown for polyalcohols.

the upper bound for Ds. For maltitol, we obtain Ds < 4x10-17 m2/s at 315 K (Tg – 2 K). We assume this upper bound applies to the other polyalcohols studied as well. Note that this upper bound is below all previously measured Ds values. More important, since the polyalcohols have similar sizes as OTP, TNB, NIF, and -6

IMC, but more extensive hydrogen bonding, our result

Binary LJ, A = Ar

-8

supports a general relationship between hydrogen

-10

SiO2

bonding and surface diffusion. Comparison between Experiments, Simulations, and Theories. In Figure 5, we compare the Ds values

log Ds (m2/s)

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

Page 10 of 31

-12

ZrNi OTP

-14

TNB

-16 -18

from experiments, simulations, and theories in the format Ds vs. Dv. The data symbols are the experimental results on OTP,7 TNB,19 IMC,5 and the polyalcohols of

Ds = Dv

IMC

polyalcohols upper bound

-20 -22

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6

log Dv (m2/s)

Figure 5. Bulk and surface diffusion coefficients (Dv

this study, as well as the simulation results on the binary and Ds) from experiments, simulations, and theories, compared in the format Ds vs. Dv.


Page 11 of 31

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


Lennard-Jones (LJ) mixture,12 the metallic glass-former ZrNi,10 and SiO2.11 In general, we find Ds > Dv, but their difference varies strongly system to system. This variation is seen by comparing the Ds values at the same Dv. Surface diffusion is greatly enhanced over bulk diffusion in OTP, TNB, IMC, the LJ mixture, and ZrNi, while the enhancement is much smaller for the polyalcohols and SiO2. The Ds of SiO2 is 2 orders of magnitude smaller than that of the binary LJ mixture at the same bulk diffusivity (Dv = 10-11 m2/s);11,12 and the Ds upper bound for polyalcohols is 4 orders of magnitude smaller than the Ds of OTP at Dv = 10-20 m2/s (typical bulk diffusivity at the laboratory Tg).7 It is noteworthy that the slow and fast surface diffusers are roughly divided along the line of network/nonnetwork systems. Each system in the fast group contains quasi-spherical particles interacting mainly through van der Waals or metallic interactions, whereas those in the slow group are characterized by highly directional network bonds (Si-O or hydrogen bonds). Figure 5 also includes the predictions of two theories (ECNLE36and RFOT37), both intended to describe van der Waals systems without network bonds. According to these theories, surface enhancement of diffusion is largely a consequence of the loss of nearest neighbors and a proportional decrease of the kinetic barrier for diffusion. This picture seems to be an accurate description of the fast group. (The two ECNLE lines and are obtained assuming surface diffusion is determined by the average friction within a surface layer d/2 and d thick, where d is the particle diameter.36) An important point raised by Figure 5 is that relative to the ECNLE and RFOT predictions, surface diffusion in SiO2 and polyalcohols is substantially slower. We speculate that the slower surface diffusion of these network glass-formers results from the preservation of network bonds even in the surface environment, so that the decrease of the kinetic barrier for diffusion is not as great as in the case of van der Waals systems. For silica, Roder et al. find that the radial distribution of oxygen atoms around silicon is largely unchanged from the bulk to the surface and the surface diffusion of silicon is only mildly enhanced relative to the bulk (Figure 5).11 For water, each molecule has ~3.2 hydrogen bonds at the liquid/vapor 11 ACS Paragon Plus Environment


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

Page 12 of 31

interface, relative to ~3.8 in the bulk,38 implying that in terms of hydrogen bonding, the surface environment is substantially unchanged from the bulk environment. For glycerol, a smaller polyalcohol than those studied here, all OH groups are fully engaged in hydrogen bonds in the bulk,39 and the same holds at the free surface according to sum-frequency spectroscopy, which detects no free OH.40,41 It is speculated that a polyalcohol molecule can rotate or twist to maximize hydrogen bonding. Thus, the loss of nearest neighbors at the surface need not mean a proportional loss of hydrogen bonds, and this preservation of hydrogen bonds may account for the slower lateral surface diffusion of polyalcohol molecules relative to nonhydrogen-bonding molecules like OTP. Correlation between Fragility and Surface Enhancement of Diffusion. The ratio Ds/Dv is a measure of the degree to which mobility increases if a molecule’s environment changes from the bulk to the surface. This environmental change is a kind of “excitation” in which some nearest neighbors are removed for a tagged molecule. Another kind of excitation process has been studied in glassforming liquids, namely, excitation by increasing temperature. In this process, “fragility” measures the degree to which mobility increases upon Figure 6. Correlation between fragility and surface heating above Tg. In the standard Angell plot (Figure 6a, populated with data relevant for this study23,27,30,35,42,43,44), viscosity  is the mobility

diffusion. (a) The Angell plot of viscosity vs. Tg/T, where Tg is the DSC Tg. Viscosity  at 1.25 Tg is used as a measure of fragility. (b) Observed Ds at Tg (solid circles) decreases with  at 1.25 Tg. This empirical relation predicts the Ds values for sorbitol and maltitol (open symbols), consistent with the upper bound from this work (inverted triangle).


Page 13 of 31

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


indicator and mobility enhancement is compared between various systems for a given temperature rise normalized by Tg. The mobility enhancement is large for OTP (fragile) and small for SiO2 (strong). We speculate that the two kinds of excitations just described – removing nearest neighbors and raising temperature – are both related to the nature of intermolecular interactions, and thus correlated. We examine this correlation in Figure 6b, where the bulk and surface diffusion coefficients at Tg (Figure 4) are plotted against fragility. We choose as our fragility measure the liquid’s viscosity at 1.25 Tg (or Tg/T = 0.8). This value is indicated with a vertical line in Figure 6a; a more fragile liquid has smaller at 1.25 Tg. (Many measures of fragility have been proposed to capture, in a single parameter, the profile of thermal excitation in the Angell plot. The m index is the slope of the Angell plot at Tg; the F1/2 metric describes the temperature increase needed to reach a fixed relaxation time ( = 1 s). Our measure is analogous to F1/2; it is chosen so that the value is easily read off from the Angell plot and has a large dynamic range.) Notice a strong correlation in Figure 6b between the Ds values (solid circles) and fragility: Ds at Tg decreases with decreasing fragility (increase of  at 1.25 Tg). This trend holds for all the systems for which Ds has been measured, over 4 orders of magnitude of change in Ds. For comparison, Figure 6b also shows the Dv data where available.20,21,22,23,45,46 For SiO2, Tg is taken to be 1480 K.47 Note a slight increase of Dv at Tg with increasing fragility, which likely reflects the breakdown of the Stokes-Einstein relation in fragile glassformers.21 The empirical relation between fragility and Ds is consistent with our result on polyalcohols and other reports in the literature. According to their viscosities at 1.25 Tg, maltitol and sorbitol are stronger liquids than the other systems whose Ds has been measured; they are expected to have slower surface diffusion. Extrapolating the available data, we obtain Ds ≈ 10-18 m2/s for maltitol and sorbitol at Tg (open symbols in Figure 6b), in agreement with the upper bound from this study, 10-16.4 m2/s. Similarly, the strong liquid SiO2 is expected to have slow surface diffusion, which agrees with the finding of Roder et al.11 (even though their simulations were limited to relatively high levels of mobility). To the extent that surface diffusion is needed 13 ACS Paragon Plus Environment


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

Page 14 of 31

for the formation of stable glasses by vapor deposition, our present study of a relation between fragility and surface diffusion can draw on the continuing work on the relation between fragility and a liquid’s ability to form stable glasses.48,49 For glycerol, slow surface diffusion is predicted on the basis of its low fragility, and this is consistent with the report that glycerol does not form stable glasses by vapor deposition,25 while more fragile systems do under similar conditions.16,17,24 Future work is warranted to test the relation between surface diffusivity and fragility. The existence of such a relation would be highly valuable for predicting the surface mobility of amorphous materials. A noteworthy feature of Figure 6b is that the Ds value decreases so rapidly with decreasing fragility that it is expected to join the Dv curve. It is unclear whether this is a physical scenario; it is likely that Ds approaches Dv but never becomes smaller. In summary, the available data indicate a strong correlation between the dynamic excitation of a glassforming liquid by heating (measured by fragility) and by an environmental change from the bulk to the surface (measured by Ds/Dv). It appears that systems with extensive network bonds (hydrogen bonds in polyalcohols and covalent Si-O bonds in silica) are more resistant to dynamic excitation, either by temperature rise or by the loss of nearest neighbors, than van der Waals systems. Slow Surface Diffusion Correlates with Slow Surface Crystal Growth. Many molecular glasses can grow crystals more rapidly on the free surface than in the interior,7,50,51,52 a result of fast surface diffusion. Given the slower surface

Figure 7. Crystal growth rates of maltitol and IMC. IMC shows fast surface crystal growth (in two polymorphs,  and ), while the process in maltitol is too slow to measure (only 14 an upper bound is given, based on no growth in 61 days). ACS Paragon Plus Environment

Page 15 of 31

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


diffusion of polyalcohol glasses, it is of interest to learn whether their surface crystal growth is also slow. Figure 7 shows the rates of crystal growth in amorphous maltitol. For reference, the data are also shown for IMC to illustrate the behavior of a molecular glass with fast surface diffusion and surface crystal growth. These two systems have nearly the same Tg (317 and 315 K, respectively); their viscosities (shown in Figure 7 using the y axis) almost overlay each other near Tg, as expected. On heating, the viscosity of maltitol decreases more slowly than that of IMC, a feature captured by the  at 1.25 Tg fragility measure but not m. Note that in the bulk, the crystal growth rate ub has the common bell-shaped curve for both systems, peaking near 1.3 Tg. This shape results from a thermodynamic control of the process at high temperatures and a kinetic control at low temperatures. At the same viscosity, the ub of maltitol is roughly 10 times smaller than that of IMC. On the free surface, IMC glasses grow crystals rapidly (us), but the process is much slower in maltitol. In fact, no crystal growth was observed on the surface of a maltitol glass at 313 K by light microscopy in 61 days. This yields an upper bound for us at 10-12.4 m/s, almost 4 orders of magnitude smaller than the us of IMC. In Figure 8, the velocity of surface crystal growth us is plotted against the surface diffusion coefficient Ds. Included are the data on several molecular glasses7,19 and amorphous Si.53 For systems of relatively fast surface diffusion (OTP, NIF, IMC, TNB, and Si), a good correlation is seen between us and Ds. Figure 8 also shows the upper bounds for maltitol’s us and Ds from this work. These limits are roughly consistent with the trend of the previous data. From the estimated Ds of 10-18 m2/s at Tg (Figure 6b), the us is expected to be ~ 10-12.5 m/s, comparable to the upper bound from the direct crystal growth measurement. Figure 8. Correlation between the rates of surface crystal growth and surface diffusion.



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

Page 16 of 31

CONCLUSIONS Surface grating decay has been measured for three organic glasses with extensive hydrogen bonding: sorbitol, maltitol, and maltose. For 1000 nm wavelength surface gratings, the decay occurs by viscous flow in the entire range of temperature studied, covering the viscosity range 105 – 1011 Pa s. Under the same condition, the decay mechanism transitions from viscous flow to surface diffusion for organic glasses that are composed of similarly sized molecules but have no or limited hydrogen bonding. These results indicate that extensive hydrogen bonding slows down surface diffusion in organic glasses. This effect arises because molecules can preserve hydrogen bonding in the surface environment so that the kinetic barrier for diffusion is not reduced in proportion to the loss of nearest neighbors. This picture is consistent with the correlation between liquid fragility and the surface enhancement of diffusion, as both reflect a liquid’s resistance to dynamic excitation. Slow surface diffusion is expected to inhibit any process that relies on surface molecular transport. This work has found that surface crystal growth is very slow in maltitol, consistent with its slow surface diffusion and the trend of the available data on faster surface diffusers (Figure 8). In the formation of stable glasses by vapor deposition,16 it is speculated that newly deposited molecules take advantage of high surface mobility to equilibrate quickly into well-packed structures before being embedded into the bulk. The available results on small-molecule glasses suggest that systems with faster surface diffusion produce more stable glasses by vapor deposition.24 Given the slow surface diffusion of polyalcohols, one would expect difficulty to prepare stable glasses of these molecules by vapor deposition. This appears to be the case based on the recent report25 that vapor deposition of glycerol and other polyalcohols does not produce glasses with enhanced kinetic stability, as measured by increased onset temperature for the glass-to-liquid transition. By inference, formation of stable glasses by vapor deposition would be difficult for network glass-formers like silica. In future work, it is desirable to follow the change of surface diffusivity for a series of molecules in which hydrogen bonding systematically changes. (The hydrogen-bond density in polyalcohol glasses is apparently 16 ACS Paragon Plus Environment

Page 17 of 31

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


too high for us to measure their surface diffusion.) To test the effect of network bonds on surface diffusion, experiments and simulations can be performed to investigate the state of network bonding at surfaces, in reference to van der Waals systems like OTP.

ACKNOWLEDGMENTS. We thank the NSF (DMR-1206724) for supporting this work and Karen Jones, Lei Zhu, Max Purro and Mark Sacchetti for experimental assistance. *Corresponding author: Lian Yu, E-mail: [email protected]. Office phone: +1 608 263 2263.  REFERENCES

(1) Ehrlich, G.; Stolt, K. Surface Diffusion. Annu. Rev. Phys. Chem. 1980, 31, 603 – 637. (2) Seebauer, E. G.; Allen, C. E. Estimating Surface Diffusion Coefficients. Prog. Surf. Sci. 1995, 49, 265 – 330. (3) Sallese, J. M.; Ils, A.; Bouvet, D.; Fazan, P.; Merritt, C. Modeling of the Depletion of the AmorphousSilicon Surface During Hemispherical Grained Silicon Formation. J. Appl. Phys. 2000, 88, 5751 – 5755. (4) Llera-Hurlburt, D.; Dalton, A. S.; Seebauer, E. G. Temperature-Dependent Surface Diffusion Parameters on Amorphous Materials. Surf. Sci. 2002, 504, 244 – 252. (5) Zhu, L.; Brian, C. W.; Swallen, S. F.; Straus, P. T.; Ediger, M. D.; Yu, L. Surface Self-Diffusion of an Organic Glass. Phys. Rev. Lett. 2011, 106, 256103. (6) Brian, C. W.; Yu, L. Surface Self-Diffusion of Organic Glasses. J. Phys. Chem. A 2013, 117, 13303 – 13309. (7) Zhang, W.; Brian, C. W.; Yu, L. Fast Surface Diffusion of Amorphous o-Terphenyl and Its Competition with Viscous Flow in Surface Evolution. J. Phys. Chem. B 2015, 119, 5071 – 5078. (8) Zhang, W.; Yu, L. Surface Diffusion of Polymer Glasses. Macromolecules 2016, 49, 731 – 735. (9) Cao, C. R.; Lu, Y. M.; Bai, H. Y.; Wang, W. H. High Surface Mobility and Fast Surface Enhanced Crystallization of Metallic Glass. Appl. Phys. Lett. 2015, 107, 141606. (10) Boddeker, B.; Teichler, H. Dynamics Near Free Surfaces of Molecular Dynamics Simulated Ni0.5Zr0.5 Metallic Glass Films. Phys. Rev. E 1999, 59, 1948 – 1956. 17 ACS Paragon Plus Environment


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

Page 18 of 31

(11) Roder, A.; Kob, W.; Binder, K. Structure and Dynamics of Amorphous Silica Surfaces. J. Chem. Phys. 2001, 114, 7602 – 7614. (12) Malshe, R.; Ediger, M. D.; Yu, L.; de Pablo, J. J. Evolution of Glassy Gratings with Variable Aspect Ratios Under Surface Diffusion. J. Chem. Phys. 2011, 134, 194704. (13) Haji-Akbari, A.;Debenedetti, P. G. The Effect of Substrate on Thermodynamic and Kinetic Anisotropies in Atomic Thin Films. J. Chem. Phys. 2014, 141, 024506. (14) Sun, Y.; Zhu, L.; Kearns, K. L.; Ediger, M. D.; Yu, L. Glasses Crystallize Rapidly at Free Surfaces by Growing Crystals Upward. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 5990 – 5995. (15) Hasebe, M.; Musumeci, D.; Powell, C. T.; Cai, T.; Gunn, E.; Zhu, L.; Yu, L. Fast Surface Crystal Growth on Molecular Glasses and Its Termination by the Onset of Fluidity. J. Phys. Chem. B 2014, 118, 7638 – 7646. (16) Swallen, S. F.; Kearns, K. L.; Mapes, M. K.; Kim, Y. S.; McMahon, R. J.; Ediger, M. D.; Wu, T.; Yu, L.; Satija, S. Organic Glasses with Exceptional Thermodynamic and Kinetic Stability. Science 2007, 315, 353 – 356. (17) Zhu, L.; Yu, L. Generality of Forming Stable Organic Glasses by Vapor Deposition. Chem. Phys. Lett. 2010, 499, 62 − 65. (18) Wang, L.; Ellison, A. J. G.; Ast, D. G. Investigation of Surface Mass Transport in Al-Si-Ca-Oxide Glasses via the Thermal Induced Decay of Submicron Surface Gratings. J. Appl. Phys. 2007, 101, 023530. (19) Ruan, S.; Zhang, W.; Sun, Y.; Ediger, M. D.; Yu, L. Surface Diffusion and Surface Crystal Growth of tris-Naphthyl Benzene Glasses. J. Chem. Phys. in review. (20) Mapes, M. K.; Swallen, S. F.; Ediger, M. D. Self-Diffusion of Supercooled o-Terphenyl near the Glass Transition Temperature. J. Phys. Chem. B 2006, 110, 507 − 511. (21) Swallen, S. F.; Ediger, M. D. Self-Diffusion of the Amorphous Pharmaceutical Indomethacin near Tg. Soft Matter 2011, 7, 10339 − 10344. (22) Swallen, S. F.; Traynor, K.; McMahon, R. J.; Ediger, M. D. Self-Diffusion of Supercooled trisNaphthylbenzene. J. Phys. Chem. B 2009, 113, 4600 – 4608. (23) Urakawa, O.; Swallen, S. F.; Ediger, M. D.; von Meerwall, E. D. Self -Diffusion and Viscosity of Low Molecular Weight Polystyrene Over a Wide Temperature range. Macromolecules 2004, 37, 1558 – 1564. (24) Whitaker, K. R.; Tylinski, M.; Mathias, A.; Schick, S.; Ediger, M. D. Kinetic Stability and Heat Capacity of Vapor-Deposited Glasses of o-Terphenyl. J. Chem. Phys. 2015, 143, 084511. (25) Capponi, S.; Napolitano, S.; Wübbenhorst, M. Supercooled Liquids with Enhanced Orientational Order. Nature Comm. 2012, 3, 1233. (26) Kasina, A.; Putzeys, T.; Wübbenhorst, M. Dielectric and Specific Heat Relaxations in Vapor Deposited Glycerol. J. Chem. Phys. 2015, 143, 244504. 18 ACS Paragon Plus Environment

Page 19 of 31

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


(27) Nakheli, A.; Elijazouli, A.; Elmorabit, M.; Ballouki, E; Fornazero, J.; Huck, J. The Viscosity of Maltitol. J. Phys.: Condens. Matter 1999, 11, 7977 – 7994. (28) Yoshioka, M.; Hancock, B. C.; Zografi, G. Crystallization of Indomethacin from the Amorphous State Below and Above Its Glass Transition Temperature. J. Pharm. Sci. 1994, 83, 1700-1705. (29) Naoki, M.; Koeda, S. Pressure-Volume-Temperature Relations of Liquid, Crystal, and Glass of oTerphenyl Excess Amorphous Entropies and Factors Determining Molecular Mobility. J. Phys. Chem. 1989, 93, 948 – 955. (30) Plazek, D. J.; Magill, J. H. Physical Properties of Aromatic Hydrocarbons. I. Viscous and Viscoelastic Behavior of 1:3:5Tri-α-Naphthyl Benzene. J. Chem. Phys. 1966, 45, 3038 – 3050. (31) Simon, S. L; Sobieski, J. W.; Plazek, D. J. Volume and Enthalpy Recovery of Polystyrene. Polymer 2001, 42, 2555 – 2567. (32) Mullins, W. W. Flattening of a Nearly Plane Solid Surface due to Capillarity. J. Appl. Phys. 1959, 30, 77 − 83. (33) Alkindi, A. S.; Al-Wahaibi, Y. M.; Muggeridge, A. H. Physical Properties (Density, Excess Molar Volume, Viscosity, Surface Tension and Refractive Index) of Ethanol + Glycerol. J. Chem. Eng. Data 2008, 53, 2793 – 2796. (34) Panzer, J. Component of Solid Surface Free Energy from Wetting Measurements. J. Colloid Interface Sci. 1973, 44, 142 – 161. (35) Andronis, V.; Zografi, G. Molecular Mobility of Supercooled Amorphous Indomethacin, Determined by Dynamic Mechanical Analysis. Pharm. Res. 1997, 14, 410 – 414. (36) Mirigian, S.; Schweizer, K. S. Theory of activated glassy relaxation, mobility gradients, surface diffusion, and vitrification in free standing thin films. J. Chem. Phys. 2015, 143, 244705. (37) Stevenson, J. D.; Wolynes, P. G. On the Surface of Glasses. J. Chem. Phys. 2008, 129, 234514. (38) Fábián, B.; Senćanski, M. V.; Cvijetić, I. N.; Jedlovszky, P.; Horvai, G. Dynamics of the Water Molecules at the Intrinsic Liquid Surface As Seen from Molecular Dynamics Simulation and Identification of Truly Interfacial Molecules Analysis. J. Phys. Chem. C 2016, 120, 8578 – 8588. (39) Sillrén P.; Matic, A.; Karlsson, M.; Koza, M.; Maccarini, M.; Fouquet, P.; Götz, M.; Bauer, Th.; Gulich, R.; Lunkenheimer, P.; et al. Liquid 1-Propanol Studied by Neutron Scattering, Near-Infrared, and Dielectric Spectroscopy. J. Chem. Phys. 2014, 140, 124501. (40) Baldelli, S.; Schnitzer, C.; Shultz, M. J.; Campbell, D. J. Sum Frequency Generation Investigation of Glycerol/Water Surfaces. J. Phys. Chem. B 1997, 101, 4607 – 4612. (41) Oh-e, M.; Yokoyama, H.; Baldelli, S. Structure of the Glycerol Liquid/Vapor Interface Studied by Sum-Frequency Vibrational Spectroscopy. Appl. Phys. Lett. 2004, 84, 4965 – 4967. (42) Plazek, D. J.; Bero, C. A.; Chay, I.-C. The Recoverable Compliance of Amorphous Materials. J. NonCryst. Solids 1994, 172-174, 181 – 190. 19 ACS Paragon Plus Environment


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

Page 20 of 31

(43) Schröter, K.; Donth, E. Viscosity and Shear Response at the Dynamic Glass Transition of Glycerol. J. Chem. Phys. 2000, 113, 9101 – 9108. (44) Urbain, G.; Bottinga, Y.; Richet, P. Viscosity of Liquid Silica, Silicates and Alumino-Silicates. Geochimica et Cosmochimica Acta 1982, 46, 1061 – 1072. (45) Brebec, G.; Seguin, R.; Sella, C.; Bevenot, J.; Martin, J. C. Diffusion Du Silicium Dans La Silice Amorphe. Acta Metallurgica 1980, 28, 327 – 333. (46) Chang, I.; Sillescu, H. Heterogeneity at the Glass Transition: Translational and Rotational SelfDiffusion. J. Phys. Chem. B 1997, 101, 8794 – 8801. (47) Navrotsky, A. Thermochemistry of Crystalline and Amorphous Silica. Rev. Mineral. Geochem 1994, 29, 309 – 329. (48) Chen, Z.; Richert, R. Dynamics of Glass-Forming Liquids. XV. Dynamical Features of Molecular Liquids That Forms Ultra-Stable Glasses by Vapor Deposition. J. Chem. Phys. 2011, 135, 124515. (49) Sepúlveda, A.; Tylinski, M.; Guiseppi-Elie, A.; Richert, R.; Ediger, M. D. Role of Fragility in the Formation of Highly Stable Organic Glasses. Phys. Rev. Lett. 2014, 113, 045901. (50) Zhu, L.; Wong, L.; Yu, L. Surface-enhanced Crystallization of Amorphous Nifedipine. Mol. Pharm. 2008, 5, 921 – 926. (51) Hasebe, M.; Musumeci, D.; Powell, C. T.; Cai, T.; Gunn, E.; Zhu, L.; Yu, L. Fast Surface Crystal Growth on Molecular Glasses and Its Termination by the Onset of Fluidity. J. Phys. Chem. B 2014, 118, 7638 – 7646. (52) Hasebe, M.; Musumeci, D.; Yu, L. Fast Surface Crystallization of Molecular Glasses: Creation of Depletion Zones by Surface Diffusion and Crystallization Flux. J. Phys. Chem. B 2015, 119, 3304 – 3311. (53) Sakai, A.; Tatsumi, T.; Ishida, K. Growth Kinetics of Si Hemispherical Grains on Clean Amorphous-Si Surfaces. J. Vacuum. Sci. Technol. A: Vacuum, Surface, Film 1993, 11, 2950 – 2953.


Page 21 of 31

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


TOC Graphic in actual dimension



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

Page 22 of 31

No hydrogen bonding OTP

TNB

Limited hydrogen bonding IMC

NIF

Extensive hydrogen bonding HO O OH

OH OH OH

HO

HO

OH OH

sorbitol

HO OH O

HO

maltitol

OH OH OH

ACS Paragon Plus Environment

maltose

Page 23 of 31

1

I/I0

265 K

283 K

0.8 0.6 0.4 0.2

Sorbitol λ = 1000 nm

0 1E-3

273 K

1E-1

1E+1

1E+3

1E+5

1E+7

1

I/I0

0.8

338 K

323 K

315 K

0.6 0.4 0.2

Maltitol λ = 1000 nm

0 1E-3

1E-1

1E+1

1E+3

1E+5

1E+7

1E+5

1E+7

1 371 K

396 K

0.8

I/I0

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


0.6 0.4 0.2

Maltose λ = 1000nm

0 1E-3

1E-1

383 K

1E+1

1E+3

t (s)



1

log K (s-1), log Fq (s-1) + C

a

maltitol

sorbitol

0

maltose

-1 -2

Fq

-3

Fq

-4 -5

λ= 1000 nm

-6

Fq

-7 250

270

290

310

330

350

370

390

410

T (K)

b -0.5

-1

-1.5

log K (s-1)

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

Page 24 of 31

maltose, 391 K, slope s = -1.0

-2 -2.5

sorbitol, 278 K, s = -1.0

-3 -3.5

maltitol, 328 K, s = -1.1

-4 2.8

3

3.2 3.4 3.6 3.8

4

4.2

log  (nm)


Page 25 of 31

log K (s‐1), log Fq (s‐1) + C

a

1

OTP PS1.1k

0

PS 1.7k

-1 TNB

-2 -3

Fq

-4 -5 -6 -7

= 1000 nm

-8 200 220 240 260 280 300 320 340 360 380

T (K)

b

1 0

log K (s‐1), log Fq (s‐1) + C

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


= 1000 nm

-1 -2 -3 -4 -5 -6 -7

Fq

NIF IMC

-8 200 220 240 260 280 300 320 340 360 380

T (K)



-9

-10

Ds

-11

-12

log D (m2/s)

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

Page 26 of 31

OTP

TNB

-13

-14

Dv

-15

◇

OTP □ TNB + IMC ● PS1.9k

-16 -17

NIF IMC

-18

PS 1110 PS 1700

-19

-20 -21

-22 0.6

0.7

0.8

0.9

Tg/T


1

1.1

1.2

Page 27 of 31

-6 Binary LJ, A = Ar

-8

-10

log Ds (m2/s)

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


SiO2

-12 -14 -16 -18 -20

ZrNi OTP TNB

Ds = Dv

IMC

polyalcohols upper bound

-22 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6

log Dv (m2/s)



SiO2 glycerol h at 1.25 Tg maltitol sorbitol PS 1.9k IMC TNB strong OTP

12

a 10 log h (Pa s)

8 6 4 2

fragile

0 -2 -4 0.5

0.6

0.7

0.8

0.9

1

Tg/T

b -10 -12 log D at Tg (m2/s)

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

Page 28 of 31

-14 -16 -18

OTP

Ds

TNB NIF IMC PS1.1k PS1.7k

upper bound sorbitol maltitol

Dv

-20 -22

OTP IMC TNB PS1.9k

SiO2

-24 -2 -1 fragile

0

1

2 3 4 5 log h at 1.25Tg (Pa s)

6 7 strong


8

Page 29 of 31

-2

-1

-3

h maltitol

h IMC

-4 IMC

-7

4

us

◆ a IMC □ g IMC

5

-9

ub maltitol

-10 -11 -12 -13

3

6

log η (Pa s)

2

ub

-6

-8

0 1

-5

log u (m/s)

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


7 8

us maltitol upper bound 260

280

300

9 10 320

340

360

380

400

420

T (K)

313 K t0

50 µm

+ 61 days


440


-6

OTP NIF alpha IMC gamma IMC Silicon TNB

-7 -8

log us (m/s)

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

Page 30 of 31

-9 -10 -11 -12

↓ us upper bound

maltitol

-13 -19

-18

-17

←Ds upper bound -16

-15

-14

log Ds (m2/s)


-13

-12

-11

Page 31 of 31

TOC Graphic, High Resolution Image

-6 Binary LJ, A = Ar

-8 -10

log Ds (m2/s)

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


SiO2

-12 -14 -16 -18 -20

ZrNi

OTP TNB

IMC polyalcohols upper bound

Ds = Dv

-22 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6

log Dv (m2/s)


Hydrogen Bonding Slows Down Surface Diffusion of Molecular

Recommend Documents