P

Na

b

a

ARRAA

KPKISA

1

rmitetipb

itiwstatbsco

0d

Applied Surface Science 262 (2012) 19– 23

Contents lists available at SciVerse ScienceDirect

Applied Surface Science

j our nal ho me p age: www.elsev ier .com/ loc ate /apsusc

rotein adsorption kinetics from single- and binary-solution

aris Barnthipa,∗, Erwin A. Voglerb

Division of Physics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathum Thani 12110, ThailandDepartments of Materials Science and Engineering and Bioengineering, The Pennsylvania State University, PA 16802, USA

r t i c l e i n f o

rticle history:eceived 13 July 2011eceived in revised form 4 December 2011ccepted 4 December 2011vailable online 13 December 2011

a b s t r a c t

Comparison of protein mass-adsorption-rates to rates-of-change in interfacial tensions reveals that massadsorption is decoupled from interfacial energetics. This implies that energy-barrier theories describingprotein-adsorption kinetics do not accurately capture the physics of the process. An alternative paradigmin which protein molecules rapidly diffuse into an inflating interphase which subsequently slowly shrinksin volume, concentrating adsorbed protein and causing slow concomitant decrease in interfacial tensions,

eywords:rotein adsorptioninetics

nterphaseurfacedsorption competition

is shown to be consistent with adsorption kinetics measured by solution depletion and tensiometry. Massadsorption kinetics observed from binary-protein solution is compared to adsorption kinetics from single-protein solution, revealing that organization of two different-sized proteins within the interphase canrequire significantly longer than that adsorbed from single-protein solution and may require expulsionof initially adsorbed protein which is not observed in the single-protein case.

© 2011 Elsevier B.V. All rights reserved.

. Introduction

One of the more interesting and important outcomes of recentesearch into protein-adsorption kinetics is that the rate-of-ass-adsorption is significantly faster than the rate-of-change in

nterfacial energetics [1]. This finding alerts us that the conven-ional understanding of adsorption kinetics could be significantly inrror as applied to large molecules such as proteins. Furthermore,his new knowledge could revolutionize the way those involvedn biomaterials surface science conceive of the protein-adsorptionrocess that is so fundamental to understanding mechanisms ofiocompatibility [2].

It is evident from the literature that we have changed our think-ng about the fundamental aspects adsorption kinetics a number ofimes [3]. In the early 1900s it was thought that adsorption kinet-cs was diffusion controlled [4]. Later, it was shown that diffusion

as far too fast to limit mass transport and control the observedlow rates-of-change in the interfacial tension of surfactant solu-ions [5,6]. By the late 1980s, various kinetic theories positingn energy barrier to adsorption came forward [7–10], explaininghat diffusion toward a freshly created interface was indeed fastut that the rate at which solute crossed from an imaginary sub-

urface region into the interface was slow, accounting for slowhange in interfacial energetics. Perhaps the most advanced versionf these energy-barrier theories is that of Varoqui and Pefferkorn

∗ Corresponding author. Tel.: +66 25494186/+66 814206611; fax: +66 25494187.E-mail addresses: naris.bt@gmail.com (N. Barnthip), eav3@psu.edu (E.A. Vogler).

169-4332/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.apsusc.2011.12.014

[10] who combined Fick’s law with the notion of a semi-reflectingenergy barrier. A reflecting plane was envisioned to reside belowthe authentic interface that increasingly retarded passage of soluteinto the interface as it became increasingly populated with solutemolecules diffusing in from bulk solution against a concentrationgradient. In this way, concentration-dependent adsorption kineticswas accommodated by phenomenological rate equations.

Thus the basic paradigm of adsorption arising from energy-barrier theories is that of interfacial tension changing as a functionof time as solute adsorbs to the interface as a function of time. Insharp contrast, recent work by Clark et al. using a modified reso-nant microbalance method [1] experimentally demonstrates thatproteins arrive at the interface quickly relative to slower change ininterfacial tensions. It is apparent that another change in the waywe think about protein-adsorption kinetics is required. Althoughchange in paradigm is sometimes disconcerting, a new approachto adsorption kinetics relieves us of certain conceptual difficultiesabout the surface region that accompany energy-barrier theories.Notably in this latter regard, it is not clear why a semi-reflectingplane and an interfacial plane do not together constitute an inter-phase similar to that employed by Gibbs [11] and Guggenheim [12]in development of surface thermodynamics. And it is not clear whymolecules collected at a semi-reflecting plane do not qualify asadsorbed from solution and do not contribute to decay in interfacialtensions.

The fundamental equilibrium adsorption equation for a twocomponent system consisting of solvent “1” and solute (pro-tein) “2” according to either Gibbs or Guggenheim [13] statesthat d� = − [� 2 − (nB,2/nB,1)� 1]d�2, where � is interfacial tension

2 d Surf

(otbiataatd(srsaipacAo

tiicwt[qfbaofibows

2

eps[6GspdasBoatprrpaL

0 N. Barnthip, E.A. Vogler / Applie

ergs/cm2 = mJ/m2), � ≡ (nI/A) measures the number of moles of 1r 2 within the interphase nI per-unit-area (moles/cm2), and nB ishe mole number within bulk solution. The subscripts B and I trackulk solution and interphase, respectively. Evidentially, change

n � is an explicit function of solute chemical potential �2, notbsolute adsorbed mass per se. That is to say, interfacial tensionracks solute concentration within the interphase. In fact, therere three ways interphase concentration can increase: (i) totaldsorbed mass within a fixed interphase volume can increase, (ii)he interphase volume containing a fixed total adsorbed mass canecrease, or (iii) both (i) and (ii) can simultaneously occur. Optioni) is effectively the old paradigm of adsorption kinetics: masslowly accumulates at the interface (a pseudo-two-dimensionalegion with fixed volume) and causes decrease in interfacial ten-ions. Option (ii) is consistent with the new finding that massdsorption is much faster than change in interfacial tension becauset does not insist that mass-adsorption rates are directly cou-led to rates-of-change in interfacial tensions. Rather, option (ii)llows for rapid accumulation of protein mass and subsequentoncentration of this mass in a decreasing interphase volume.nd of course option (iii) is not viable if option (i) does notccur.

An alternative paradigm of protein adsorption arising fromhese considerations is that of protein rapidly diffusing into annflating interphase volume which subsequently slowly decreasesn volume, increasing interphase protein concentration and con-omitantly causing decrease in interfacial tensions [3,14]. Hereine test this idea using an electrophoretic implementation of

he venerable solution-depletion method of measuring adsorption15–18]. Use of electrophoresis as a multiplexing separation anduantification tool permitted us to measure kinetics of adsorptionrom single- and binary-protein solutions to the same hydropho-ic adsorbent surface. Results are completely consistent with thislternative paradigm, leading us to conclude that the initial ratef protein adsorption is indeed diffusion controlled but that thenal concentration of protein within the interphase is controlledy slow reorganization of the interphase region. Reorganizationf the interphase region has profound consequences in the casehen two proteins participate in adsorption competition to the

ame adsorbent surface.

. Materials and methods

Both materials and methods applied in this work have beenxtensively described elsewhere [3,14–18]. Briefly for the pur-oses of this report, adsorption of five different proteins weretudied singly and in pairs at different solution concentrations3,14]: ubiquitin (Ub), 10.7 kDa; human serum albumin (HSA),6.3 kDa; prothrombin (FII), 72 kDa; human immunoglobulin type

(IgG), 160 kDa; and fibrinogen (Fib), 341 kDa. These proteins wereelected to provide a broad range in size. Proteins were prepared inhosphate buffer saline solution (PBS, at pH 7.4 prepared from pow-er as received from Sigma in 18 m� distilled/deionized water from

Millipore Simplicity ion-exchange unit). Both hydrophobic octylepharose (OS, Octyl Sepharose Fast Flow Adsorbent, Amershamiosciences) and hydrophobic glass particles (Sigma) silanized withctadecyltricholorosilane (OTS, Sigma) were used as adsorbentsnd found to give essentially identical results. SDS-PAGE elec-rophoresis was carried out using 26 lane NuPage Novex tris-aceaterecast gels (Invitrogen) stained with SimplyBlue Safestain (Invit-ogen) according to manufacturer’s directions. Band intensity was

ead on a Gel–doc system (Bio-Rad Labs). A standard curve wasrepared for each protein and each gel using the first 6–8 lanes bypplying solutions of known concentration of each probe protein.inear calibration curves were obtained within the concentration

ace Science 262 (2012) 19– 23

range of interest that permitted estimation of unknown proteinconcentrations.

Computational and statistical methods have been welldescribed in refs. [3,14–18]. Again briefly for the purposes of thisreport, solution depletion Di = (W0

Bi− WBi

) in mg/mL bulk solution

was the experimental parameter, where W0Bi

is the initial proteinconcentration before contact with adsorbent and WBi

is the solutionconcentration measured at time t, both in mg/mL. The subscript itracks protein identity and used to differentiate from a second pro-tein j used in binary-protein-adsorption studies. Binary mixtureswere differentiated from single mixtures using an i, j subscript as in,for example, (W0

B )i,j

referring to the total binary-protein concentra-tion prepared by combining protein i and protein j in a mixture. Theabsolute adsorbed mass mi = DiVB in mg, where the bulk solutionvolume VB = 30 �L in this work.

3. Results

3.1. Adsorption isotherms by solution depletion

The solution depletion has been used to collect adsorptionisotherms of many different proteins and protein mixtures formany different surface types embracing a wide range of sur-face chemistries and water wetting characteristics [3,14–21].Results obtained are consistent with that obtained by tensiometry[22–27] and quartz-crystal microbalance (QCM) [21]. These adsorp-tion isotherms approximate a Henry isotherm wherein adsorbedamount is in direct proportion to solution concentration W0

Biup

to a maximum solution depletion (Di)max obtained at a particu-lar solution concentration (W0

Bi)max

at which the adsorbent surfacearea is saturated with protein. We have implemented the solutiondepletion method using spectroscopy [19,20] for single-proteinsolutions or electrophoresis for single- or binary-protein solutions[3,14–18].

The solution depletion method of measuring adsorption frombinary-protein solution is complicated by the fact that there aretwo broad categories of adsorption competition falling into 5 sep-arate cases that can be studied [14]. The first category consists of asingle experimental situation termed Case 1 in which total binary-mixture concentration is insufficient to saturate the adsorbentsurface. The second category consists of four different experimen-tal situations termed Cases 2–5 in which the total-mixed-solutionconcentration is sufficient to saturate the adsorbent surface thatcan be obtained by combining i, j proteins at different concentra-tions relative to that required to saturate the adsorbent surface areawith either pure i or pure j. Case 5 differed from surface-saturatingCases 2–4 in that both competing proteins were mixed at solutionconcentrations well in excess of the amount needed to saturateavailable adsorbent. At least one of the competing proteins wasat under-saturating solution concentration in Cases 2–4. We haveextensively tested each of these conditions with proteins listed inSection 2 [14] but disclose results herein for Case 5 for i = FII andj = Fib which has not been illustrated previously.

3.2. Adsorption from single-protein solution

Fig. 1 collects adsorption kinetics measured by the solution-depletion method for HSA adsorbing to hydrophobic OS adsorbentat five different initial solution concentrations W0

Bi(3.9, 3.2, 2.4, 1.6,

and 0.8 mg/mL) corresponding to the five solution-depletion levels

indicated by right-hand annotations running from top-to-bottomof Fig. 1, respectively. There was no detectable adsorption kineticsover the 5–90 min timeframe studied for any of the solution con-centrations. Similar results were obtained for the other proteins

N. Barnthip, E.A. Vogler / Applied Surface Science 262 (2012) 19– 23 21

2.5

2.0 2.01 ±0.43 mg/ml

1.5

1.75 ±0.25 mg/ml

Dep

letio

n (m

g/m

l)

1.01.18 ±0.26 mg/ml

0.96 ±0.15 mg/ml

0.5 0.44 ±0.11 mg/ml

60005000400030002000100000.0

Time (seconds)

Fig. 1. Mass-adsorption kinetics of human serum albumin (HSA) adsorbing tohydrophobic octyl sepharose adsorbent particles. Similar adsorption kinetics wereobserved for hydrophobized glass particles. The ordinate plots amount of HSAadsorbed as the depletion Di = (W0

Bi− WBi

) in mg/mL bulk, where W0Bi

is the ini-

tial protein concentration before contact with adsorbent and WBiis the solution

concentration measured at time t, both in mg/mL. The subscript i tracks proteinidentity and used to differentiate from a second protein j used in binary-protein-adsorption studies (see Fig. 2). Di listed on the right-hand axis correspond to fivedifferent initial solution concentrations W0

Bi(3.9, 3.2, 2.4, 1.6, and 0.8 mg/mL read-

ing top-to-bottom), respectively, with listed error representing mean and standarddeviation of the individual time points. Lines through the data represent mean solu-te

mcesuc[

3

t

W

bbebAs6

tutlStdIFbtmuft

3.5 max( )jD Fib

3.0

inflection line

2.5State 2

2.0 ( )i, jDmax( )iD FII

1.5

State 1

( )i i, jD

Dep

letio

n (m

g/m

l)

0.5

1.0

Time (minutes )

100806040200

j

Fig. 2. Adsorption competition between prothrombin (FII) and human fibrinogen(Fib) for the same hydrophobic octyl sepharose adsorbent under Case 5 adsorptioncondition (Section 2) in which both FII and Fib are at solution concentrations capableof individually and collectively saturating the adsorbent surface. Similar adsorptionkinetics were observed for hydrophobized glass particles. Two adsorption regimeswere observed: a supersaturated State 1 over the time range 5 ≤ t ≤ 60 min followedby a final State 2 over the time range 70 ≤ t ≤ 90 min with a transition centeredat 60 min lasting for about 20 min. Horizontal dashed lines indicate the solutiondepletions (Dmax

i)FII and (Dmax

j) obtained from single-protein solution at the same

concentration used in the adsorption-competition experiment. Notice that moreFII was adsorbed in State 1 from binary-protein solution than from single-protein

experimental conditions. This observation is entirely consistent

ion depletion. Error bars are calculated from calibration curves used to translatelectrophoresis-band intensity to solution concentrations.

entioned in Section 2 (not shown) [3,14]. These kinetics wereompared to slow change in interfacial energetics of adsorption toither the hydrophobic buffer–air (liquid–vapor, lv) or hydrophobicolid–liquid (sl) interfaces lasting between 30 and 60 min observedsing time- and concentration-dependent interfacial tensions andontact angles for these same proteins at similar concentrations22–27].

.3. Adsorption from binary-protein solution

Fig. 2 compiles adsorption kinetics observed with two pro-eins (i = FII, closed circles, W0

Bi= 6 mg/mL; j = Fib, open circles,

0Bi

= 7 mg/mL) competing from the solution for the same adsor-ent surface under Case 5 conditions specified in Section 2 withoth i, j proteins mixed in binary-solution at concentrations inxcess of that required to saturate the adsorbent surface indicatedy dashed horizontal lines annotated either (Dmax

i)FII or (Dmax

i)Fib.

pseudo-steady-state 1 was observed which was followed by alow transition to a final state 2, with an inflection half-time of0 min.

It was observed that less Fib was adsorbed from the binary mix-ure in State 1 than was adsorbed from single-protein solutionnder identical conditions (vertical arrow pointing downward fromhe (Dmax

j) dashed line lines on the left side of the vertical inflection

ine). By contrast more FII was adsorbed from the binary mixture intate 1 than was absorbed from single-protein solution under iden-ical conditions (vertical arrow pointing upward from the (Dmax

j)FII

ashed line lines on the left side of the vertical inflection line).n the State 1 → State 2 transition, initially adsorbed mass of bothib and FII was desorbed from the adsorbent surface as indicatedy decreasing solution depletion (increasing bulk solution concen-ration). Less of both Fib and FII were adsorbed from the binary

ixture in State 2 than absorbed from single-protein solutions

nder identical conditions (vertical arrows pointing downwardrom the (Dmax

j)Fib and (Dmax

j)FII dashed lines on the right side of

he vertical inflection line).

solution whereas less Fib was adsorbed in State 1 from binary-protein solution thanfrom single-protein solution. Transition to State 2 involved expulsion of both FII andFib initially adsorbed in State 1.

4. Discussion

4.1. Adsorption from single-protein solutions

It has been well established from tensiometric studies thatinterfacial tensions and contact angles of protein solutions slowlydecrease with time (see, as examples, refs. [22–29] and citationstherein). Kinetics for larger proteins are observed to be slower thanfor smaller proteins. Drops of protein solution held either pendanton a needle or placed on an adsorbent surface are usually stagnant,except in the first moments of creation of the interface, so thatmass transfer is not affected by stirring. Accordingly, slow changein interfacial tensions and contact angles in the hour timeframehave been interpreted to be due to slow arrival at, and adsorptionto, the interface (either liquid–vapor or solid–liquid; see furtherSection 1).

Adsorption studies carried out by solution-depletion can mimicconditions employed in tensiometry by mixing protein solutionswith adsorbent, leaving adsorbent and solution unmixed there-after. Except for the initial mixing in the first few moments of theexperiment, mass transfer is unassisted by mixing. Alternatively,the solution-depletion experiment can be performed with continu-ous mixing. In either event, mixed or not mixed, no mass adsorptionkinetics can be detected within the 5 ≤ t ≤ 90 min timeframe acces-sible to solution depletion as implemented in our experimentalprogram [3,15–18] for adsorption from single-protein solution. Sta-tistically flat kinetics are obtained for a wide range of proteins anddifferent hydrophobic adsorbents, like that shown in Fig. 1.

Quite evidentially, factors influencing rates-of-change in inter-facial energetics are not the same as those influencing massadsorption. Mass adsorption is prompt whereas change in inter-facial tensions and contact angles is far slower under similar

with those by made Clark et al. mentioned in Section 1 using athird kind of experimental technique. Collectively, these observa-tions are inconsistent with the adsorption paradigm evolved from

2 d Surf

esiqdidcb

4

s[iccf[tfocii

arbpSais

tw[tsaol

ssdatmoplitt

4

ppoor

2 N. Barnthip, E.A. Vogler / Applie

nergy-barrier theories that attempt to reconcile fast diffusion withlow change in interfacial tensions. A new adsorption paradigmn which protein diffuses into an inflating interface which subse-uently slowly shrinks in volume is consistent with the observedecoupling of mass adsorption and change in interfacial energet-

cs. A slowly shrinking interphase captures adsorbed protein in aecreasing volume which increases interphase concentrations andauses concomitant change in interfacial energetics, as anticipatedy the standard adsorption equation mentioned in Section 1.

.2. Adsorption from binary-protein solution

Measurement of adsorption of two-or-more proteins to theame adsorbent surface by tensiometry is not generally possible28] but can be achieved using the solution-depletion methodmplemented with electrophoresis as a separation and quantifi-ation tool [14,17]. This work is tedious because at least twoategories of relative protein concentration consisting of five dif-erent cases must be studied to obtain a comprehensive picture14]. The first category embraces all combinations of i, j proteinshat neither separately nor collectively saturate the adsorbent sur-ace. The second category embraces combinations that separatelyr collectively saturate the adsorbent surface. Among the four casesomprising this second category, the case when either-and-both, j proteins saturate the adsorbent surface is perhaps the mostnteresting and informative about the protein-adsorption process.

Fig. 2 shows that two pseudo-steady state adsorption regimesre obtained. The State 1 interphase is super-saturated with proteinelative to the final State 2 obtained within 90 min. State 1 is unsta-le and slowly decays to a State 2 by expelling initially adsorbedrotein. Interestingly, more FII is adsorbed from binary solution intate 1 than adsorbed from single-protein solution and less Fib isdsorbed than from single-protein solution. Less of both proteinss adsorbed in State 2. The transition between State 1 and State 2 islow, lasting for more than 20 min.

Interestingly, unlike results obtained with single-protein solu-ion discussed in Section 4.1, continuous mixing binary solutionith adsorbent strongly affects adsorption outcomes (not shown)

14]. We find that mixing prevents or significantly delays theransition between State 1 and State 2, apparently favoring theuper-saturated State 1. We infer from this observation that proteindsorbed in the State 2 interphase is a more organized collectionf proteins than State 1 and that mixing prevents or delays estab-ishment of organized adsorbed protein layer(s).

In this latter regard, it has been shown that a relativelytraightforward sphere-packing model of protein adsorbed fromingle-protein solution predicts measurements by both solutionepletion and QCM with almost analytical accuracy [21]. Proteinsdsorb into one or two layers depending on size, with larger pro-eins requiring two square-or-hexagonally packed layers. This in

ind, we speculate that proteins of a single size can promptlyrganize into the interphase and concentrate within that inter-hase by expulsion of interphase water but not adsorbed protein,

eading to the flat kinetics observed in Fig. 1. By contrast, find-ng the most efficient packing of two dissimilar proteins requiresime and the expulsion of initially adsorbed protein, leading to thewo-adsorption states observed in Fig. 2.

.3. Implications for biomaterials surface science

The overall paradigm of protein adsorption from multiple-rotein solutions evolving from this work is that of individual

roteins diffusing into an inflating interphase against individual (aspposed to collective) concentration gradients. The interphase canver fill very rapidly from concentrated (mg/mL) protein solutionselative to a final steady-state and can remain in this overfilled

ace Science 262 (2012) 19– 23

condition under conditions of flow, apparently indefinitely.Adsorption specificity from binary protein solution appearsto be related to relative diffusion rates and concentra-tions. In fact, adsorption specificity predicted by the classicalStokes–Einstein–Sutherland (SES) equation varies systematicallyfrom experimental measurements [14], suggesting that a modifiedSES equation taking into account changes in diffusivity due tocrowding within the interphase could predict protein-adsorptionspecificity, although this yet remains to be demonstrated.

This new paradigm is quite different than the popular concept ofselective protein adsorption due to differential adsorption affinitiesof different proteins for a particular adsorbent surface. However,it is important to stress that this work is restricted to the firsthours of contact of an adsorbent with relatively simple solutionsof one or two purified proteins containing no other entities such asbiological cells. Extrapolation to long term adsorbent contact withcomplex biological milieu such as occurs in clinical applications ofbiomaterials or civil-engineering applications of materials in theenvironment should be made with great caution.

5. Conclusions

The experimental observation that mass-adsorption kineticsare decoupled from rates-of-change in interfacial tensions impliesthat energy-barrier theories are inadequate to describe protein-adsorption kinetics. An alternative paradigm in which proteinmolecules rapidly diffuse into an inflating interphase which subse-quently slowly shrinks in volume concentrating adsorbed proteinand causing slow concomitant decrease in interfacial tensions isconsistent with adsorption kinetics measured by solution depletionand tensiometry. Mass adsorption kinetics observed from binary-protein solution is much more complex than from single-proteinsolution but can be explained with the same basic adsorptionparadigm. The primary difference between adsorption from single-and binary-protein solutions is that the organization of two differ-ent sized proteins within the interphase can require significantlylonger and may require expulsion of initially adsorbed protein.

Acknowledgments

This work was supported, in part, by the Office of the HigherEducation Commission, the Office of National Research Council ofThailand. NB appreciates additional support from the Division ofPhysics, Faculty of Science and Technology, Rajamangala Univer-sity of Technology Thanyaburi. Thailand. EAV appreciates supportfrom the National Institutes of Health grant PHS 2R01HL069965,and the Departments of Materials Science and Engineering andBioengineering, Pennsylvania State University, USA.

References

[1] A.J. Clark, A. Kotlicki, C.A. Haynes, L.A. Whitehead, A new model of proteinadsorption kinetics derived from simultaneous measurement of mass loadingand changes in surface energy, Langmuir 23 (2007) 5591–5600.

[2] D.F. Williams, On the mechanisms of biocompatibility, Biomaterials 29 (2008)2941–2953.

[3] N. Barnthip, H. Noh, E. Leibner, E.A. Vogler, Volumetric interpretation of pro-tein adsorption: kinetic consequences of a slowly concentrating interphase,Biomaterials 29 (2008) 3062–3074.

[4] S.R. Milner, On the surface concentration and the formation of liquid films,Philos. Mag. 13 (1907) 96–110.

[5] S. Ross, The change of surface tension with time. I. Theories of diffusion to thesurface, J. Am. Chem. Soc. 67 (1945) 990–994.

[6] A.F.H. Ward, L. Tordai, Time-dependence of boundary tensions of solutions I.

The role of diffusion in time-effects, J. Chem. Phys. 14 (1946) 453–461.

[7] A.F.H. Ward, L. Tordai, Time-dependence of boundary tensions of solutions,Recueil 71 (1952) 572–584.

[8] A.F.H. Ward, L. Tordai, Existence of time-dependence for interfacial tension ofsolutions, Nature (1944) 146–147.

d Surf

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

N. Barnthip, E.A. Vogler / Applie

[9] P. Schaff, P. Dejardin, Coupling between interfacial protein adsorption and bulkdiffusion. A numerical study, Colloids Surf. 24 (1987) 239–247.

10] R. Varoqui, E. Pefferkorn, Adsorption kinetics at a plane interface: the excludedsurface effect, J. Colloid Interface Sci. 109 (1986) 520–526.

11] J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Dover Publications, NewYork, 1961.

12] E.A. Guggenheim, Thermodynamics: An Advanced Treatment for Chemists andPhysicists, 5th ed., Wiley, New York, 1967.

13] R. Aveyard, D.A. Haydon, An Introduction to the Principles of Surface Chemistry,Cambridge University Press, London, 1973.

14] N. Barnthip, P. Parhi, A. Golas, E.A. Vogler, Volumetric interpretation of proteinadsorption: kinetics of protein–adsorption competition from binary solution,Biomaterials 30 (2009) 6495–6513.

15] H. Noh, E.A. Vogler, Volumetric interpretation of protein adsorption: partitioncoefficients, interphase volumes, and free energies of adsorption to hydropho-bic surfaces, Biomaterials 27 (2006) 5780–5793.

16] H. Noh, E.A. Vogler, Volumetric interpretation of protein adsorption:mass and energy balance for albumin adsorption to particulate adsor-bents with incrementally increasing hydrophilicity, Biomaterials 27 (2006)5801–5812.

17] H. Noh, E.A. Vogler, Volumetric interpretation of protein adsorption: com-petition from mixtures and the Vroman effect, Biomaterials 28 (2007)405–422.

18] H. Noh, E.A. Vogler, Volumetric interpretation of protein adsorption:

ion-exchange adsorbent capacity, protein pI, and interaction energetics, Bio-materials 29 (2008) 2033–2048.

19] P. Parhi, A. Golas, N. Barnthip, E.A. Vogler, Volumetric interpretation of proteinadsorption: capacity scaling with adsorbate molecular weight and adsorbentsurface energy, Biomaterials 30 (2009) 6814–6824.

[

[

ace Science 262 (2012) 19– 23 23

20] P. Parhi, A. Golas, E.A. Vogler, Role of water and proteins in the attachmentof mammalian cells to surfaces: a review, J. Adhes. Sci. Technol. 24 (2010)853–888.

21] P. Kao, P. Parhi, A. Krishnan, H. Noh, W. Haider, S. Tadigadapa, D.L. Allara, E.A.Vogler, Volumetric interpretation of protein adsorption: interfacial packingof protein adsorbed to hydrophobic surfaces from surface-saturating solutionconcentrations, Biomaterials 32 (2010) 969–978.

22] A. Krishnan, J. Sturgeon, C.A. Siedlecki, E.A. Vogler, Scaled interfacial activityof proteins at the liquid–vapor interface, J. Biomed. Mater. Res. 68A (2004)544–557.

23] A. Krishnan, C. Siedlecki, E.A. Vogler, Traube-rule interpretation of proteinadsorption to the liquid–vapor interface, Langmuir 19 (2003) 10342–10352.

24] A. Krishnan, A. Wilson, J. Sturgeon, C.A. Siedlecki, E.A. Vogler, Liquid–vaporinterfacial tension of blood plasma, serum and purified protein constituentsthereof, Biomaterials 26 (2005) 3445–3453.

25] A. Krishnan, Y.-H. Liu, P. Cha, D.L. Allara, E.A. Vogler, Interfacial energetics ofglobular-blood protein adsorption to a hydrophobic surface from aqueous-buffer solution, J. R. Soc. Interface 3 (2006) 283–301.

26] A. Krishnan, Y.-H. Liu, P. Cha, D.L. Allara, E.A. Vogler, Scaled interfacial activityof proteins at a hydrophobic solid/aqueous-buffer interface, J. Biomed. Mater.Res. 75A (2005) 445–457.

27] P. Cha, A. Krishnan, V.F. Fiore, E.A. Vogler, Interfacial energetics of proteinadsorption from aqueous buffer to surfaces with varying hydrophilicity, Lang-muir 24 (2008) 2553–2563.

28] A. Krishnan, C.A. Siedlecki, E.A. Vogler, Mixology of protein solutions and theVroman effect, Langmuir 20 (2004) 5071–5078.

29] A. Krishnan, Y.-H. Liu, P. Cha, D.L. Allara, E.A. Vogler, Interfacial energetics ofblood plasma and serum adsorption to a hydrophobic self-assembled mono-layer surface, Biomaterials 27 (2006) 3187–3194.