Thermodiffusion of nanoparticles in waterand the thermal boundary conditionso of solid-liquid interfacesDavid CahillShawn Putnam, Zhenbin Ge,Profs. Paul Braun, Gerard WongCenter of Advanced Materials for the Purification ofWater with Systems,Frederick Seitz Materials Research Laboratory,Department of Materials Science,University of Illinois, Urbana, IL, USA
Outline• Motivation• Micron-scale beam deflection apparatus– short digression on thermal conductivity of particlesuspensions• Thermodiffusion of charged particles in water– thermoelectric fields in electrolytes– temperature dependence of the Soret coefficient• Thermal conductance of solid-liquid interfaces– Transient adsorption and time-domainthermoreflectance– Hydrophilic and hydrophobic interfaces• Summary and questions
An idea: Probe thermodynamics of aqueousinterfaces through a transport measurementAnderson, Ann. Rev. Fluid Mech. 21 66-99(1989), building on work by Derjaguiny = distance normal to theparticle surface• In electrophoresis, we probethe charge distribution ib ti in h(y) = the excess enthalpy perthe double-layer.• In the Seebeck coefficient ofa crystal, we probe the Λ = thermal conductivity ofentropy of the charge liquid (l) and particle (p)carriers.h(y) = the excess enthalpy perunit volume of the fluid createdby the presence of the particle
Build on our extensive experience with the“3ω method” for thermal conductivityHeater line separation:2a ≈ 25 μmHeater line width:2b ≈ 7 μmPutnam and Cahill, RSI (2004)
Measurement of optical beam deflectionSmall length scales increases frequency scales butmay be introducing low-frequency noise due to √Nfluctuations in the number of particles in the probevolume.
Solve heat diffusion equation andoptical beam deflection in the frequency domainthermo-opticcontribution fromglass slide andliquidthermodiffusionPutnam and Cahill, RSI (2004)
Also an excellent method for measuring heatdiffusion in liquidsRaw data for ethanolChange in thermalconductivity upon addingwater to ethanolSymmetric effectivemedium theoryPutnam and Cahill, JAP (2006)
Reports of anomalous (wrong?) thermalconductivity of nanoparticle suspensions!!effective medium limititKeblinski et al., Materials Today(2006)
• 4 nm diameter Au inethanol functionalizedby 11-mercapto-1-undecanol (MUD)• 2 nm diameter Au intoluene functionalizedby dodecanethiol• fullerene mixture ofC 60 -C 70 in tolueneMeasure three types ofnanoparticle suspensionsNull result(No observable thermodiffusion in these samples)Putnam and Cahill, JAP (2006)
Back to thermodiffusion• Commercially supplied d=26 nm polystyrene latexspheres, COOH functionalityFit one freeparameter:S T = -0.30 K -1 •102 wt% PS spheres/H 2 O
Survey of Interfacial Dynamics Corp.polystyrene latex suspensions (2%)New experiment sopick the sample withthe largest signal forfurther study (perhapsa poor choice inhindsight).Putnam and Cahill, Langmuir (2005)
Add buffer, vary ionic strengthcitric Acid pH ≈ 3.3; CAPS pH ≈ 10.526 nm polystyrene latex(TEA=tetraethylammonium)Putnam and Cahill, Langmuir (2005)
Temperature gradients separate cations andanions and produce an electric-fieldData from Snowden and Turner, Trans. Farad. Soc. (1960)See also more thorough treatments:Würger, PRL (2008)Rasuli et al., PRL (2008)Morthamus, et al., EPJ E (2008)Würger, Langmuir (2009)
Electrophoresis driven by thermallygenerated fields might even be usefulMeasured:Thermoelectric fields areon the order of k B /e, asin semiconductors,∼10 -4 V/K
Cleaner experiment: dialyze, no buffers,focus on LiCl electrolytesWeak dependence onparticle concentrationLiCl I=2 mMAre thermoelectric fieldsunimportant here?High concentration LiClelectrolyte quenchesthermodiffusion
Unfortunately, the 26 nm particlesare somewhat anomalous• Improved cell tocontrol temperatureand suppressconvection.I∼1 mM• Temperaturedependence of 26 nmpolystyrenelatexdiffers from theothers samples.Putnam and Cahill, Langmuir (2007)
Mutant variants of lysozyme provide a uniqueway of controlling the charge of a “nanoparticle”• T4 bacteriophage lysozyme kindly supplied by Dr. LoriSanders and Prof. Gerard Wong.• Hydrodynamic diameter is 3.6 nm, smaller compared toDebye lengths of 5-12 nm.Note we did not adjust ionic strengthto a common value; ;perhaps p a badchoice in hindsight
S T does not seem to depend on charge• Temperaturedependence of S T isapproximately thesame as forpolystyrene latex.• Thermoelectric fieldsso no seem to play animportant role in thisregime of low ionicstrength : the particlecharge is + forlysozyme and – forlatexPutnam and Cahill, Langmuir (2007)
What mechanism creates the strongtemperature dependence?• Thermodiffusion is probably driven by a combinationof mechanism.• Importance of the thermal expansion of solvent hasbeen discussed, see, e.g., Iacopini et al., EPJ E(2006), Brenner, PRE (2006)ST≈DsD βcD s = solvent self diffusivityD c = particle concentration diffusionβ = thermal expansion coefficient ofthe solvent
ST≈What mechanism creates the strongtemperature dependence?DsDβc• D s /D c ∼20 forlysozyme; y ∼400 forlargest latex particles.• In both cases, thismechanism is a factorof 3-to-4 too small toexplain the data.• Is that t close enough?waterΔβ≈300 ppm/K
Interface thermal conductance• Thermal conductivity Λ is a property of thecontinuum• Thermal conductance (per unit area) G is aproperty of an interface
Factor of 60 range at room temperatureAu/surfactant/waterPMMA/Al 2 O 3nanotube/alkane
Time domain thermoreflectance since 2003• Improved optical design• Normalization by out-of-phase signal eliminatesartifacts, increases dynamicrange and improvessensitivity• Exact analytical model forGaussian beams andarbitrary layered geometries• One-laser/two-colorapproach tolerates diffusescatteringClone built at Fraunhofer Institute forPhysical Measurement, Jan. 7-8 2008
Solid-liquid interfaces: Two approaches• Transient optical absorption of nanoparticles andnanotubes in liquid suspensions.– Measure the thermal relaxation time of a suddenlyheat particle. Interface sensitive if the particle issmall enough.– limited to interfaces that give good stability of thesuspension, e.g., hydrophilic particles in H 2 O• Time-domain thermoreflectance of thin planar Aland Au films.– heat flows both directions: into the fluid and intothe solid substrate.
Hydrophilic metal nanoparticles:4 nm diameter Au:Pd nanoparticles in watertransient absorption data∆αl (ppm)2 8G = ∞(a)71G = 2.0×10 8HS(CH 2 ) 11OEG401 10 100t(ps)OH4∆αl (ppm)6543210G = ∞G = 1.8×10 8SHO(b)NHCOHOTiopronin1 10 100t (ps)Ge et al., JPC B (2004)
777777Nanoparticle summaryIn waterIn TolueneOOH4OOH4OOH OH OHO O4Br Br BrN N NHNOHNOSSN N NSS SSBr Br BrSSG ~ 200 MW m -2 K -1G ~ 15 MW m -2 K -1Ge et al., JPC B (2004)
Application of this data: Criticalparticle radius for a suspension• Interface conductance and thermal conductivityof the fluid determine a critical particle radiusr c = Λ/G• For particles in water, r c = 3 nm.• For high thermal conductivity particles, dilutelimit of effective medium theoryr >> r cr
Thermoreflectance of solid/H 2 O interfaceshydrophobic50 MW/m 2 -Kno waterhydrophilichili100 MW/m 2 -KGe et al., PRL (2006)
Thermoreflectance of solid/H 2 O interfaces• Experiments contain many interfaces and layersso look at the difference in the conductancecreated by changing from hydrophobic tohydrophilic.• Define Kapitza length, equivalent thickness ofwater: h =Λ/G– Au/hydrophobic h = 12 nm– Au/hydrophilic h = 6 nm• Difference Δh=6 nm
Summary• At high ionic strength, thermodiffusion of charged particlesin water is driven by thermoelectric fields.– This might be useful for generating small electric fields.• Mechanisms driving thermodiffusion at low ionic strength arestill unclear (at least to me).– Rule out thermoelectric fields at low ionic strength (?).– At high temperatures, enthalpy of dielectric in an electric fieldgives the right magnitude but lysozyme does not show theexpected dependence on zeta-potential. (Theory is incomplete?Experiments are incorrect?)– Temperature dependence of thermodiffusion is stronger thanpredicted by the thermal expansion of water.• Kapitza lengths for hydrophilic interfaces are on the order ofa few nm. For sufficiently small nanoparticles, even highthermal conductivity particles behave as thermal insulators.
Some questions• What is the temperature dependence of thethermoelectric voltage?– Is there a convenient way to measure these smallfields directly?• Could we advance the subject using “pressuretuning”of thermodiffusion, i.e., hydrostatic pressureup to ∼1 GPa?• How can we experimentally explore the role ofparticle thermal conductivity and interface thermalconductance on the thermodiffusion i ofnanoparticles?
Backup slide—comparisons to theorieslysozyme90 nm latexPutnam and Cahill, Langmuir (2007)