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Andrew Ylitalo1, Huikuan Chao1,2, Thomas Fitzgibbons3, James Griffith3, Valeriy Ginzburg2, Weijun Zhou3, Ernesto Di Maio4, Zhen-Gang Wang1, and Julie Kornfield1

1Caltech, Pasadena, CA; 2Dow, Inc., Midland, MI; 3Dow, Inc., Lake Jackson, TX, 4Università degli Studi di Napoli Federico II, Naples, Italy

In collaboration

with the University

of Naples

Federico II

This material is based upon

work supported by the National

Science Foundation Graduate

Research Fellowship under

Grant No. DGE‐1745301

This project is

supported by the

Dow University

Partnership Initiative

Adams, L.L.A. “Physics in Drops”

100 μm

Cao, X. et al. 2005, Polymer 46, 775-783

500 μm

Haji-Akbari, scholar.princeton.edu

1. Nucleation

2. Growth &

Coalescence

3. Solidification

Nucleation is most difficult to measure

- Stochastic

- Occurs in milliseconds

- Nanometer length scales

Xu , X. et al. 2013, Soft Matter, 9, 9675-9683Kim, Park, Chen, and Thompson, 2011, Soft Matter, 7(16):7351

CNT

SCFT

𝑁𝑢𝑐𝑙𝑒𝑎𝑡𝑖𝑜𝑛𝐵𝑎𝑟𝑟𝑖𝑒𝑟[𝑘

𝐵𝑇]

𝑅𝑎𝑑𝑖𝑢𝑠 [𝑅𝑔]

Comparison of Self-consistent Field Theory

(SCFT) and Classical Nucleation Theory (CNT)

10

5

0

-5

-10

0 0.2 0.4 0.6 0.8 1 1.2

Disagreement in Theoretical Models

Increasing Bubble Nucleation Important to Reduce

Thermal Conductivity of Polyurethane Insulating FoamsNanofoam

10-100 nm per cell

Best insulation

(Knudsen regime)

Microfoam

10-1000 um per cell

Minimizes radiative

heat transfer

“Macro”foam

Cells ~ 1-10

mm

.

10 um

1 um

50 um:

Goal for PU

Insulating Foams

Model System

Polyol-CO2

Polyurethane Foaming Reaction

Urea

500 μm

Cao, X. et al. 2005, Polymer 46, 775-783

www.zhilint.com/polyol.html

Struts slow IR: More bubbles = more struts

Empirical Parameters

Ni = beads per chain

σi =bead diameter

εi = energy parameter

kij = aijT + bij energy

modification for beads of

different chemical species

ULJ(rij)

1 2

3

…… N

σ

1 2

polyol

CO2

PC-SAFT and other

model development

performed by Dr.

Huikuan Chao @ Caltech

J. Gross & G. Sadowski, Ind. Eng. Chem. Res. 2001

X. Xu, et al., JCP 2012

Modeling of Bubble Nucleation Requires Equilibrium

and Interfacial Properties

CO2-rich

Polyol-richPhase 1

Phase 2Interface

Parent

Phase

Nucleating

Phase

-3 -2 -1 0 1 2 3z [nm]

0

0.1

0.2

0.3

0.4

0.5

rs

3

PMMACO

2

Measure Solubility and Specific Volume to Fit PC-SAFT Material Parameters

Using Gravimetry-Axisymmetric Drop-shape Analysis (G-ADSA)

Atmosphere

1 mm

𝑉𝑑𝑟𝑜𝑝𝑎𝑡𝑚

Buoyancy correction to weight from CO2

= 𝜌𝐶𝑂2(𝑉𝑠𝑎𝑚𝑝𝑙𝑒,0 + 𝑽𝒔𝒘𝒆𝒍𝒍 + 𝑉𝑐𝑟𝑢𝑐𝑖𝑏𝑙𝑒)

G-ADSA

developed by

Prof. Ernesto Di

Maio

U. Naples

Federico II

Sapphire window allows

camera to film pendant drop

55 bar 𝑉𝑑𝑟𝑜𝑝

Polyurethane foam

is not too different

from the crust of a

pizza, a Neapolitan

creation and classic

(Ciro Cascella,

Naples, Italy)

Measurements by Dr. Jacob Crosthwaite @ Dow, Midland and

Andy Ylitalo & Prof. Ernesto Di Maio @ U. Naples

CO2 Solubility in

PPG, 1000 g/mol

1 2 3 4 5

0.05

0.10

0.15

0.20

Wt.

fra

c.

CO

2(w

/w)

Pressure (MPa)

T = 30.5 C

60 C

Interfacial Tension

PPG, 1000 g/mol

Pendant-drop measurements by Andy Ylitalo &

Prof. Ernesto Di Maio @ U. Naples

Exp.

Theory

Exp.

Theory

26 mm (63 bar)

No bubbles

40 mm (51 bar)

Small bubbles58 mm (35 bar)

Bubbles coalesce

48 mm (44 bar)

Bubbles grow

90 mm (8 bar)

Continuous foam

85 bar,

psat 72 bar

100 um

Outer

stream

(polyol)

Inner

stream

(polyol

-CO2)

Observation

capillary

Barrier = 43 kBT, Rcrit = 3.5 nm

Barrier = 21 kBT, Rcrit = 2.5 nm

𝑃𝑖𝑛 = 85 𝑏𝑎𝑟

Δ𝑃

Distance x

Δx

Poiseuille Flow𝑑𝑃

𝑑𝑥=

8 𝜇 𝑣

𝜋𝑅4 𝑄𝑑𝑃

𝑑𝑥Δx

𝑃𝑜𝑢𝑡 = 0.1 𝑏𝑎𝑟

0.1 bar

Based on Hessberger et al., J. Mater. Chem.

C, 2016, 4, 8778

Outer stream

Inner Stream

Outer Stream

X-rays,

Visible,

IR

Inner Capillary

Observation Capillary

Detector/

Microscope

Inner stream in inner capillary 20–50 μm

ID = 500 μm

Predicting Effect of “C5” on

Bubble NucleationVerify Equilibrium Properties Predicted by PC-SAFT Model with Gas Chromatography (GC)

15% Liquid

(Polyol + C5)

85% Vapor

(C5)

Exp. (liq)

Exp.

(headspace)

Exp.

Est. comp.

in ParrTheory

Exper.PC-SAFT

(polyol; 3-

phase)

Theory (c5;

3-phase)

Theory (co2; 3-

phase)

PC-

SAFT

(liq)

Theory (vap)

Theory

(liq)

Infer a 3rd, C5-rich

phase by mass

balance on

measured

compositions from

top and bottom of

Parr reactor

15-20% Liquid

(Polyol + C5 + CO2)

80-85% Vapor

(C5 + CO2)

Sample

Headspace

with GC

Aerosolize

volatiles in

liquid phase

Sample

with GC

Add CO2 Add CO2

𝑔

𝑔

References

*Seeing initial nuclei requires X-rays (prelim. work at Argonne not shown)

mm

ms

𝒗 = 𝟏𝒎/𝒔𝟏𝒎𝒔 → 𝟏𝒎𝒎

Implementation for High-pressure Foaming

Experiment Theory

Rcrit

Barrier

Microfluidic

Hydrodynamic-focusing:

A “Film Reel” of Bubble

Nucleation

“HPLIS”

Initial Setup

(0.01 MPa)2.2 MPa, 37 C 7.5 MPa, 37 C

Ternary Phase Diagrams with Measured

and Predicted Compositions

*Internship at Dow, Lake Jackson, TX

9/19-10/19

Bubble volume

Nu

cle

atio

n e

ne

rgy b

arr

ier

Increasing C5Predicted Nucleation Barrier by

String Method Model Based on PC-

SAFT Parameters Validated by GC

Measurements Above

1) Increasing C5 reduces nucleation

barrier dramatically (4x)

2) Above threshold C5, nucleation

occurs in two steps: liquid-liquid

separation followed by vaporization

Instrument Development for “Seeing” Bubble Nucleation

Like a movie editor with a film reel, we

can scrutinize each moment of bubble

nucleation as long as desired

Linear pressure drop is predictably

governed by Poiseuille flow since

flow behavior is dominated by an

incompressible outer stream

Re << 1 due to microfluidic

dimensions ensures laminar flow at

constant velocity, ensuring the

nucleation time is proportional to

distance along the channel

Future quantitative experiments will

be used to validate predictions

based on string method

Purely schematic. Not to scale

Outer stream

“ensheathes” inner stream

Initially developed to watch protein folding with x-

rays, hydrodynamic-focusing effectively creates a

“film reel” of fast (~millisecond) kinetics along the

physical length of a microfluidic channel.

Here, the inner stream of interest passes through

a tee junction from within a small capillary. The

outer stream ensheathes this capillary and, later,

the inner stream, protecting it from the effects of

the walls of the channel, essential for preventing

premature bubble nucleation.

Apparatus

High-pressure

vessel maintains

CO2 atmosphere

Different methods predict vastly different nucleation energy barriers 𝛥𝑊 (and

nucleation rate ∝ 𝑒𝛥𝑊/𝑘𝐵𝑇), but experiments to validate them are lacking

Oil bath

maintains

temperature

Add CO2

Pendant drop is used to

measure interfacial tension

CO2 swells polyol drop,

measure swelling volume

Swelling volume is used to

calculate buoyancy

correction to MSB to

estimate density,

solubility, and diffusivity

Magnetic Suspension Balance

(MSB) measures weight

Fit Parameters of

PC-SAFT Model to

Solubility

Measurements

Use linear regression on

PC-SAFT parameters

𝑁, 𝜎, 𝜖, 𝑘 to fit solubility

measurements for each

polyol for different p, T Pressure (MPa)

Inte

rfa

cia

l te

nsio

n (

mN

/m)

Validate DFT Model

Against Measured

Interfacial TensionPredictions of interfacial

tension by DFT model

using PC-SAFT

parameters are consistent

with experimental

measurements, supporting

the validity of this model

Alberto Giacomello et al. PNAS 2016;113:3:E262-E271

Schematic

Diagram of

String Method

Adjust “String”

to Minimize

Nucleation

Barrier

Nucleation:

String

Method

Equilibrium

Behavior:

PC-SAFT

Interfacial

Properties:

DFT

Pass Parameters

Assumes

homogeneous

phases in

equilibrium

Models molecules

as chains of beads

with Lennard-Jones

interactions

polyol

CO2

z (nm)* Dashed lines indicate bulk densities from PC-SAFT calculations

De

nsity (

be

ad

s/𝜎

3)

DFT Predicts CO2

Aggregation Along InterfaceThe string method calculates the energy

landscape as a bubble grows based on DFT,

then perturbs the nucleation pathway to find

the lowest energy barrier

Calculate Energy

Landscape

ABC

D

AB

CD

250 um:

Current minimum

for PU Insulating

Foams

Appl.: freezers

30x

CO2 drives

much of foam

expansion

Still makes a

reasonable foam!

Polymer Foams Undergo 3 Stages: Nucleation is Least Understood

Conclusions: Technical• Models based on PC-SAFT and DFT predict interfacial properties essential for

bubble nucleation models in agreement with measurements

• Preliminary results from microfluidic hydrodynamic-focusing suggest novel

method for measuring bubble nucleation to validate string method predictions

• Experiments support accuracy of extension of model to ternary system; model

predicts substantial reduction in bubble nucleation with addition of C5

• The Kornfield group has supported my collaboration with leading scientists

within Caltech and around the world (U. Naples, Dow, and Argonne)

• Collaboration with industry (Dow) connected me with over a dozen industrial

experts to design unique instrumentation for fundamental scientific study

• Theory and experiment beautifully support each other when done in parallel

1. Pastore Carbone, Di Maio, Iannace, and Mensitieri, Simultaneous experimental evaluation of solubility, diffusivity,

interfacial tension and specific volume of polymer/gas solutions, 2011, Polymer Testing, 30, 303-309

2. Xu, Cristancho, Costeux, and Wang, Bubble nucleation in polymer-CO2 mixtures, 2013, Soft Matter, 9, 9675-9683

3. Pollack, Tate, Darnton, Knight, Gruner, Eaton, and Austin, Compactness of the denatured state of a fast-folding protein

measured by submillisecond small-angle x-ray scattering, 1999, Biophysics, 96, 10115-10117

Conclusions: Personal

Polystyrene-CO2 Foaming:

String Method with DFT

Dip tube

2.2 MPa, 37 C 7.5 MPa, 37 C

High-speed micrographs of observation capillary

For Polyurethane Foam, “More” Means “Less”:

Adding “C5” Dramatically Reduces Nucleation Barrier of CO2