a study on the ion dynamics of polyelectrolyte hydrogels and their...

A study on the ion dynamics of polyelectrolyte hydrogels and their application for soft

robotsCurrent Status of Structural Materials

Advisor: Jeong-Yun SunPresenter: Hyeon-Uk Na

Ph.D StudentMulti-Functional Soft Materials LaboratoryDept. of Materials Science and Engineering

Seoul National Univeristy

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Polyelectrolyte hydrogels

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Polyanionic Polycationic

Three dimensional networks forming by polymer chains with fixed charge and mobile counter ions

Multi-Functional Soft M

aterials Laboratory

Electro-active hydrogels

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• Electrical fields in aqueous solutions induce actuation by re-distribution of ions.

• Easily bend and fold to make versatile motion.

ACS Appl. Mater. Interfaces 2018, 10, 21, 17512-17518

Soft Matter, 2014, 10, 1337–1348


aterials Laboratory

Conventional mechanism for electroactuation

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𝜋𝜋 = 𝑅𝑅𝑅𝑅∑𝑖𝑖(𝐶𝐶𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − 𝐶𝐶𝑖𝑖𝑠𝑠𝑠𝑠𝑔𝑔)

𝜋𝜋1 < 𝜋𝜋2Bend toward anode

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(+) (-)

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𝜋𝜋1 𝜋𝜋2

Polyanionic


aterials Laboratory

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Electroactuation of polyelectrolyte hydrogels

Various types of electroactuation

In the system the current flows through polyelectrolyte hydrogels,the gel can swell and shrink depending on the concentration of solution in anode side


aterials Laboratory

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Electroactuation of polyelectrolyte hydrogel

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20 Vx10 (+) (-)

In low concentration electrolyte solution,the polyelectrolyte hydrogel bend toward anode


aterials Laboratory

In high concentration electrolyte solution,the polyelectrolyte hydrogel bend toward cathode

20 V, 1.1A x10

20 Vx10 (+) (-)

Expansion

System for reversible electroactuation

1 M PSPA

(+) (-)

Salt bridge1 M PAAm (0.01M LiCl, NaCl, KCl)

High concentration electrolyte solution(3 M LiCl, NaCl, KCl)

Salt bridge1 M PAAm (3 M LiCl, NaCl, KCl)

Low concentration electrolyte solution(0.01 M LiCl, NaCl, KCl)

50𝝁𝝁m VHB


aterials Laboratory

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□(Left) / 0.005 M (Right) – 3 min0.005 M / 0.005 M 0.05 M / 0.005 M 3 M / 0.005 M0.5 M / 0.005 M

Expansion near anode Shrinkage near anode

Concentration of solution in anode side determine the bending direction

Dependence of the concentration of electrolyteM

ulti-Functional Soft Materials Laboratory

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3 M (Left) / □(Right)3 M / 0.005 M 3 M / 0.05 M 3 M / 3 M3 M / 0.5 M

Curvature increase

Concentration of solution in cathode side affects the rate of actuation

Dependence of the concentration of electrolyteM


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Assumption

1) When ion migrate into hydrogels by electric field, hydrated ion carries water molecules into the hydrogel.

2) Hydration number of ion differs depending on the concentration

Li+ Na+ K+

Hydration number

2-22 2-13 1-6

전기화학, 제 2판, 2014, 오승모


aterials Laboratory

Dependence of the type of electrolyte


Hydrated lithium ion Hydrated sodium ion Hydrated potassium ion

Li+ Na+


aterials Laboratory

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0.00

15.00

30.00

45.00

60.00

Weight change ratio (%)

Li

Na

K

0.00

0.04

0.08

Curvature (mm-1)

Li

Na

K

n=3 n=3

Li Na K

Atomic weight : Li < Na < KWeight change : Li > Na > K

Hydrated ion weight : Li > Na > K

10mA, 60 s


aterials Laboratory

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Calculation of hydration number of each ion

Equation

(𝑚𝑚𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑚𝑚𝑠𝑠𝑜𝑜𝑜𝑜𝑖𝑖 ) ∗ (𝑁𝑁𝑜𝑜𝑡𝑡𝑡𝑠𝑠𝑜𝑜𝑔𝑔𝑡𝑖𝑖 ) = ∆𝑚𝑚𝑔𝑔𝑔𝑔𝑔𝑔𝑖𝑖

{(들어가는수화이온질량)− (나가는수화이온질량)} ∗ (젤을통과한이온의개수) = 젤의질량변화

Li Na K TPB

Hydrationnumber

5203 5140 4880 6672

The hydration number calculated was too large to consider the electroactuation mechanism as hydrated ion migration


aterials Laboratory

13

0.000

0.020

0.040

0.060

0.080

Curvature (mm-1)

Li

Na

K

0

15

30

45

60

75


Li

Na

K

0

15

30

45

60

75


Li

Na

K

0.000

0.020

0.040

0.060

0.080

Curvature (mm-1)

Li

Na

K


Comparison between free swelling and electroactuation

Absence of voltage source, 60s With voltage source, 10 mA, 60s

20% increase

50% increase

Free swell accounts for a large proportion of electroactuation.Electroactuation mechanism can be considered as osmosis, a mechanism of free swell.


aterials Laboratory

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Kinetics of polyelectrolyte free swellingM


• 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝑒𝑒𝐶𝐶𝑒𝑒𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑓𝑓𝐶𝐶𝑓𝑓 𝑚𝑚𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝑓𝑓 𝑔𝑔𝐶𝐶𝑔𝑔• 𝑁𝑁𝐶𝐶𝑁𝑁𝐶𝐶𝐶𝐶𝐶𝐶𝑁𝐶𝐶 𝑔𝑔𝑒𝑒𝑁𝑁 𝐶𝐶𝑓𝑓 𝑚𝑚𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑁𝑁𝑤𝐶𝐶𝑔𝑔𝐶𝐶 𝐶𝐶𝐶𝐶𝑢𝑢𝐶𝐶𝑓𝑓𝑔𝑔𝐶𝐶𝐶𝐶𝐶𝐶𝑔𝑔 𝑒𝑒 𝐶𝐶𝑚𝑚𝑒𝑒𝑔𝑔𝑔𝑔 𝑢𝑢𝐶𝐶𝑓𝑓𝐶𝐶𝑓𝑓𝑚𝑚𝑒𝑒𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝑒𝑒𝑔𝑔 𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶

𝑢𝑢𝑓𝑓𝑒𝑒𝑔𝑔 𝑓𝑓𝐶𝐶𝑓𝑓𝑓𝑓𝐶𝐶 𝑔𝑔𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓𝑒𝑒𝐶𝐶𝐶𝐶𝑢𝑢 𝑏𝑏𝑏𝑏 𝐶𝐶𝑤𝐶𝐶 𝑓𝑓𝑔𝑔𝐶𝐶𝐶𝐶𝑢𝑢 𝐶𝐶𝐶𝐶 𝐶𝐶𝑤𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝑁𝑁𝐶𝐶𝑓𝑓𝑛𝑛

𝜌𝜌 𝜕𝜕2𝑜𝑜𝜕𝜕𝑜𝑜2

= 𝛻𝛻 � �𝜎𝜎 − 𝑓𝑓 𝜕𝜕𝑜𝑜𝜕𝜕𝑜𝑜

• 𝐹𝐹𝐶𝐶𝑓𝑓 𝑤𝐶𝐶𝑔𝑔𝑤𝐶𝐶𝑓𝑓 𝑓𝑓𝑓𝑓𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶, 𝑓𝑓𝐶𝐶𝑓𝑓 𝑒𝑒𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓 − 𝑢𝑢𝑒𝑒𝑚𝑚𝑑𝑑𝐶𝐶𝑢𝑢 𝑚𝑚𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝑓𝑓 𝐶𝐶𝑤𝐶𝐶 𝑔𝑔𝐶𝐶𝑔𝑔 → 𝜌𝜌 𝜕𝜕2𝑜𝑜𝜕𝜕𝑜𝑜2

= 0

𝛻𝛻 � �𝜎𝜎 = 𝑓𝑓 𝜕𝜕𝑜𝑜𝜕𝜕𝑜𝑜

15



• 𝑆𝑆𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓 �𝜎𝜎 𝐶𝐶𝐶𝐶 𝑓𝑓𝐶𝐶𝑔𝑔𝑒𝑒𝐶𝐶𝐶𝐶𝑢𝑢 𝐶𝐶𝐶𝐶 𝐶𝐶𝑤𝐶𝐶 𝑢𝑢𝐶𝐶𝐶𝐶𝑑𝑑𝑔𝑔𝑒𝑒𝑓𝑓𝐶𝐶𝑚𝑚𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝑓𝑓 𝐶𝐶 𝐶𝐶𝐶𝐶 𝐶𝐶𝑤𝐶𝐶 𝑓𝑓𝐶𝐶𝑔𝑔𝑔𝑔𝐶𝐶𝑁𝑁𝐶𝐶𝐶𝐶𝑔𝑔 𝑁𝑁𝑒𝑒𝑏𝑏

𝜇𝜇: 𝐶𝐶𝑤𝐶𝐶𝑒𝑒𝑓𝑓 𝑚𝑚𝐶𝐶𝑢𝑢𝐶𝐶𝑔𝑔𝐶𝐶𝐶𝐶,𝐾𝐾:𝐵𝐵𝐶𝐶𝑔𝑔𝑛𝑛 𝑚𝑚𝐶𝐶𝑢𝑢𝐶𝐶𝑔𝑔𝐶𝐶𝐶𝐶 𝐶𝐶𝑓𝑓 𝐶𝐶𝐶𝐶𝐶𝐶𝑁𝑁𝐶𝐶𝑓𝑓𝑛𝑛

𝛻𝛻 � �𝜎𝜎 = 𝑓𝑓 𝜕𝜕𝑜𝑜𝜕𝜕𝑜𝑜

16



• 𝐼𝐼𝐶𝐶 𝐶𝐶𝑤𝐶𝐶 𝑓𝑓𝑒𝑒𝐶𝐶𝐶𝐶 𝐶𝐶𝑓𝑓 𝐶𝐶𝑤𝐶𝐶 𝐶𝐶𝑁𝑁𝐶𝐶𝑔𝑔𝑔𝑔𝐶𝐶𝐶𝐶𝑔𝑔 𝐶𝐶𝑓𝑓 𝑒𝑒 𝐶𝐶𝑑𝑑𝑤𝐶𝐶𝑓𝑓𝐶𝐶𝑓𝑓𝑒𝑒𝑔𝑔 𝑔𝑔𝐶𝐶𝑔𝑔

𝐶𝐶 𝒓𝒓, 𝐶𝐶 = 𝐶𝐶 𝑓𝑓, 𝐶𝐶 𝒓𝒓/𝑓𝑓

𝜎𝜎𝑡𝑡𝑡𝑡 = 𝐾𝐾 +4𝜇𝜇3

𝑢𝑢𝐶𝐶𝑢𝑢𝑓𝑓 + 2(𝐾𝐾 −

2𝜇𝜇3 )(

𝐶𝐶𝑓𝑓)

𝜕𝜕u𝜕𝜕𝐶𝐶 = 𝑫𝑫

𝜕𝜕𝜕𝜕𝑓𝑓 {

1𝑓𝑓2

𝜕𝜕𝜕𝜕𝑓𝑓 𝑓𝑓

2𝐶𝐶 } 𝑫𝑫 =𝐾𝐾+4𝜇𝜇3𝑓𝑓 : diffusion coefficient of the gel

Displacement of a point in the network from its final equilibrium location after the gel is fully swollen

17



• 𝐼𝐼𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑒𝑒𝑔𝑔 𝑓𝑓𝐶𝐶𝐶𝐶𝑢𝑢𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶

𝑒𝑒𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑒𝑒𝑔𝑔

𝑓𝑓𝐶𝐶𝑔𝑔𝑔𝑔𝑏𝑏 𝐶𝐶𝑁𝑁𝐶𝐶𝑔𝑔𝑔𝑔𝐶𝐶𝐶𝐶

∆𝑒𝑒0𝑓𝑓

𝑒𝑒𝐶𝐶 𝐶𝐶𝐶𝐶𝑚𝑚𝐶𝐶 𝐶𝐶𝐶𝐶(𝑓𝑓, 𝐶𝐶)𝐶𝐶 𝑓𝑓, 0 : 𝑓𝑓 = ∆𝑒𝑒0:𝑒𝑒

• 𝐵𝐵𝐶𝐶𝐶𝐶𝐶𝐶𝑢𝑢𝑒𝑒𝑓𝑓𝑏𝑏 𝑓𝑓𝐶𝐶𝐶𝐶𝑢𝑢𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶

𝐶𝐶𝑤𝐶𝐶 𝐶𝐶𝐶𝐶𝑓𝑓𝑓𝑓𝑒𝑒𝑓𝑓𝐶𝐶 𝐶𝐶𝑓𝑓 𝐶𝐶𝑤𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝑁𝑁𝐶𝐶𝑓𝑓𝑛𝑛 𝑏𝑏𝐶𝐶𝑓𝑓𝐶𝐶𝑚𝑚𝐶𝐶𝐶𝐶 𝑓𝑓𝑓𝑓𝐶𝐶𝐶𝐶

𝜎𝜎𝑡𝑡𝑡𝑡 = 𝐾𝐾 +4𝜇𝜇3

𝑑𝑑𝑜𝑜𝑑𝑑𝑡𝑡

+ 2 𝐾𝐾 − 2𝜇𝜇3

𝑜𝑜𝑡𝑡

= 0 (𝑒𝑒𝐶𝐶 𝑓𝑓 = 𝑒𝑒)

𝐶𝐶 𝑓𝑓, 0 = ∆𝑒𝑒0𝑓𝑓𝑒𝑒 , (𝐶𝐶 = 0)

𝜎𝜎𝑡𝑡𝑡𝑡 = 𝐾𝐾/𝑓𝑓2𝜕𝜕𝜕𝜕𝑡𝑡

𝑓𝑓2𝐶𝐶 = 0 (𝑒𝑒𝐶𝐶 𝑓𝑓 = 𝑒𝑒) 𝜇𝜇



• 𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶

𝐶𝐶 𝑓𝑓, 𝐶𝐶∆𝑒𝑒0

𝐶𝐶𝐶𝐶 𝑒𝑒 𝑓𝑓𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝑔𝑔𝑏𝑏 𝐶𝐶𝑓𝑓𝒓𝒓𝒂𝒂𝑒𝑒𝐶𝐶𝑢𝑢

𝒕𝒕𝝉𝝉

𝐶𝐶𝑓𝑓 𝐶𝐶𝐶𝐶𝑚𝑚𝐶𝐶 𝐶𝐶 𝐶𝐶𝐶𝐶 𝐶𝐶𝑓𝑓𝑒𝑒𝑔𝑔𝐶𝐶𝑢𝑢 𝑏𝑏𝑏𝑏 𝐶𝐶𝑤𝐶𝐶 𝑓𝑓𝑤𝑒𝑒𝑓𝑓𝑒𝑒𝑓𝑓𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓 𝐶𝐶𝐶𝐶𝑚𝑚𝐶𝐶 𝐶𝐶𝑓𝑓 𝐶𝐶𝑁𝑁𝐶𝐶𝑔𝑔𝑔𝑔𝐶𝐶𝐶𝐶𝑔𝑔 𝜏𝜏,the swelling pattern is always the same for any spherical gel

𝐶𝐶 𝑓𝑓, 𝐶𝐶 = −6∆𝑒𝑒0�𝑖𝑖=1

∞−1 𝑖𝑖

𝐶𝐶𝜋𝜋[(𝑋𝑋𝑖𝑖𝑓𝑓𝐶𝐶𝐶𝐶𝑋𝑋𝑖𝑖 − 𝐶𝐶𝐶𝐶𝐶𝐶𝑋𝑋𝑖𝑖)/𝑋𝑋𝑖𝑖2] × exp(−𝐶𝐶2𝐶𝐶/𝜏𝜏),

𝑁𝑁𝑤𝐶𝐶𝑓𝑓𝐶𝐶 𝑋𝑋𝑖𝑖 ≡ 𝐶𝐶𝜋𝜋𝑓𝑓𝑒𝑒

, 𝜏𝜏 ≡ 𝑒𝑒2/𝐷𝐷

19

∆𝑒𝑒 𝐶𝐶 = −𝐶𝐶(𝑒𝑒, 𝐶𝐶)



• 𝑆𝑆𝐶𝐶𝑔𝑔𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶

𝐶𝐶𝑏𝑏𝐶𝐶𝑒𝑒𝐶𝐶𝐶𝐶 𝐷𝐷 (3.2 × 10−7 𝑓𝑓𝑚𝑚2/𝐶𝐶)

Experiment

∆𝑒𝑒 𝐶𝐶 = ∆𝑒𝑒0(6𝜋𝜋2)�𝐶𝐶

−2exp(−𝐶𝐶2𝐶𝐶𝜏𝜏

)

20



• 𝐶𝐶𝐶𝐶𝑚𝑚𝑑𝑑𝑒𝑒𝑓𝑓𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑁𝑁𝐶𝐶𝐶𝐶𝑤 𝐷𝐷 𝐶𝐶𝑏𝑏𝐶𝐶𝑒𝑒𝐶𝐶𝐶𝐶𝐶𝐶𝑢𝑢 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑔𝑔 𝑔𝑔𝑒𝑒𝐶𝐶𝐶𝐶𝑓𝑓 𝑔𝑔𝐶𝐶𝑔𝑔𝑤𝐶𝐶 𝐶𝐶𝑓𝑓𝑒𝑒𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝑔𝑔 𝐶𝐶𝑑𝑑𝐶𝐶𝑓𝑓𝐶𝐶𝑓𝑓𝐶𝐶𝐶𝐶𝑓𝑓𝐶𝐶𝑑𝑑𝑏𝑏

It was shown that concentration fluctuations can be experimentally observed using laser light scattering spectroscopy

T . Tanaka, L. Hocker, and G. B. Benedek, J. Chern. Phys.59, 5151 (1973);J. P. Munch et al., J. Polyrn. Sci. Polyrn. Phys. Ed. 14, 1097 (1976).

Using this method, the measured D was 𝐷𝐷 = 3(±0.5) × 10−7𝑓𝑓𝑚𝑚2/𝐶𝐶𝐶𝐶𝑓𝑓

Well matched with the macroscopic swelling techniques 𝐷𝐷 (3.2 × 10−7 𝑓𝑓𝑚𝑚2/𝐶𝐶)

21

• Apply to polyelectrolyte hydrogels (PSPA 1M spherical hydrogel)

0

1

2

3

4

5

6

7

0 2000 4000 6000

Rad

ius

of gel

(m

m)

Time(sec)

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00 0.2 0.4 0.6 0.8

lnΔa(

t)/Δ

a 0

Scaled time(t/𝜏𝜏 )

0

1

2

3

4

5

6

7

8

0 1000 2000 3000 4000 5000

Rad

ius

of gel

(m

m)

Time(sec)

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00 0.2 0.4 0.6 0.8

lnΔa(

t)/Δ

a0


Sample 1 Sample 2 Sample 3

a = 9.63 mm𝜏𝜏 = 6459.57

D = 1.357 x 10-4 cm2/s

a = 11.35 mm𝜏𝜏 = 7252.364

D = 1.778 x 10-4 cm2/s

0

1

2

3

4

5

6

7

0 2000 4000 6000

Rad

ius

of gel

(m

m)

Time(sec)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6 0.8 1

lnΔa(

t)/Δ

a0


a = 8.94 mm𝜏𝜏 = 5697.996

D = 1.403 x 10-4 cm2/s

𝐷𝐷 (3.2 × 10−7 𝑓𝑓𝑚𝑚2/𝐶𝐶) from uncharged gel


aterials Laboratory

22

Thermodynamics of electroactuationM


• Flory theory (equilibrium volume)

𝜋𝜋𝑖𝑖𝑔𝑔𝑜𝑜𝑛𝑛𝑠𝑠𝑡𝑡𝑛𝑛 𝑉𝑉 + 𝑅𝑅𝑅𝑅�𝑖𝑖

(𝑓𝑓𝑖𝑖𝑔𝑔 − 𝑓𝑓𝑖𝑖𝑠𝑠) = 0

1. Attractive interaction between polymer and solvent2. Network elasticity

Πnetwork 𝑉𝑉 = 0 determines the equilibrium volume of the neutral gel

∆𝜋𝜋 ≡ 𝑅𝑅𝑅𝑅�𝑖𝑖

(𝑓𝑓𝑖𝑖𝑔𝑔 − 𝑓𝑓𝑖𝑖𝑠𝑠)

Since 𝜋𝜋𝑖𝑖𝑔𝑔𝑜𝑜𝑛𝑛𝑠𝑠𝑡𝑡𝑛𝑛 𝑉𝑉 is a decreasing function, if ∆𝜋𝜋 increases, the gel expands.

M. Doi, et al., Macromolecules (1992).23



• Donnan equilibrium

• Charge neutrality

where 𝑓𝑓Cg is the concentration of the dissociated -COO- ions in the gel

• Dissociation equilibria

where 𝑓𝑓M is the concentration of the carboxyl groups in the gel, and 𝐾𝐾g is theirdissociation constant 24



∆𝜋𝜋 ≡ 𝑅𝑅𝑅𝑅�𝑖𝑖

(𝑓𝑓𝑖𝑖𝑔𝑔 − 𝑓𝑓𝑖𝑖𝑠𝑠)

Osmotic pressure map

25



• Diffusion equations

𝐷𝐷A, 𝐷𝐷B : diffusion constantsΨ : nondimensional electric potential

• Time derivative of the charge neutrality conditions

Ion dynamics

𝜕𝜕𝑓𝑓𝐴𝐴𝜕𝜕𝐶𝐶

= 𝐷𝐷𝐴𝐴𝜕𝜕𝜕𝜕𝑥𝑥

(𝜕𝜕𝑓𝑓𝐴𝐴𝜕𝜕𝑥𝑥

+ 𝑓𝑓𝐴𝐴𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥

)

𝜕𝜕𝑓𝑓𝐵𝐵𝜕𝜕𝐶𝐶

= 𝐷𝐷𝐵𝐵𝜕𝜕𝜕𝜕𝑥𝑥

(𝜕𝜕𝑓𝑓𝐴𝐴𝜕𝜕𝑥𝑥

− 𝑓𝑓𝐵𝐵𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥

)

�𝑖𝑖

𝜕𝜕𝜕𝜕𝑥𝑥

𝜕𝜕𝑓𝑓𝑖𝑖𝜕𝜕𝑥𝑥 + 𝑧𝑧𝑖𝑖𝑓𝑓𝑖𝑖

𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥 = 0

𝐽𝐽 = 𝐶𝐶�𝑖𝑖

𝜕𝜕𝜕𝜕𝑥𝑥

𝜕𝜕𝑓𝑓𝑖𝑖𝜕𝜕𝑥𝑥 + 𝑧𝑧𝑖𝑖𝑓𝑓𝑖𝑖

𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥

The electric current 𝐽𝐽 is constant. 26



Ion dynamics

• Boundary condition at gel-solution boundary

• Donnan condition

𝑓𝑓𝑖𝑖𝑔𝑔𝑓𝑓𝑖𝑖𝑠𝑠

= exp −𝑧𝑧𝑖𝑖 𝜕𝜕𝑠𝑠 − 𝜕𝜕𝑔𝑔 for i = A, B

𝐷𝐷𝑖𝑖𝜕𝜕𝑐𝑐𝑖𝑖𝑠𝑠𝜕𝜕𝑥𝑥

+ 𝑧𝑧𝑖𝑖𝑓𝑓𝑖𝑖𝑠𝑠𝜕𝜕𝜓𝜓𝑠𝑠𝜕𝜕𝑥𝑥

= 𝐷𝐷𝑖𝑖𝜕𝜕𝑐𝑐𝑖𝑖𝑔𝑔𝜕𝜕𝑥𝑥

+ 𝑧𝑧𝑖𝑖𝑓𝑓𝑖𝑖𝑔𝑔𝜕𝜕𝜓𝜓𝑔𝑔𝜕𝜕𝑥𝑥

for i = A, B

• Continuity in the ionic currents

27



Numerical simulation

The gel is placed between the electrodes, sufficiently separated from them

ci(x,t)

Equilibrium volume

Osmotic pressure map

28



Apply to closed system

1 M PSPA

(+) (-)

Salt bridge1 M PAAm (0.01M LiCl, NaCl, KCl)

High concentration electrolyte solution(3 M KCl)

Salt bridge1 M PAAm (3 M LiCl, NaCl, KCl)

High concentration electrolyte solution(3M KCl)

50𝝁𝝁m VHB

1M PSPA hydrogel was fully swollen in 3 M KCl solution

0.5 A, 300 s 29



Apply to closed system

As-prepared Fully swollen in 3 M KCl After electroactuation0.5 A, 300s

1cm 1cm 1cm

30

Local actuation

31

Condition : 20 V, 3 min

Only when the PAAc face up to anode, electroactuation occur.

PAAm(neutral)

PAAc(polyanionic)

(+) (-) (+) (-)

Before AfterAfter

(+) (-) (+) (-)

Single component PAAm/PAAc bilayerPAAc PAAm


aterials Laboratory

PAAc PAAm PAAcPAAm

Diffusion-patterned hydrogel

b

Semi-permeable membrane

15 min

Diffusion time

2 h

0.005 M (Left) / 3 M (Right) 3 M (Left) / 3 M (Right)

− +

PAAcPAAm

Actuation 1 Actuation 2As fabricated

+ −


aterials Laboratory

32

3D printed hydrogel

33

Electro-active hydrogel Electro-active hydrogel

DLP 3D printing

Adhesion

Electro-activehydrogel hemisphere

Inactive hydrogel printed on hemisphere


aterials Laboratory

electrode

object

Polyanion hydrogel

Polycation hydrogel

Electrolyte of high concentration

Electrolyte of low concentration

( + )

( - )

( - )

( + )

Soft convey sheet

34

Polyanionic hydrogel

Polycationic hydrogel

electrode

Upright Left Right Forward Backward

Polyanionic - swell shrink - -

Polycationic - - - swell shrink

Pneumatics + Electroactuation


aterials Laboratory

35

Summary• Various types of electroactuation M


• Analysis for electroactuation

• Free swell accounts for a large proportion of electroactuation.• Electroactuation mechanism can be considered as osmosis, a mechanism of free swell• Force balance between osmotic pressure and frictional force can explain fast swelling rate

of polyelectrolyte hydrogel• Thermodynamics of electroactuation including osmotic pressure and ion dynamics could

explain the direction of bending in equilibrium state.• However, it does not explain the shrinkage of polyelectrolyte in non-equilibrium state.• Kinetics including ion dynamics and osmotic pressure change would explain non-

equilibrium state electroactuation.36

Summary

− +

Electro-responsive materialsElectro-inactive materials

Actuation 1 Actuation 2As fabricated

+ −

• Diffusion-patterned hydrogel

• 3D printed hydrogel

stimuli-responsive hydrogel Inactive hydrogel

Adhesion

• Applications

• Local actuation occur only when polyelectrolyte face up to specific electrode


aterials Laboratory

37

Thank you for listening

38

A study on the ion dynamics of polyelectrolyte hydrogels and their application for soft robotsPolyelectrolyte hydrogelsElectro-active hydrogelsConventional mechanism for electroactuationElectroactuation of polyelectrolyte hydrogelsElectroactuation of polyelectrolyte hydrogelSystem for reversible electroactuation□(Left) / 0.005 M (Right) – 3 min3 M (Left) / □(Right)슬라이드 번호 10슬라이드 번호 11슬라이드 번호 12슬라이드 번호 13슬라이드 번호 14슬라이드 번호 15슬라이드 번호 16슬라이드 번호 17슬라이드 번호 18슬라이드 번호 19슬라이드 번호 20슬라이드 번호 21슬라이드 번호 22슬라이드 번호 23슬라이드 번호 24슬라이드 번호 25슬라이드 번호 26슬라이드 번호 27슬라이드 번호 28슬라이드 번호 29슬라이드 번호 30Local actuationDiffusion-patterned hydrogel 3D printed hydrogel슬라이드 번호 34슬라이드 번호 35SummarySummaryThank you for listening��

a study on the ion dynamics of polyelectrolyte hydrogels and their...

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