### Abstract

Adhesion of dense linear polymer chains containing a small number of randomly distributed sticker groups (φ_{X}) to a solid substrate containing receptor groups (φ_{Y}) has been analyzed by a single-chain scaling approach. An entanglement sink probability (ESP) model motivated by vector percolation explains the nonmonotonic influences of sticker concentration (φ_{X}), receptor concentration (φ_{Y}), and their interaction strength (χ) on the adhesion strength G_{IC} of the polymer-solid interface. The ESP model quantifies the degree of interdigitation between adsorbed and neighboring chains on the basis of the adsorbed chain domain with an extension of the scaling treatment of de Gennes. Here, the adsorbed chain domain changes thermodynamically with respect to the energy of interaction parameter, r = χφ_{X}φ_{Y}. This model considers the situation of a blend consisting of a small volume fraction of adhesive molecules as a compatibilizer at the interface, where these molecules promote adhesion by adsorbing to the surface via sticker-receptor interactions. The percolation model scales solely with r = χφ_{X}φ_{Y}, and this parameter can be related to both the adhesive potential (G_{A}) and the cohesive potential (G_{C}). G_{A} describes adhesive failure between adsorbed chains and the solid surface and linearly behaves as G_{A} ∼ r = χφ_{X}φ_{Y}. The cohesive strength between adsorbed and neighboring chains corresponds to G_{C} ∼ r^{-0.5∼-1.0} = (χφ_{X}φ_{Y})^{-0.5∼-1.0}. When the fracture stresses for cohesive and adhesive failure are equal, the model predicts maximum adhesion strength at an optimal value of r* = (χφ_{X}φ_{Y})*. Thus, for a given χ value, optimal values φ_{X}* and φ_{Y}* exist for the sticker and receptor groups, above or below which the fracture energy will not be optimized. Alternatively, if the X-Y interaction strength χ increases, then the number of sticker groups required to achieve the optimum strength decreases. Significantly, the optimum strength is not obtained when the surface is completely covered with receptor groups (φ_{Y} = 1) but is closer to 30%. For polybutadiene, the optimum value of r* was determined experimentally (Lee, I.; Wool, R. P. J Adhesion 2001, 75, 299), and typically φ_{X}* ≈ 1-3%, φ_{Y}* ≈ 25-30%.

Language | English (US) |
---|---|

Pages | 2343-2353 |

Number of pages | 11 |

Journal | Journal of Polymer Science, Part B: Polymer Physics |

Volume | 40 |

Issue number | 20 |

DOIs | |

State | Published - Oct 15 2002 |

Externally published | Yes |

### Profile

### Keywords

- Adhesion
- Fracture
- Functionalization of polymers
- Polybutadiene
- Strength
- Structure-property relations
- Theory
- Thermodynamics
- Thin films

### ASJC Scopus subject areas

- Polymers and Plastics
- Materials Chemistry

### Cite this

*Journal of Polymer Science, Part B: Polymer Physics*,

*40*(20), 2343-2353. DOI: 10.1002/polb.10286

**Thermodynamic analysis of polymer-solid adhesion : Sticker and receptor group effects.** / Lee, Ilsoon; Wool, Richard P.

Research output: Research - peer-review › Article

*Journal of Polymer Science, Part B: Polymer Physics*, vol 40, no. 20, pp. 2343-2353. DOI: 10.1002/polb.10286

}

TY - JOUR

T1 - Thermodynamic analysis of polymer-solid adhesion

T2 - Journal of Polymer Science, Part B: Polymer Physics

AU - Lee,Ilsoon

AU - Wool,Richard P.

PY - 2002/10/15

Y1 - 2002/10/15

N2 - Adhesion of dense linear polymer chains containing a small number of randomly distributed sticker groups (φX) to a solid substrate containing receptor groups (φY) has been analyzed by a single-chain scaling approach. An entanglement sink probability (ESP) model motivated by vector percolation explains the nonmonotonic influences of sticker concentration (φX), receptor concentration (φY), and their interaction strength (χ) on the adhesion strength GIC of the polymer-solid interface. The ESP model quantifies the degree of interdigitation between adsorbed and neighboring chains on the basis of the adsorbed chain domain with an extension of the scaling treatment of de Gennes. Here, the adsorbed chain domain changes thermodynamically with respect to the energy of interaction parameter, r = χφXφY. This model considers the situation of a blend consisting of a small volume fraction of adhesive molecules as a compatibilizer at the interface, where these molecules promote adhesion by adsorbing to the surface via sticker-receptor interactions. The percolation model scales solely with r = χφXφY, and this parameter can be related to both the adhesive potential (GA) and the cohesive potential (GC). GA describes adhesive failure between adsorbed chains and the solid surface and linearly behaves as GA ∼ r = χφXφY. The cohesive strength between adsorbed and neighboring chains corresponds to GC ∼ r-0.5∼-1.0 = (χφXφY)-0.5∼-1.0. When the fracture stresses for cohesive and adhesive failure are equal, the model predicts maximum adhesion strength at an optimal value of r* = (χφXφY)*. Thus, for a given χ value, optimal values φX* and φY* exist for the sticker and receptor groups, above or below which the fracture energy will not be optimized. Alternatively, if the X-Y interaction strength χ increases, then the number of sticker groups required to achieve the optimum strength decreases. Significantly, the optimum strength is not obtained when the surface is completely covered with receptor groups (φY = 1) but is closer to 30%. For polybutadiene, the optimum value of r* was determined experimentally (Lee, I.; Wool, R. P. J Adhesion 2001, 75, 299), and typically φX* ≈ 1-3%, φY* ≈ 25-30%.

AB - Adhesion of dense linear polymer chains containing a small number of randomly distributed sticker groups (φX) to a solid substrate containing receptor groups (φY) has been analyzed by a single-chain scaling approach. An entanglement sink probability (ESP) model motivated by vector percolation explains the nonmonotonic influences of sticker concentration (φX), receptor concentration (φY), and their interaction strength (χ) on the adhesion strength GIC of the polymer-solid interface. The ESP model quantifies the degree of interdigitation between adsorbed and neighboring chains on the basis of the adsorbed chain domain with an extension of the scaling treatment of de Gennes. Here, the adsorbed chain domain changes thermodynamically with respect to the energy of interaction parameter, r = χφXφY. This model considers the situation of a blend consisting of a small volume fraction of adhesive molecules as a compatibilizer at the interface, where these molecules promote adhesion by adsorbing to the surface via sticker-receptor interactions. The percolation model scales solely with r = χφXφY, and this parameter can be related to both the adhesive potential (GA) and the cohesive potential (GC). GA describes adhesive failure between adsorbed chains and the solid surface and linearly behaves as GA ∼ r = χφXφY. The cohesive strength between adsorbed and neighboring chains corresponds to GC ∼ r-0.5∼-1.0 = (χφXφY)-0.5∼-1.0. When the fracture stresses for cohesive and adhesive failure are equal, the model predicts maximum adhesion strength at an optimal value of r* = (χφXφY)*. Thus, for a given χ value, optimal values φX* and φY* exist for the sticker and receptor groups, above or below which the fracture energy will not be optimized. Alternatively, if the X-Y interaction strength χ increases, then the number of sticker groups required to achieve the optimum strength decreases. Significantly, the optimum strength is not obtained when the surface is completely covered with receptor groups (φY = 1) but is closer to 30%. For polybutadiene, the optimum value of r* was determined experimentally (Lee, I.; Wool, R. P. J Adhesion 2001, 75, 299), and typically φX* ≈ 1-3%, φY* ≈ 25-30%.

KW - Adhesion

KW - Fracture

KW - Functionalization of polymers

KW - Polybutadiene

KW - Strength

KW - Structure-property relations

KW - Theory

KW - Thermodynamics

KW - Thin films

UR - http://www.scopus.com/inward/record.url?scp=0037108343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037108343&partnerID=8YFLogxK

U2 - 10.1002/polb.10286

DO - 10.1002/polb.10286

M3 - Article

VL - 40

SP - 2343

EP - 2353

JO - Journal of Polymer Science, Part B: Polymer Physics

JF - Journal of Polymer Science, Part B: Polymer Physics

SN - 0887-6266

IS - 20

ER -