Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological...
Transcript of Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological...
![Page 1: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/1.jpg)
Theory of
Supramolecular Polymer Systems
Edward H. Feng and Glenn H. Fredrickson
Department of Chemical Engineering
University of California, Santa Barbara
![Page 2: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/2.jpg)
Reversible Intermolecular Bonding
Meijer and coworkers, Science. 278, 1601, 1997.
2−ureido 4−pyrimidone bonding group
forms linear and network structures.
![Page 3: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/3.jpg)
Potential Technological Applications
use temperature to control the number of bonds and hence
the physical properties and processability of the material.
Higher Temperature
![Page 4: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/4.jpg)
Inhomogeneous Supramolecular Polymers
J. Ruokolainen et. al., Science, Vol. 280, 557-560. ’98.
A
C
B
3 component graft copolymer, C conducts electricity
χAB small, χAC and χBC large
![Page 5: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/5.jpg)
Inhomogeneous Supramolecular Polymers
melting of "inner" lamellae
breaking of hydrogen bonds
higher T
![Page 6: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/6.jpg)
Electrical Conductivity
use temperature to control the properties of the material.
![Page 7: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/7.jpg)
Supramolecular Diblock Copolymer
• consider the most simple system that will form inhomo-
geneous phases.
• the energy of bonding will compete with the immiscibility
of the two types of polymers.
• started a collaboration with experimentalists at UCSB to
study this model system
![Page 8: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/8.jpg)
Model for Supramolecular Diblock
• use a continuous Gaussian chain model
• assume an energy change for the reversible reaction of
two different homopolymers forming a diblock: ε
• an incompressible melt in the grand canonical ensemble
![Page 9: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/9.jpg)
Parameters for Supramolecular Diblock
• zA/zB: ratio of activities of the two polymer species
• g = NB/NA: ratio of length of B to length of A polymer
• χAB: Flory-Huggins parameter that captures chemical
immiscibility of two species
• ε: energy of bonding
![Page 10: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/10.jpg)
Model for Supramolecular Diblock
• for ε → −∞, this system is a binary blend
• for ε → ∞, this system has only diblock copolymers
• for intermediate values of ε, this system contains both
homopolymers and diblock copolymer
![Page 11: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/11.jpg)
Theoretical Resultsparameters: zA, g, χAB, and ε.
Ξ(zA, V, T) =
∫DW+
∫DW−e−H[W±]
H[W±] =C
χABNA
∫dxW2
−(x) − iC∫
dxW+(x)
−V̄ (zAeεQAB[W±] + zAQA[W±] + QB[W±])
• for each choice of parameters, there is a corresponding
ternary blend system
P.K. Jannert, M. Schick, Macro. 30:137 , ’97. 30:3916, ’97.
![Page 12: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/12.jpg)
Mean Field Equations
Ξ(µA, V, T) =∫
DW+
∫DW−e−H[W±]
δH[W±]
δW+(x)= φA(x; [W±]) + φB(x; [W±]) − 1 = 0
δH[W±]
δW−(x)=
2
χABNAW−(x) − φA(x; [W±]) + φB(x; [W±]) = 0
• find the mean field solution computationally by relaxing
the W± fields from random initial conditions
• calculate φA and φB density fields with pseudospectral
algorithm
![Page 13: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/13.jpg)
Density Profile Results
parameters are zA = 1, ε = 0, χABNA = 4.0 and g = 1.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 2 4 6 8 10 12 14 16 0
2
4
6
8
10
12
14
16
lamellar structures for this system with equal parts A and B
![Page 14: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/14.jpg)
Order Disorder Transition, zA = 1, g = 1.
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0 0.2 0.4 0.6 0.8
tem
pera
ture
bonding energy
Lamellar
Disorder
![Page 15: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/15.jpg)
Equilibrium Polymers
• system with annealed disorder in the polymer length
distribution.
• this is a model for giant micelles, which can break and
recombine at any point along the micelle.
• we will study this model in confined environments, such
as between two parallel plates
![Page 16: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/16.jpg)
Equilibrium Polymer Model
• use energy of bonding idea and formulate model in grand
canonical ensemble
• parameters of model:
– z, monomer activity
– u0, excluded volume parameter
– ε, bonding energy
• study this system confined between two parallel plates
separated by distance L.
![Page 17: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/17.jpg)
Equilibrium Polymer Model
• effective Hamiltonian:
H[w] =1
2u0
∫w(r)2dr − V̄ e−2ε
∫ ∞
0zNQ(N ; [iw])dN
• the polymer length distribution ∼ zNQ(N ; [iw])
• mean field equation:
δH[w]
δw=
1
u0w(r) + iρ(r; [iw]) = 0 (1)
where density involves integral over all polymer lengths
![Page 18: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/18.jpg)
Homogeneous Limit
H[w] =1
2u0
∫w(r)2dr − V̄ e−2ε
∫ ∞
0zNQ(N ; [iw])dN
• u0 → 0 implies w(r) = 0
• zNQ(N ; [iw]) = zN = e(ln z)N
• for z < 1, polymer length distribution is exponential with
characteristic length 〈N〉 = −(ln z)−1
![Page 19: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/19.jpg)
Confined Equilibrium Polymer
Polymer Length Distribution
0
2
4
6
8
10
12
14
0 0.5 1 1.5 2
prob
abili
ty
polymer length
homoL=1L=2L=4L=6
L=10
![Page 20: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/20.jpg)
Confined Equilibrium Polymer
Density Within Slit
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1
rho
r
![Page 21: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/21.jpg)
Conclusions
• formulated a field theoretic model for a supramolecular
polymer systems with reversible intermolecular bonding
• used computational methods to find saddle point solu-
tions of the model
• future work will involve graft copolymer systems
![Page 22: Theory of Supramolecular Polymer Systemsghf/cfdc_2005/feng_cfdc_2005.pdfPotential Technological Applications use temperature to control the number of bonds and hence the physical properties](https://reader033.fdocuments.us/reader033/viewer/2022050311/5f73ad0d80427477ad0d762e/html5/thumbnails/22.jpg)
Effect of Temperature
• in original formulation, we scale chemical and bonding
energy by kT
χNA =eNA
kT, ε =
b
kT
• now we scale the temperature and bonding energy by eNA
by kT
Θ =kT
eNA, E =
b
eNA