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Analysis of the effect of the interaction parameters of copolymer blocks on their efficiency in reducing the interfacial tension between the components of immiscible polymer blends

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Abstract

Block and graft copolymers with blocks that are identical to, miscible with or adhere to related components of a polymer blend can serve as compatibilizers. The relatively simple models established by Leibler and Noolandi provide the basis for addressing the influence of partial interaction parameters between the individual segments of two homopolymers and one copolymer and the influence of the copolymer block length ratio on the compatibilization efficiency. The maximum compatibilization efficiency for both the wet and dry brush formulae is obtained for a slightly longer chain of units compatible with the dispersed phase than that compatible with the matrix. A negative interaction parameter between a copolymer block and any homopolymer leads to lower copolymer contents at the interface and thus to a weaker compatibilization effect. If the units of one block of copolymer are miscible with one of the homopolymers and the units of the second block are immiscible with the second homopolymer, the copolymer content at the interface is lower than that when the mentioned interaction parameters are zero, and the compatibilization effect becomes weaker.

The copolymer block lengths and the Flory-Huggins interaction parameters between individual segments of two homopolymers and one copolymer providing the best compatibilisation efficiency are evaluated, based on models by Leibler and Noolandi for systems called by them as the wet brush and the dry brush, and for systems with a low copolymer content at the interface.

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Data availability

Supplementary electronic material is available as an OriginLab file.

Code availability

The program is written in FreePascal. The code is available on reasonable request. If used, this or the previous [4] work should be cited as its source.

Abbreviations

a :

segment length

d :

differentiation operator

F f,L, F f,N :

free energy of the interfacial film in the Leibler model and in the Noolandi model, respectively

g C, g D :

free energy per C and D copolymer chain brush, respectively, in phases A and B

k :

the Boltzmann constant

L i :

thickness of the interfacial layer in phase i

N :

total number of segments in the copolymer molecule

N j :

number of segments j in the copolymer block (j can be C or D)

P i :

number of segments i in the homopolymer chain (i can be A or B)

Q :

total number of copolymer molecules in the system, with Qk in the k phase

S :

interfacial area per unit volume

T :

temperature

z:

coefficient between 0 and 1

α, β:

superscripts denoting phases

Γ :

auxiliary parameter Γ = aS/φA

γ :

interfacial tension

γ 0 :

interfacial tension between the A and B phases

∂:

partial derivative operator

η i :

the average volume fraction of segments of the ith block in the interfacial layer

μ k :

chemical potential of the copolymer in the k phase, where k is the A or B homopolymer phase or interface I

π:

Ludolf number

Σ :

interfacial area per copolymer joint, Σ = S/QI

φ A, φ B, φ CD :

volume fractions of homopolymers A and B and of copolymer CD in the system, respectively

φ CD (k) :

copolymer volume fraction in the k phase, where k is the A or B homopolymer phase or interface I

\( {\tilde{\varphi}}_i \) :

reduced (relative) volume fraction of the component i, with \( {\tilde{\varphi}}_i \) = φi/φA

χ ij :

partial Flory-Huggins interaction parameters between the segments i and j, where i and j represent the A and B homopolymer segments and the C and D copolymer segments (χii = 0), respectively

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Funding

This research was funded by the Technology Agency of the Czech Republic (Technologická Agentura České Republiky), project number TN01000008.

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Authors and Affiliations

  1. Institute of Macromolecular Chemistry, Czech Academy of Sciences, Heyrovského náměstí 2, CZ 162 06, Praha 6, Czechia

    Josef Jůza & Ivan Fortelný

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  1. Josef Jůza
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  2. Ivan Fortelný
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Contributions

Ivan Fortelný: The idea that inspired this article, the first version of Sections 1 (Introduction) and 2 (Theoretical), the choice of systems, and the input parameters. Josef Jůza: Reproduction of the derivation of formulae in Section 2 to eliminate possible mistakes, implementation and calculations with particular data, image production, and the first version of Section 3 (Results and discussion), and the auxiliary sections. Both authors: the conclusions and final approval of the text.

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Correspondence to Josef Jůza.

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Jůza, J., Fortelný, I. Analysis of the effect of the interaction parameters of copolymer blocks on their efficiency in reducing the interfacial tension between the components of immiscible polymer blends. Colloid Polym Sci 299, 1247–1269 (2021). https://doi.org/10.1007/s00396-021-04809-6

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