Scaling and Interactions of Linear and Ring Polymer Brushes via DPD Simulations

• Main Authors: Martin Jehser, Gerhard Zifferer, Christos N. Likos
• Format: Article
• Language: English
• Published: MDPI AG 2019-03-01
• Series: Polymers
• Subjects: DPD; polymer brush; polymer rings; computer simulation; scaling theory; effective interactions
• Online Access: https://www.mdpi.com/2073-4360/11/3/541

Single and double layers of polymer coated surfaces are investigated by means of Dissipative Particle Dynamics (DPD), focusing on the difference between grafted ring and linear chains. Several different surface coverages <inline-formula> <math display="inline"> <semantics> <mi>σ</mi> </semantics> </math> </inline-formula>, as well as chain lengths <i>N</i> and brush separations <i>D</i>, are analyzed for athermal, i.e., good solvent, conditions. The size in the form of the radius of gyration <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mi>g</mi> </msub> </semantics> </math> </inline-formula>, the shape as asphericity <inline-formula> <math display="inline"> <semantics> <msup> <mi>δ</mi> <mo>∗</mo> </msup> </semantics> </math> </inline-formula>, and orientation <inline-formula> <math display="inline"> <semantics> <msup> <mi>β</mi> <mo>∗</mo> </msup> </semantics> </math> </inline-formula>, as well as density profiles as functions of distance from grafting plane <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, are studied. The effect of an added bond repulsion potential to suppress bond crossing in DPD is analyzed. Scaling laws of <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mi>g</mi> </msub> </semantics> </math> </inline-formula> and its components <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>⊥</mo> </mrow> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>∥</mo> </mrow> </msub> </semantics> </math> </inline-formula> are investigated. We find <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mi>g</mi> </msub> <mo>∝</mo> <msup> <mi>N</mi> <mi>ν</mi> </msup> <mo>,</mo> <mi>ν</mi> <mo>=</mo> <mn>0.588</mn> </mrow> </semantics> </math> </inline-formula> for surface coverages below the overlap surface concentration <inline-formula> <math display="inline"> <semantics> <msub> <mi>σ</mi> <mo>∗</mo> </msub> </semantics> </math> </inline-formula>. For <inline-formula> <math display="inline"> <semantics> <mrow> <mi>σ</mi> <mo>&gt;</mo> <msub> <mi>σ</mi> <mo>∗</mo> </msub> </mrow> </semantics> </math> </inline-formula> we find <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>⊥</mo> </mrow> </msub> <mo>∝</mo> <msup> <mi>N</mi> <msub> <mi>ν</mi> <mo>⊥</mo> </msub> </msup> <mo>,</mo> <msub> <mi>ν</mi> <mo>⊥</mo> </msub> <mo>≅</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>∥</mo> </mrow> </msub> <mo>∝</mo> <msup> <mi>N</mi> <msub> <mi>ν</mi> <mo>∥</mo> </msub> </msup> <mo>,</mo> <msub> <mi>ν</mi> <mo>∥</mo> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> of ring brushes with the standard DPD model and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>ν</mi> <mo>∥</mo> </msub> <mo>≅</mo> <mn>2</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics> </math> </inline-formula> with added bond repulsion. The <inline-formula> <math display="inline"> <semantics> <mi>σ</mi> </semantics> </math> </inline-formula> dependence of the radius of gyration was found to be <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mi>g</mi> </msub> <mo>∝</mo> <msup> <mi>σ</mi> <mi>μ</mi> </msup> </mrow> </semantics> </math> </inline-formula> with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula> for surface coverages grater than <inline-formula> <math display="inline"> <semantics> <msub> <mi>σ</mi> <mo>∗</mo> </msub> </semantics> </math> </inline-formula>. The perpendicular component <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>⊥</mo> </mrow> </msub> </semantics> </math> </inline-formula> scales independent of the bond repulsion potential as <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>⊥</mo> </mrow> </msub> <mo>∝</mo> <msup> <mi>σ</mi> <msub> <mi>μ</mi> <mo>⊥</mo> </msub> </msup> <mo>,</mo> <msub> <mi>μ</mi> <mo>⊥</mo> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula>, whereas the scaling of the parallel component exhibits a topological repulsion dependence <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>g</mi> <mo>∥</mo> </mrow> </msub> <mo>∝</mo> <msup> <mi>σ</mi> <msub> <mi>μ</mi> <mo>∥</mo> </msub> </msup> <mo>,</mo> <msub> <mi>μ</mi> <mo>∥</mo> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>12</mn> </mrow> </semantics> </math> </inline-formula> for standard DPD and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mo>∥</mo> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>6</mn> </mrow> </semantics> </math> </inline-formula> for bond repulsion.