Molecular Dynamics Simulations of Bottle-Brush Polymers with a Flexible Backbone under Theta and Good Solvent Conditions

Abstract

Using molecular dynamics simulations of a standard bead-spring model for polymer chains,bottle-brush polymerswith a flexible backbone of N<SUB>b</SUB>effective units,where side chains of length N are grafted under theta and good solvent conditionsin the range<img src=image/10.5923.j.ajcmp.20120204.05_001.gif></img><SUP>, </SUP>are studied.The range of backbone and side chains' length varies correspondingly as<img src=image/10.5923.j.ajcmp.20120204.05_002.gif></img>and<img src=image/10.5923.j.ajcmp.20120204.05_003.gif></img>for two different grafting densities σ, namely σ=0.5 and 1.0.Even at temperatures T close to the theta point the side chains are significantly stretched, as it has been confirmed for bottle brushes with a rigid backbone, their linear dimension depending on the solvent quality only weakly. However, the distribution of monomers shows a more pronounced dependence, which we characterize through the asphericity and acylindricity as functions of σ, T, N<SUB>b</SUB>, and N. In particular, increase of σ, T, N<SUB>b</SUB>, and N increases the normalized asphericity and acylindricity of the macromolecule. Interestingly, we also find that the dimensions of the side chains reveals differences in the distributions of side chain monomers by changing the backbone length N<SUB>b</SUB> as the region between the two backbone-ends increases. A method to extract the persistence length of bottle-brush macromolecules and its drawbacks is also discussed given that different measures of the persistence length are not mutually consistent with each other and depend distinctly both on N<SUB>b</SUB> and the solvent quality.Macromolecules which consist of a backbone where side chains are graftedrandomly or regularly have recently found much interest[1-6]. Such macromolecules are described in terms of their structure by a multitudeof parameters, such as the backbone length N<SUB>b</SUB> and the grafting densitythat the side chains with length N are grafted ontothe flexible backbone, while solvent conditions may also varyby variation of the temperature T or the pH of the solution resulting inthe structural change of these stimuli-responsive macromolecules.The response of the large scale structure of bottle-brush polymers tosolvent conditions is an intriguing We recall that for linear chains, the theta temperaturefor the present (implicit solvent) model has been roughlyestimated[46] as T<SUB>theta</SUB>≈ 3.0 (note, however, that there is still some uncertainty about the precise value of T<SUB>theta</SUB>,for a similar model[47] T<SUB>theta</SUB>= 3.18 in this case, couldonly be established for chain lengths exceeding N= 200).Thus, in the present work we have thoroughly studied thetemperature range<img src=image/10.5923.j.ajcmp.20120204.05_009.gif></img>. From previous work[48] on rather long chains in polymer brushes on flat surfaces, using the same model[Eqs. (1) and (2)] to describe the interactions, it is known that for T= 4.0 one finds a behaviour characteristicfor (moderately) good solvents. Very good solvent conditionscould be obtained from a slightly different model that hasextensively been studied for standard polymer brushes[40,49],where the cut-off in Eq. (1) is chosen to coincide with theminimum of the potential, <img src=image/10.5923.j.ajcmp.20120204.05_010.gif></img> (and then also T= 1 can be chosen for this essentially a-thermal model).