Stretching Homopolymers

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {{sufficiently large}} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $\sim f$ for small $f$, and $\sim f^{{2/3}}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for \la Z\ra as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {{We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.Comment: 24 pages, 7 figure

Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions

Discrete wavelets are applied to parametrization of the intra-chain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulation. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. Quality of the approximation has been assessed by calculation of the scaling exponents obtained from des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in a better agreement with those from the recent renormalisation group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR

Continuous Model for Homopolymers

We consider the model for the distribution of a long homopolymer in a potential field. The typical shape of the polymer depends on the temperature parameter. We show that at a critical value of the temperature the transition occurs from a globular to an extended phase. For various values of the temperature, including those at or near the critical value, we consider the limiting behavior of the polymer when its size tends to infinity

Monte Carlo simulations of copolymers at homopolymer interfaces: Interfacial structure as a function of the copolymer density

By means of extensive Monte Carlo simulations of the bond fluctuation model, we study the effect of adding AB diblock copolymers on the properties of an interface between demixed homopolymer phases. The parameters are chosen such that the homopolymers are strongly segregated, and the whole range of copolymer concentrations in the two phase coexistence region is scanned. We compare the ``mushroom'' regime, in which copolymers are diluted and do not interact with each other, with the ``wet brush'' regime, where copolymers overlap and stretch, but are still swollen by the homopolymers. A ``dry brush'' regime is never entered for our choice of chain lengths. ``Intrinsic'' profiles are calculated using a block analysis method introduced by us in earlier work. We discuss density profiles, orientational profiles and contact number profiles. In general, the features of the profiles are similar at all copolymer concentrations, however, the profiles in the concentrated regime are much broader than in the dilute regime. The results compare well with self-consistent field calculations.Comment: to appear in J. Chem. Phy

Structure and stability of helices in square-well homopolymers

Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. 96, 207802 (2006)] that isolated, square-well homopolymers can spontaneously break chiral symmetry and freeze into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics, combined with an optimized parallel tempering scheme, to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to lambda) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a window of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature, however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.Comment: Submitted to Physical Review

Side-chain and backbone ordering in Homopolymers

In order to study the relation between backbone and side chain ordering in proteins, we have performed multicanonical simulations of deka-peptide chains with various side groups. Glu10, Gln10, Asp10, Asn10, and Lys10 were selected to cover a wide variety of possible interactions between the side chains of the monomers. All homopolymers undergo helix-coil transitions. We found that peptides with long side chains that are capable of hydrogen bonding, i.e. Glu10, and Gln10, exhibit a second transition at lower temperatures connected with side chain ordering. This occurs in gas phase as well as in solvent, although the character of the side chain structure is different in each case. However, in polymers with short side chains capable of hydrogen bonding, i.e. Asp10 and Asn10, side chain ordering takes place over a wide temperature range and exhibits no phase transition like character. Moreover, non-backbone hydrogen bonds show enhanced formation and fluctuations already at the helix-coil transition temperature, indicating competition between side chain and backbone hydrogen bond formation. Again, these results are qualitatively independent of the environment. Side chain ordering in Lys10, whose side groups are long and polar, also takes place over a wide temperature range and exhibits no phase transition like character in both environments. Reasons for the observed chain length threshold and consequences from these results for protein folding are discussed.Comment: 12 pages,11 figure

A graph theoretical analysis of the energy landscape of model polymers

In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and splitting of metastable states, have non trivial effects on such networks and must be taken into account. We do this by means of a recently proposed renormalization procedure. This method is applied to analyze the topology of the network of metastable states for different polypeptidic sequences in a minimalistic polymer model. A smaller spectral dimension emerges as a hallmark of stability of the global energy minimum and highlights a non-obvious link between dynamic and thermodynamic properties.Comment: 15 pages, 15 figure

Monte Carlo Study of the Phase Structure of Compact Polymer Chains

We study the phase behavior of single homopolymers in a simple hydrophobic/hydrophilic off-lattice model with sequence independent local interactions. The specific heat is, not unexpectedly, found to exhibit a pronounced peak well below the collapse temperature, signalling a possible low-temperature phase transition. The system size dependence at this maximum is investigated both with and without the local interactions, using chains with up to 50 monomers. The size dependence is found to be weak. The specific heat itself seems not to diverge. The homopolymer results are compared with those for two non-uniform sequences. Our calculations are performed using the methods of simulated and parallel tempering. The performances of these algorithms are discussed, based on careful tests for a small system.Comment: 13 pages LaTeX, 6 Postscript figures, References adde

Diblock copolymers at a homopolymer-homopolymer-interface: a Monte Carlo simulation

The properties of diluted symmetric A-B diblock copolymers at the interface between A and B homopolymer phases are studied by means of Monte Carlo (MC) simulations of the bond fluctuation model. We calculate segment density profiles as well as orientational properties of segments, of A and B blocks, and of the whole chain. Our data support the picture of oriented ``dumbbells'', which consist of mildly perturbed A and B Gaussian coils. The results are compared to a self consistent field theory (SCFT) for single copolymer chains at a homopolymer interface. We also discuss the number of interaction contacts between monomers, which provide a measure for the ``active surface'' of copolymers or homopolymers close to the interface