3.014 Materials Laboratory Sept. 18th – Sepy.22nd, 2006 Lab Week 1 – Module α2 Polymer Conformation Lab. Instructor: Francesco Stellacci OBJECTIVES 9 Review random walk model for polymer chains 9 Introduce dynamic light scattering as a technique to obtain dimensions of polymer chains in solution 9 Investigate conformational differences between proteins and synthetic polymers SUMMARY OF TASKS 1) Prepare dilute polymer and protein solutions 2) Perform dynamic light scattering on all solutions to obtain hydrodynamic radius 3) Determine scaling relationship between radius and molecular weight for polymers and proteins 4) Investigate temperature effects on chain dimensions 1BACKGROUND Polymer Conformations Polymer Melts Polymers are covalently bonded long chain molecules composed of repeating units, called monomers, comprised of carbon and hydrogen, and sometimes oxygen, nitrogen, sulfur, silicon and/or fluorine. The ability of polymer chains to pack into an ordered array depends strongly on the stereoregularity of their pendant groups. For example, depending on the method of polymerization, polystyrene may exhibit isotactic, syndiotactic or atactic structure. Atactic polystyrene, which is widely used commercially, is entirely amorphous due to the random arrangement of the pendant phenyl groups, while syndiotactic and isotactic polystyrene, having more regular structures, exhibit crystallinity. CCHHHIsotactic PS (highly crystalline)Syndiotactic PS (semi-crystalline) Styrene monomer Linear polymer chains in the amorphous (melt or glassy) state adopt conformations characteristic of a “random walk” due to the presence of both gauche and trans bond conformations along the backbone. A random walk denotes a path of successive steps in which the direction of each step is uncorrelated with, or independent of, previous steps—steps forward and backward, left and right, up and down are all equally probable. Atactic PS (amorphous)CCHHHIsotactic PS (highly crystalline)Syndiotactic PS (semi-crystalline)Styrene monomerAtactic PS (amorphous) 2Because of the equal probability to step in opposite directions, the average end-to-end vector of a random walk of N steps, taken over many possible conformations, is identically zero. 0<>=R The root-mean-square (rms) end-to-end distance, however, is finite, and characterizes the average spatial dimension traversed. If the length of each step is b, the rms end-to-end distance can be shown to be1,2: bR 21/2 1/2Nb<>=R For a polymer chain of N monomer segments, restrictions on available bond angles lead to an “effective” step size b, that is larger than the actual bond length l (l is ~1.54 Å for a C-C bond). The rms end-to-end distance for the polymer chain of N monomers is given by2: 2 1/2 1/2 1/2oRNC l∞<>==R where C∞ is called the characteristic ratio, which depends on the particular polymer. For polystyrene, C∞ is ~10.8 at room temperature.2 A polystyrene chain of N = 1000 would be expected to have a dimension Ro~160 Å in the melt or glassy state. 3An important feature of this result is that the polymer chain has a characteristic size which scales with the number of monomers in the chain to the one-half power: Ro ~ N1/2. The average volume occupied by the coil is therefore much greater than the volume of the chain itself, so that in the melt or glassy state, many other chains will be found intermingled with a single chain. This is very different than the case of small molecule systems, and leads to the unique rheological and mechanical properties polymers exhibit. Vcoil ≈ Ro3 ~ N3/2 Vchain = Nvmer ~ N Vcoil/Vchain ~ N1/2 = approx. # of chains that fit in a single coil volume Polymers in solution When polymers are dissolved in good solvents, the chains similarly take on coil-like conformations, but often are somewhat swelled, as a result of interactions between the monomer and solvent. The conformations of polymer chains in dilute solutions are well described as “self-avoiding” random walks (SAWs). Whereas a random walk is able to cross its own trajectory, a SAW disallows such configurations—the chain is said to have “excluded volume”.1,2 This gives rise to an effective swelling, so that: Monte Carlo simulation of swollen vs. globular states for N = 626 (from A.Y. Grosberg and A.R. Khokhlov, Statistical Physics of Macromolecules, AIP, NY, 1994, pg. 86) RSAW ~ N3/5 Note that the degree of swelling is also a function of the solution temperature—raising the temperature typically causes the 4Figure removed due to copyright restrictions.chain dimensions to expand, while at low temperatures, chains can collapse into a dense, “globular” state, before precipitating out of solution.3 Measurement of Coil Dimensions by Dynamic Light Scattering There are a number of experimental techniques by which the coil dimensions for a polymer chain can be measured. From dynamic light scattering (DLS) measurements, for instance, one can determine the hydrodynamic radius Rh of a polymer chain in dilute solution,3-5 which is directly proportional to the rms end-to-end distance for linear chains: 21/2hR const=<>R In a dynamic light scattering experiment, incident light that scatters from many individual polymer coils within a measured volume of polymer solution are detected at a fixed angle from the incident beam. Constructive and destructive interferences between scattered electromagnetic waves give rise to an average measured intensity. Because the polymer coils are moving in solution, the path length of the scattered light from a given chain within the measured volume will change as a function of time, causing the scattered intensity to fluctuate around its time-averaged mean value <I(q,0)>. By observing the decay of these fluctuations, we can obtain information about the rate at which the polymer chains diffuse through the solution, which is inversely related to their size, through the Stokes-Einstein relation: 6hskTRDπη= [1] where D is the diffusion coefficient, ηs is the solvent viscosity, k is Boltzmann’s constant, and T is temperature in Kelvin. I(q,t)time <I(q,0> 5ΔtIn DLS experiments, the measured intensity fluctuations in Ι(q,t) depend on rearrangements of molecules in solution on length scale of 1/q, where q is the scattering vector defined by: 4sinsqnπθλ= [2] where θ is the scattering angle (90°), λ is the radiation