Dynamic Light Scattering

I was asked to do simulation to calculate the spring constant of a polymer. Steered MD simulation is not acceptable by my advisor. Synthia in Materials Studio can only give a prediction, it is not accurate. I am looking for other methods to do this now.

A literature talking about test the spring constant of polystyrene mentioned dynamic light scattering is used for the measurement (Measuring the Spring Constant of a Single Polymer Chain, H. Jensenius and G. Zocchi). I am trying to extract useful information and do some similar simulation. I have no clue what DLS is. The following is a good explanation. Cited from http://pssnicomp.com/definitions/dynamic-light-scattering/.

Dynamic Light Scattering (DLS) is also known as Photon Correlation Spectroscopy (PCS). DLS is used to size particles form below 5ns to several microns. This technique operates on the principle that particles move randomly in gas or liquid. ie. undergo Brownian motion. The movement (diffusion) of these particles is described by the Stokes-Einstein equation (Eq.1).

DLSFig1 150x141 Dynamic Light Scattering

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(Eq. 1)

Where the diffusion (D) is equal to the product of Boltzman’s constant (kquicklatex.com e4feb8c2565b3905e2bbdba78607b925 l3 Dynamic Light Scattering) divided by the hydrodynamic radius of the particle (R) of the particle and the shear viscosity of the solvent (quicklatex.com 744efd79f33f65e5887066be3e0cc271 l3 Dynamic Light Scattering). Larger particles have a slower velocity and will have smaller coefficients of diffusion than larger particles.

DLSFig2 150x150 Dynamic Light ScatteringIn most DLS systems a laser (i.e. HeNe) of known wavelength passes through a dilute sample in solution and the intensity of scattered light is collected by a detector and deconvoluted by algorithms to determine the particle size distribution of the sample. Figure B shows a schematic of a DLS instrument.The amount of scattered light collected is dependent on the molecular weight, size, and shape of a particle as well as the refractive indices of the particle and solvent. Before reaching the detector, the scattered light from individual particles experiences interference from those scattered by other particles all of which are moving randomly due to Brownian motion. This results in random fluctuations in time.

DLSFig3 150x150 Dynamic Light ScatteringFigure C shows a typical intensity vs time plot for three differently sized particles diffusing in solution. The time scale of the fluctuations shown in the figure is dependent on the particle diffusivity and size of the particles. Smaller particles will jitter about more quickly than larger particles. The figure shows represenative time vs intensity plots for “small” (3a), “medium” (3b) and “large” (3c) particles.

To determine the numerical size of the particles it is necessary to correlate intensity to the diffusion coefficient of the particles. This is done using an autocorrelation function or ACF (eq. 2). This function examines the changes in scattered intensity over periods of time for a volume of particles. In the case of a simple monodisperse particle size distribution (PSD) the ACF is a single decaying exponential function (eq. 3). After a series of calculations a decay constant (tt) is found that is inversely proportional to the diffusivity of a particle as shown in equations 4(a-b) where K is a constant called the “scattering wave vector”. This constant relates the time scale of the diffusion process to the distance scale set by the laser wavelength. K is shown in equation 5 and is dependent on the wavelength of the laser (λl), q is the angle of detection and the index of refraction of the solvent (n). Once the coefficient of diffusion is known the hydrodynamic radius can be determined using the Stokes-Einstein equation (eq. 6).

  quicklatex.com 8d6df69cb9c021d5d6a51d8a5ac73453 l3 Dynamic Light Scattering

  quicklatex.com 62779230f35b8beb8d4452ef129edaa7 l3 Dynamic Light Scattering

  quicklatex.com bf0664ae8897b1b186b87da444926112 l3 Dynamic Light Scattering

  quicklatex.com a4d3557d736f1573434a05ca4ea2e8b7 l3 Dynamic Light Scattering

  quicklatex.com ea156754ef65921610b44b64406eaa55 l3 Dynamic Light Scattering

  quicklatex.com cdc0d532993f3426269f95a66ce3ac31 l3 Dynamic Light Scattering

DLSFig4 150x150 Dynamic Light ScatteringThe simplest DLS result is of a monodisperse or uniform sample with a narrow size distribution. A monodisperse sample will have a bell shaped curve of narrow width (Figure D). Such a sample is quite rare. Most samples will have either a broad Gaussian single peak PSD indicating that the sample is not uniform and has perhaps a skewed unimodal or multimodal PSD. A simple Gaussian calculation will give highly inaccurate results.

DLSFig5 150x150 Dynamic Light ScatteringIn order to analyze samples that are not perfectly monodisperse, PSS employs a proprietary inverse Laplace transform called the NICOMP distribution analysis that does not assume a particular shape for the PSD and analyzes up to four independent parameters to determine PSDs.Figure E shows a PSD for a bimodal sample containing 220nm and 340nm polystyrene latex spheres. A conventional Gaussian analysis would not be able to discern the two mean diameters and would present a result with a mean diameter somewhere in between to the two.

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