Collapse of Isolated Chains in a Network

1994 ◽  
Vol 376 ◽  
Author(s):  
R. M. Briber ◽  
X. Liu ◽  
B.J. Bauer
Keyword(s):  
Crosslink Density ◽  
Virial Coefficient ◽  
Linear Chain ◽  
Second Virial Coefficient ◽  
Polymer Chains ◽  
Network Density ◽  
Radius Of Gyration ◽  
Single Chain ◽  
Polystyrene Matrix ◽  
Wide Range

ABSTRACTIn this study we use small angle neutron scattering to investigate the conformation of linear deuterated polystyrene chains trapped in a crosslinked protonated polystyrene matrix. The second virial coefficient was obtained as a function of crosslink density for a wide range of crosslink density. It is shown that the second virial coefficient decreases with increasing crosslink density. By extrapolating the scattering to zero concentration of the linear chain at all values of q, the single chain scattering was obtained and radius of gyration was measured the function of network density. It was found that when the network density is low (NI < Nc where NI and Nc are the number of monomer units in the linear chain and the monomer units between crosslinks, respectively) the radius of gyration does not change. As the network density increases (NI > Nc ) radius of gyration decreases. In this region the inverse of the radius of gyration varies linearly with the inverse of Nc. When the crosslink density is very high (NI » Nc ), segregation of linear polymer chains occurs. These results are in agreement with prediction and computer simulation results of polymer chain conformation in a field of random obstacles where the crosslink junctions act as the effective obstacles.

Structure of Polymer Chains Confined in Vycor

1996 ◽  
Vol 464 ◽  
Author(s):  
Jyotsana Lal ◽  
Sunil K. Sinha ◽  
Loic Auvray
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Form Factor ◽  
Small Angle Neutron Scattering ◽  
Pore Diameter ◽  
Polymer Chains ◽  
Bulk Solution ◽  
Radius Of Gyration ◽  
Single Chain ◽  
Molecular Weights

ABSTRACTWe observe by Small Angle Neutron Scattering (SANS) the structure of polystyrene chains in semi-dilute solutions confined in model porous medium, Vycor. The size of the free polymer chains in solution is always larger than the pore diameter, 70 Å. The use of a suitable mixture of hydrogenated and deuterated solvents and polymers enables us to directly measure the form factor of one single chain among the others. The penetration of the chain in the porous media is almost complete for the concentration (Φ = 20%) and the range of molecular weights (35000 <M< 800000) used. The measured radius of gyration of confined chains is always smaller than the radius of gyration of free chains in the equivalent bulk solution.

scholarly journals Determination of Second Virial Coefficient of Gold by a Modified Berthelot Equation of State

2020 ◽  
Vol 1 (4) ◽  
pp. 175-180
Author(s):  
M. Sivakumar ◽  
R. Balasubramanian
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Similarity Parameter ◽  
Thermodynamic Similarity ◽  
Van Der Waals Equation ◽  
Wide Range ◽  
Law Of Corresponding States

The present study aims to determine the second virial coefficient of gold over a wide range of temperatures from the boiling point to the critical point. A three - parameter modified Berthelot equation of state has been employed to determine the second virial coefficient of gold. The parameters of the equation of state are determined through the critical - point parameters of gold. The temperature -dependence of the second virial coefficient of gold has been investigated. The obtained results are compared with that of the van der Waals equation of state, Berthelot equation of state, Tsonopoulus correlation, and McGlashan correlation. The results of this work agree well with that of other correlations in the vicinity of the critical point. It is also established that gold obeys the single - parameter law of corresponding states. And, the new parameter introduced in the attractive term of the equation of state is found to be a thermodynamic similarity parameter. Doi: 10.28991/HEF-2020-01-04-02 Full Text: PDF

Thermal Conductivity of Polyethylene Chains Using Molecular Dynamics Simulations

2008 ◽  
Author(s):  
Asegun Henry ◽  
Gang Chen
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Polymer Chains ◽  
High Thermal Conductivity ◽  
Polymer Materials ◽  
Single Chain ◽  
Wide Range ◽  
Dynamics Simulations ◽  
Limiting Case

We used molecular dynamics simulations to calculate the thermal conductivity of polyethylene chains, by employing the widely used Green-Kubo formula. The simulations use the AIREBO potential and employ periodic boundary conditions to mimic the dynamics of an infinite chain. In this limiting case, we observed that when the simulation domain is large enough the thermal conductivity diverges. The results suggest that single polymer chains intrinsically have high thermal conductivity. Although polymers are generally known to have low thermal conductivity, our observation of divergent thermal conductivity in a single chain suggests that high thermal conductivity polymer materials can be engineered, which would be of interest to a wide range of applications.

scholarly journals Mean-Square Radius of Gyration and Second Virial Coefficient of Poly(diisopropyl fumarate) in Dilute Solution

2008 ◽  
Vol 40 (6) ◽  
pp. 566-571 ◽  
Author(s):  
Masayuki Nakatsuji ◽  
Munehiro Hyakutake ◽  
Masashi Osa ◽  
Takenao Yoshizaki
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Dilute Solution

scholarly journals Topological changes in telechelic micelles: flowers versus stars

2021 ◽  
Author(s):  
Vladimir Baulin
Keyword(s):  
Smart Materials ◽  
Linear Chain ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Chains ◽  
Linear Polymers ◽  
Stimuli Responsive ◽  
Single Chain ◽  
Low Concentrations ◽  
Effective Attraction

Micellization and morphology of spherical telechelic micelles formed by tri-block copolymers with short solvophobic end blocks at low concentrations is discussed within scaling arguments and Single Chain Mean Field Theory (SCMFT). In ultra-dilute regime, individual telechelic polymer chains can exist in solution in two distinct states: open linear chain conformation with two free ends and closed loop conformation, when two ends are connected by the effective attraction between two solvophobic ends. At concentrations below gelation point, closed loops tend to form micelles comprised mostly of loops in flower-like micelles, while linear polymers in open conformations tend to form star-shaped aggregates with one hydrophobic dangling end. Resulting two kinds of micelles have remarkably different topology and dimensions, while the transition between them can be driven by the entropy, namely conformation changes between domination of the looped and linear conformations. As a result, the transition between two types of micelles lies in a narrow interaction parameters range. Thus, these topological micelles are very sensitive to the changes in external environment and they can serve as a very sensitive stimuli-responsive smart materials.

scholarly journals Structural Characterization of a Polymer Substituted Fullerene (Flagellene) by Small Angle Neutron Scattering

1994 ◽  
Vol 359 ◽  
Author(s):  
K.A. Affholter ◽  
G.J. Bunick ◽  
J.M. Desimone ◽  
M.O. Hunt ◽  
Y.Z. Menceloglu ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Virial Coefficient ◽  
Scattering Length ◽  
Second Virial Coefficient ◽  
Radius Of Gyration ◽  
Polystyrene Sample ◽  
Negative Scattering Length

ABSTRACTSmall-angle neutron scattering (SANS) can structurally characterize fullerenes1in solvents with strong SANS contrast (e.g. CS2). Deuterated solvents (e.g. toluene-d8) have a high scattering length density (SLD), which is close to that of C60and C70moieties. Hence, there is virtually no SANS contrast with the solvent and these particles are practically “invisible” in such media. On the other hand, the negative scattering length of hydrogen means that the SLD of H1-containing materials is much lower, so they have strong contrast with toluene-d8. Thus, SANS makes it possible to study the size and shapes of modified buckyballs such as the polymer-substituted fullerenes, or flagellenes2. These consist of C60cores to which 1-4 polystyrene chains (with a molecular weight, MW ≃ 2000) are attached. The extrapolated cross section at zero angle of scatter [dΣ/dΩ(0)]s is a function of the number of pendant chains, so SANS can be used to assess the number of “arms” which are covalently attached to the fullerene “sphere”. Close agreement (± 4%) between the measured and calculated values of dΣ/dΩ(0) along with independent estimates of the radius of gyration (Rg) and second virial coefficient (A2) for a calibration linear polystyrene sample serves as a cross check on the validity of this methodology.

scholarly journals Bayesian analysis of static light scattering data for globular proteins

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258429
Author(s):  
Fan Yin ◽  
Domarin Khago ◽  
Rachel W. Martin ◽  
Carter T. Butts
Keyword(s):  
Experimental Data ◽  
Light Scattering ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Ordinary Least Squares ◽  
Static Light Scattering ◽  
Index Of Refraction ◽  
Scattering Data ◽  
Radius Of Gyration ◽  
Joint Inference

Static light scattering is a popular physical chemistry technique that enables calculation of physical attributes such as the radius of gyration and the second virial coefficient for a macromolecule (e.g., a polymer or a protein) in solution. The second virial coefficient is a physical quantity that characterizes the magnitude and sign of pairwise interactions between particles, and hence is related to aggregation propensity, a property of considerable scientific and practical interest. Estimating the second virial coefficient from experimental data is challenging due both to the degree of precision required and the complexity of the error structure involved. In contrast to conventional approaches based on heuristic ordinary least squares estimates, Bayesian inference for the second virial coefficient allows explicit modeling of error processes, incorporation of prior information, and the ability to directly test competing physical models. Here, we introduce a fully Bayesian model for static light scattering experiments on small-particle systems, with joint inference for concentration, index of refraction, oligomer size, and the second virial coefficient. We apply our proposed model to study the aggregation behavior of hen egg-white lysozyme and human γS-crystallin using in-house experimental data. Based on these observations, we also perform a simulation study on the primary drivers of uncertainty in this family of experiments, showing in particular the potential for improved monitoring and control of concentration to aid inference.

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