Screening effects

In the previous chapter, we considered the structures of single chains in the dilute regime. Now we may inquire, how these become altered in semi-dilute solutions. Discussions can be based on the pair distribution function of the individual chains, thereby focusing on the structure of single chains in states where chains overlap and interpenetrate. We choose for this intramolecular pair correlation function a symbol with a hat, g(r), to distinguish it from the general pair distribution function g(r) which includes monomers from all chains. 

For g(r), we can assess the behavior for both limits, dilute solutions and the melt. As explained earlier, in Sect.2.3.2, we find for isolated expanded chains g for distances in the range r Rp. On the other 

S q) can be measured, if the dissolved polystyrene includes a small fraction of deuterated molecules. Due to the large difference in the scattering length of protons and deuterium, the deuterated chains dominate the scattering pattern which then indeed may be described as 

For a dilute solution, one observes the scattering function of expanded chains, I - g-5/3, which corresponds to the straight line shown previously in 

This pertains up to the cross-over at r and then we enter again into an ideal regime 

---

The ernes of ionic surfactants are usually depressed by tire addition of inert salts. Electrostatic repulsion between headgroups is screened by tire added electrolyte. This screening effectively makes tire surfactants more hydrophobic and tliis increased hydrophobicity induces micellization at lower concentrations. A linear free energy relationship expressing such a salt effect is given by ... 

Also use constant dielectric Tor MM+aiul OPLS ciilciilatimis. Use the (lislance-flepeiident dielecinc for AMBER and BlO+to mimic the screening effects of solvation when no explicit solvent molecules are present. The scale factor for the dielectric permittivity, n. can vary from 1 to H(l. IlyperChem sets tt to 1. .5 for MM-r. Use 1.0 for AMBER and OPLS. and 1.0-2..5 for BlO-r. 

In practice the. VIXDO approximation to the screening effect is similar to that of MIXDO/i) but h as a differen t fun cl ion al form ... 

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

A third screening smoke-type is white phosphoms [7723-14-0] (WP), P (see Phosphorus and THE phosphides), which reacts spontaneously with air and water vapor to produce a dense cloud of phosphoms pentoxide [1314-56-3]. An effective screen is obtained as the P2O5 hydrolyzes to form droplets of dilute phosphoric acid aerosol. WP produces smoke in great quantity, but it has certain disadvantages. Because WP has such a high heat of combustion, the smoke it produces from bulk-filled munitions has a tendency to rise in pillarlike mass. This behavior too often nullifies the screening effect, particularly in stiU air. Also, WP is very brittle, and the exploding munitions in which it is used break it into very small particles that bum rapidly. 

Use of screened cables in the communication network and grounding the screen effectively. Metallic-sheath or armoured cables are not recommended. 

In these approximations for the K series the value 1 is subtracted from the atomic number Z to correct for the screening of the nuclei by the remaining K-shell electron. For the L series the screening effect of the two K-shell electrons and the seven remaining L-shell electrons must be taken into consideration by subtracting 7.4. 

The correlation functions of the partly quenched system satisfy a set of replica Ornstein-Zernike equations (21)-(23). Each of them is a 2 x 2 matrix equation for the model in question. As in previous studies of ionic systems (see, e.g.. Refs. 69, 70), we denote the long-range terms of the pair correlation functions in ROZ equations by qij. Here we apply a linearized theory and assume that the long-range terms of the direct correlation functions are equal to the Coulomb potentials which are given by Eqs. (53)-(55). This assumption represents the mean spherical approximation for the model in question. Most importantly, (r) = 0 as mentioned before, the particles from different replicas do not interact. However, q]f r) 7 0 these functions describe screening effects of the ion-ion interactions between ions from different replicas mediated by the presence of charged obstacles, i.e., via the matrix. The functions q j (r) need to be obtained to apply them for proper renormalization of the ROZ equations for systems made of nonpoint ions. 

The function / incorporates the screening effect of the surfactant, and is the surfactant density. The exponent x can be derived from the observation that the total interface area at late times should be proportional to p. In two dimensions, this implies R t) oc 1/ps and hence x = /n. The scaling form (20) was found to describe consistently data from Langevin simulations of systems with conserved order parameter (with n = 1/3) [217], systems which evolve according to hydrodynamic equations (with n = 1/2) [218], and also data from molecular dynamics of a microscopic off-lattice model (with n= 1/2) [155]. The data collapse has not been quite as good in Langevin simulations which include thermal noise [218]. 

Depending on the dose and temperature regime, the screening effect azomopine is observed after intoxication by chlorophos. The survival of white rats injected with this preparation is 50% higher than that of control rats. When toxic doses of copper sulfate were injected for 7 days, 70 and 36% of the rats survived. After the simultaneous injection of azomopine, their survival increased to 100 and 70% (74MI1). 

As a first approximation, each electron in a many-electron atom can be considered to have the distribution in space of a hydrogen-like electron under the action of the effective nuclear charge (Z—Ss)e, in which 5s represents the screening effect of inner electrons. In the course of a previous investigation,6 values of S5 for a large number of ions were derived. 

Internal shells are thus seen to screen completely, and the screening effects of penetrated shells are additive. Moreover, it is seen that for properties proportional to different powers of n and Z the total screening defect varies directly with rjt. 

Winzor and coworkers have employed measurements of the Donnan distribution of small ions in dialysis equilibrium [14] to reinforce earlier evidence of charge-screening effects in polysaccharide anions [164,165]. These researchers used the absorption optical system of a Beckman XL-1 ultracentrifuge to monitor the distribution of ions in polysaccharide solutions... 

For poly electrolyte solutions with added salt, prior experimental studies found that the intrinsic viscosity decreases with increasing salt concentration. This can be explained by the tertiary electroviscous effect. As more salts are added, the intrachain electrostatic repulsion is weakened by the stronger screening effect of small ions. As a result, the polyelectrolytes are more compact and flexible, leading to a smaller resistance to fluid flow and thus a lower viscosity. For a wormlike-chain model by incorporating the tertiary effect on the chain... 

Ionization energies deviate somewhat from smooth periodic behavior. These deviations can be attributed to screening effects and electron-electron repulsion. Aluminum, for example, has a smaller ionization energy than either of its neighbors in Row 3 ... 

C08-0120. Make an electron density plot that shows how the 3. S and 3 p orbitals are screened effectively by the 2 p orbitals. Provide a brief explanation of your plot. 

In absence of external salt, strong electrostatic interchain interactions exist in solution causing very large increase of the reduced viscosity and the formation of a pseudo electrostatic 3D network this was recently discussed [24], It implies the salt sensitivity of the viscosity which decreases when neutral salt is added due to a screening effect on the long range electrostatic repulsions. 

The screen efficiency of a screen (known also as effectiveness of a screen) is a measure of the success of a screen in closely separating materials A and B. Provided the screen works perfectly, all of material A would be in the overflow, and all of material B would be in the underflow. An usual measure of screen effectiveness is the ratio of oversize material A that is actually in the overflow to the amount of A entering with the feed. These amounts are D mD and F mF, respectively. Thus... 

Another related theory expresses the screening effect of the macromolecu-... 

The charge screening effect of Ca2+ in increasing XCPS adsorption is more clearly seen in Figure 13 for the case of SiC where the NaCl content is lower (lg/1). Due to the low initial ionic strength, no adsorption is detected for both XCPS samples at low calcium concentration. The maximum adsorption level in this case is the same as that obtained in the presence of monovalent ions only (26). 

There are two explanations for the small shrinkage in hydrochloric acid. One is that the deformation may be caused by the electrostatic forces between the anode and the negatively charged polyions in the gel. The other relates to the screening effect of COO H + by CP which comes in from the D phase. As a large number of CP ions restrain interactions between COO H+, the gel will shrink. 

Is the UV-stabilization only due to the screening effect (or more precisely light absorbing effect in a spectral region where the absorption spectra of polymer and UV-stabilizer overlap) of the UV-stabilizers and/or can it be enhanced by an energy transfer from the excited polymer to the stabilizer molecule ... 

---