To differ the surface charge densities in LUVs, membranes containing a fraction of lipids v charged head groups like PG or PS space used, supplemented with zwitterionic lipids prefer PC.

You are watching: What is the surface charge density σ?

From: developments in Biomembranes and also Lipid Self-Assembly, 2017

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A high surface ar charge thickness can stabilize a hydration class to thermal agitation. Ions with a high surface charge density can polarize the water around the ion to an extent that the hydration layer have the right to be several solvent corpuscle thick. Since of the thickness that the hydration layer, ions that are small in radius may actually find more resistance to movement through the solvent than larger ions with less charge. A cartoon illustrating the effect of surface ar charge density on the thickness of the hydration shell is offered in Figure 4-10.1.

Figure 4-10.1. Hydration layers.

The size of the +1 ion is smaller than the size of the +3 ion. What this method is the the surface ar charge thickness of the +1 ion is smaller than the of the +3 ion. The greater surface charge density can attract an ext water molecules by orienting their dipole moments. The net impact is that as the ions move through the solvent the apparent size of the +3 ion is bigger than the +1 ion.

When one ion interacts v a biopolymer, the procedure involves the removed of the hydration water and also then the location of the ion at the binding website of the biomolecule. The hydration power is correlated with the size of the bare ion for the same charges. The hydration free energy of Na+ is −72 kcal/mol, whereas for K+ that is −55 kcal/mol.

It need to be emphasized that these ions are part of a dynamic device in which the relative concentrations of all the molecules room constantly changing by authorized in reactions and in intake–output of chemistry in the system. Because of this their duty in life systems functions as gift in vain with other ions in their location in the biochemical system.

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Theory the Colloid and also Interfacial electric Phenomena

In user interface Science and also Technology, 2006

4.3.2. Communication at consistent surface charge density

For the consistent surface charge density case, one must take into consideration the internal ar within the plates, since the plate surface ar is no much longer equipotential. The potential ψ(x) satisfies Eq. (14.51) for the regions -∞(14.59)d2Ψdx2=κ2ψ,    −∞x0 and 0x≤h/2

(14.61)ψ(x)=ψo(1+α)cosh<κ(h/2−x>α+tanh(κh/2)cosh(κh/2,   0≤x≤h/2



where ψo is the unperturbed surface ar potential of the plates in ~ kh = ∞, and also α characterizes the influence of the internal electrical field in ~ the plates.


Figure 14.6 gives the potential distribution ψ(x) across two communicating plates 1 and 2 at constant surface charge density σ calculated with Eq. (14.61)–(14.63) for kh = 1, 2, and also ∞ at kd = 1 and also α = 0.1.


(14.68)ψ(x)=ψocosh<κ(h/2−x>sinh(κh/2,   0≤x≤h/2


(14.72)Vσ(h)∫h∞P(h)dh=εrεoκψo2<(1+α)1-tanh(κh/2) α+tanh(κh/2)>


For the special situation where εp = 0 and/or d= ∞, where α = 0 so that the affect of the internal areas may it is in neglected, Eqs. (14.71) and (14.72) become



Stephanie Glendinning, ... Man Lamont-Black, in Ground advancement Case Histories, 2015


A0 = surface charge thickness per unit sharp volume, C/m5

Cv = coefficient of consolidation, m2/s1

Cvr = coefficient the consolidation because that radial flow, m2/s1

C1, C1 = constants of integration, variable

D = dielectric constant, dimensionless

D10, D50 = largest bit size in smallest 10/50% of corpuscle by mass, m

E = voltage difference, V

electrical energy, Wh

ED = dilatometer modulus, N/m2

Eu = undrained Young’s modulus, N/m2

Eredϕ = palliation voltage, V

G = shear modulus, N/m2

Gs = specific gravity, dimensionless

I = electrical current, A

K = Boltzman constant, J/K1

double-layer thickness, m

Ka = active earth pressure coefficient, dimensionless

Kp = passive planet pressure coefficient, dimensionless

Lii = conductivity, variable

N = Avogadro’s number, molecules/mol1

number, dimensionless

P = electrical power, W

PR = reinforcement load, N

Ps = shear load, N

Pv = vertical load, N

Q = volume the fluid, m3

R = ratio anions/cations, dimensionless

resistance, Ω

T = temperature, K

tension in reinforcement, N

Tr = time variable for radial flow, dimensionless

Tv = time factor, dimensionless

U = average degree of consolidation, dimensionless

V = valence, dimensionless

voltage, V

Xii = driving gradient, variable

c = efficiency factor, dimensionless

Cc = effective cohesion, N/m2

cu = undrained shear strength, N/m2

e = electronic charge, C

voids ratio, dimensionless

ie = electrical potential gradient, V/m1

k = hydraulic permeability, m/s1

ke = electro-osmotic permeability, m2/s1/V1

ki = electro-osmotic efficiency, m3/s1/A1

mv = coefficient that volume compressibility, m2/N1

n = porosity, dimensionless

number of electrode pairs, dimensionless

n0 = electrolyte concentration, ions/m3

p′ = stress invariant, N/m2

q = stress invariant, N/m2

unconfined compressive strength, N/m2

qa = flow with area “a,” m3/s1

t = time, s

u = pore water pressure, N/m2

v = velocity in free pore fluid, m/s1

specific volume, dimensionless

ve = velocity of flow induced by electric potential gradient, m/s1

vh = velocity of flow induced by hydraulic gradient, m/s1

w = water content, dimensionless

wk = critical water content, dimensionless

Z = depth, m

Α = reinforcement adhesion factor, dimensionless

αb = bond coefficient, dimensionless

αds = direct sliding coefficient, dimensionless

γ = bulk unit load of soil/fluid, N/m3

γ¯ = mean activity coefficient in twin layer, dimensionless

γw = bulk unit weight of water, N/m3

δ = double great thickness, m

settlement, m

angle of friction soil/reinforcement, degrees (°)

ɛa = axial strain, dimensionless

ζ = zeta potential, V

potential across a condenser, V

η = viscosity, N s/m2

θ = angle, levels (°)

μg = geological settlement correction factor, dimensionless

v = Poisson’s ratio, dimensionless

ξ = electro-osmotic equation variable, kg/m2

π = pi, dimensionless

ρ = resistivity, Ωm

ρc = consolidation settlement, m

ρoed = oedometric settlement, m

ρw = density the water, kg/m3

σ = surface charge density, C/m2

electrical conductivity, S/m1

σ′b = effective bearing stress, N/m2

σ′n = effective normal stress, N/m2

σ1 = major primary stress, N/m2

σ2 = intermediate major stress, N/m2

σ3 = minor principal stress, N/m2

τ = shear stress, N/m2

ϕ = angle of shearing resistance, levels (°)

Ψ0 = surface potential, V

Ω = resistance, Ω

Some molecules space polar (e.g., water and also many proteins). The permanent dipole moments are oriented in ~ random, yet with one externally applied electric field they reorient statistically. Induced dipoles have the direction of the applied E-field, yet if the medium is polar, the polarizing E-field additionally rotates the long-term dipoles currently in existence (orientational polarization). Polar materials have a large permittivity in addition to the permittivity led to by the induced dipoles of the nonpolar molecule present. The permanent dipoles will suffer a rotational force, defined by the torque τ:


The polarization vector P is composed of all three components:


An outside field produces brand-new dipoles (induced dipoles)


An exterior field orients the permanent dipoles currently there


Without an exterior field, electrets have actually a long-term net dipole moment

A usual cyclic voltammogram for a dissolved species is given in Fig. 3.37.

Figure 3.37. Common cyclic voltammetry scan (100 mV s−1) perform on a pristine amorphous carbon electrode in the lack (capacitive current, ) and also in the presence of 1 mM K4 Fe(CN)6 (Faradic + capacitive current, (dark gray in print versions)). The sustaining electrolyte is 150 mM NaCl. The horizontal blue dashed lines (gray in print versions) stand for the extrapolation that the activation regions during the anodic and also cathodic scan and also are offered to calculation the oxidation and reduction existing (values shown in red (gray in print versions)). The upright black dashed lines exchange mail to the place of the peaks currents (values indicated in black).

Personal data from the author.

The CV curves of varieties dissolved in solution current a preferably in their oxidation and also reduction branches as soon as the potential is increased, respectively decreased, with respect come the recommendation electrode. This maxima are because of diffusion limitation come the oxidation and reduction currents: at sufficiently high overpotential (the potential difference between the working and the reference electrode) the oxidation/reduction rate is so high the the concentration the active types close to the electrode is close to zero: only species reaching the electrode surface ar by diffusion deserve to undergo a redox process there. In these conditions the oxidation/reduction peaks are separated by 2.3RTnT, specific 59.9nmV at 298K, wherein n is the number of exchanged electrons. The oxidation and also reduction peak currents room equal (reversible process) and should boost with the square source of the potential scan rate <123>.

Among numerous applications, CV has been used to probe the homogeneity the 3-mercaptopropyl sulfonate monolayers deposit on gold. Those monolayers were uncovered pinhole totally free in the presence of catechols, potassium ferrocyanide, and also ferrocenemethanol used as redox probes <124>.

When redox probes space immobilized in ~ a solid-fluid interface, the CV curve are different from the one presented in Fig. 3.37. For immobilized species, the oxidation and reduction peak currents are additionally equal in magnitude but are it was observed (almost in practice, strictly follow to the theory) in ~ the very same potential. When the potential scan price is increased, the peak currents are proportional come this experimental variable (Fig. 3.38).

This difference in the behavior of the height currents with respect to the potential scan rate permits hence come discriminate mobile redox types in the vicinity of one electrode from immobilized species.

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An arrangement to circumvent these obstacles is displayed in Fig. 4. The sound pressure on the membrane is transmitted to the ceramic aspect through a connecting rod. The sole function of the backplate is to carry out the required mechanical damping that the membrane. Ceramic microphones are defined by ruggedness, low cost, and basic electronics. However, there has actually been a tendency to replace them through lowcost electrets.