Lec8_OpticalTweezer_ML - Optical trapping Dielectric...

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1 Biophysical Methods Slide 1 Optical Trap Optical trapping Dielectric particles in an inhomogeneous electric field are pulled in the direction of increasing field strength To measure molecular forces optical traps are used which allow to manipulate very small particles under a microscope and to measure forces in the picoNewton range. Such forces can for example be measured during single molecular conformation changes occurring during muscle contraction. Biophysical Methods Slide 2 Optical Trap The force of light on a diffracting particle
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2 Biophysical Methods Slide 3 Optical Trap Biophysical Methods Slide 4 Optical Trap Optical trapping - ray optics and momentum
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3 Biophysical Methods Slide 5 Optical Trap Optical trapping of a small particle can be understood using simple electrostatics F + F - - q +q E s Assume an electric dipole in an electric field. If the field is homogeneous a torque will be exerted orienting the dipole but no net force will occur because the net forces on the positive and negative charges will cancel exactly. However, if the field is inhomogeneous then F + and F - will not cancel and a net force occurs: E is the difference between the field at the plus and minus ends of the dipole r F + = q r E r ! = ! q r E r = r + + r ! = q ( r E + ! r ! ) = q " r F Biophysical Methods Slide 6 Optical Trap Optical trapping of a small particle can be understood using simple electrostatics F + F - - q E s For a small dipole the change of the electric field between the position of –q and +q is approximately linear and we can write giving r = r + + r ! = q ( r + ! r ! ) = q " r E x + ( ) = E x ! ( ) + " E x ( x + ! x ! ) = E x ! ( )+ E x s x dE = E x + ( ) ! E x ! ( ) = E x s x x E x - x + E - E + x = ! E x x s x + E x y s y + E x z s z = r s " E x x , E x y , E x z # $ % & ( = r s " r ) " E x y = r s ! r " ! E y and z = r s ! r " ! E z d r = ( r s ! r " ) r For a field in x direction which varies as a function of x, y and z we may then write: If the electric field has components also in y- and z-directions we get: or in vector form
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4 Slide 7 Optical trapping of a small particle can be understood using simple electrostatics F + F - - q +q E s The force can thus be expressed as: r F = r + + r ! = q ( r E + ! r ! ) = q " r d r = ( r s ! r " ) r r = q ! d r = ( r p ! r " ) r So our force is r = ! ( r " r # ) r = 2 r # ( r " r ) We now apply the product rule for vector derivatives: or r ! ( r A " v B ) = r # ( r ! # v ) + v B # ( r ! # r ) + ( r " r ! ) v B + ( v " r ! ) r A r ! ( r E " r ) = 2 r E # ( r ! # r ) + 2( r " r ! ) r r ! r " ( ) r = 1 2 r " r ! r ( ) # r E $ r " $ r ( ) F = For dielectric material the dipole moment is induced by the applied field: α is the polarizability of the material and is related to the index of refraction Giving for the force: r p = " r r F = " ( r E # r $ ) r E Light is an electromagnetic wave and changes sign so only the quadratic term is not zero r = r 0 ! cos t Biophysical Methods Slide 8 Optical Trap F + F - - q E s r = r + + r !
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Lec8_OpticalTweezer_ML - Optical trapping Dielectric...

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