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the partition function can be written just in the terms of the fields as

Zc(ns,np, V, T) = Z0 ʃ Dw+ j Dw_ exp(-H[w+, w_]),      (8.32)

where the effective Hamiltonian

H[w+,wJ] = У dr[(p0∕χps)^i-ip0w+∖ - np∖nQp[iw+ - w_] - nslnQs[zw+ + w_].

(8.33)

Z0 represents the partition function of an ideal gas of ng solvent and np polymer
molecules in volume V, Qp is the normalized single-chain partition function of a
polymer molecule in the complex external field [iw+ — w_], given by eq. 8.20, and
Qs is the normalized partition function of a single solvent molecule in the complex
external field [zw+ + w_], given by

Qs[iw++w~] = У drexp(-[zw+(r) + w_(r)]).          (8.34)

Thus, the particle-field transformation is complete. The average segment density of
the polymer is given as, {pp(r))w+,w-, where

ʌ / r. n δ In Qp[iw+ -w_]

№(r;[.wt-W-|) = ^F              .           (8∙35)

218



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